Railway. Games iron man Card game piece of iron

Card game "railroad" came to us from France. Two, three, and so on ad infinitum can play in the Railroad, or, as we call it for short, Zhelezka, but in clubs it is considered correct game in which 12 people participate.

Rules of the game "railroad"

• one card is an eight or nine, and the other is fat, that is, a figure or ten;
• 8 or 9 are formed from the sum of the points of both cards: for example, from a three and a six, an ace and a seven, a five and a four, etc.

But it often happens that a nine or an eight at the same time are both in possession of the cards. Such a match is called "en carte". Both throw cards and the mark continues. If the punter has bad cards, i.e., there are no more than five points on both together, he says: " buy". After that, the banker gives him another card, another from the rack. With 6 or 7 points in hand, it is risky to buy, because you can buy a card that will lead to a loss. Points are counted in such a way that tens are always discarded as fat. Thus Thus, the following unpleasant combination may turn out: having 6 points in hand, we buy a four, and we get 10 points, i.e. pure fat.By buying a five, we have only one instead of the previous six points, since out of the eleven formed 10 recline like fat, etc.

Therefore, having 6 or 7 points, you should refuse to buy and declare "ours". If the banker does not have eight or nine points ready, at the request of the punter he is obliged to give him a buy-in, but he himself may not buy-in. Many players don't buy with just a five, but they take a big risk, because in case of a loss, such a player is obliged to pay the bets of all the other partners for whom he, as a senior, played the game.

The banker is, of course, free to act as he sees fit, since he only risks his bet. To fat, one, two, three and four points must be bought in any case. Wins the one who, after buybacks, applications " their"or the opening of the cards will turn out more points.

If one of the players opened the cards, having 8 or 9 points, the game is considered over and his opponent does not have the right to buy. With seven points, cards are not opened. The cards that have been in the hands of the players are thrown into a special box. When the entire prepared pile is used up, the played cards are distributed among all players and shuffling and cutting are repeated. The right to throw or hold the bank passes from one player to another in turn, to the left neighbor of the banker, however, there are exceptions due to monetary settlements.

Side stakes

As already mentioned, the maximum number of players in a piece of iron for one table is set at 12 people. But (especially in clubs) it often happens that there are more than twelve who want to play, and at the same time there are too few to fill the second table. Finally, many do not go to sit down at the table, where they have to pay for cards and, in addition, they are required to hold another pot. Such players make bets from the side.

Sitting players do not particularly like them, since among these outsiders there are often dubious elements, close to cheaters and quite deserving of the nickname "Araps", but they are reconciled with them, as with an almost inevitable evil, as if legalized by club customs. From the side, a bet is allowed only with the consent of the players between whom money is placed on the table, and, of course, those sitting have the advantage. A third party player may, by agreement with the banker, deposit money into the bank.

Rates from outside in all respects obey general rules pieces of iron, but third-party players themselves are deprived of any right to actively interfere in the game. If one of them even bets the largest amount on the show, it is still not him who leads the game, but the one who bet the largest amount from among the full-fledged players sitting at the table.

The outside player may neither throw nor buy the pot, but he is given the right to take from the pot, up to the mark, an amount proportional to his participation in it.

For example, if the bank started with 10 rubles, of which 3 were given from the side, and the banker beat 3 cards, then there are 80 rubles in the bank. The banker wants to throw for the fourth time. Then the outside player, not wanting to take further risks, demands his share and receives 80 * 0.3 = 24 rubles, and the banker continues the game at his own expense with 56 rubles, or reports the 24 rubles taken out of his pocket.

However, the latter rarely happens, since there is a superstitious sign according to which money should not be given from the table, that is, not from the bank, to the side. Each player, including the banker, can leave the table at any time.

Dmitry Stanislavovich Lesnoy

Founder of the Russian League Mind Games(1997). President (1997-2009) and Chairman of the Board of Trustees (2009 - to date). Publisher and editor-in-chief of Casino Games magazine. Author of the books Encyclopedia "Gambling House", "Russian Preference" and a series of books about casino games (co-authored with Lev Natanson). Author of the Marriage program (www.marriage.ru). Creator of the first on the Internet club of lovers of preference Maryazh (www.pref.ru).

Lev Grigorievich Natanson

Mathematician, writer and journalist, author of a series of books on the mathematics of casino games and slot machines(co-authored with Dmitry Lesny). Developer of algorithms for the computer program Mariage. Editor of the book "Russian Preference" in the section "School of the game".

We considered only the mathematical aspect of the game, and all others, such as: mystical, psychological, astrological, sacred - were ignored. Assuming that the outcome of any game depends not only on the ratio of probabilities, but also on the mental (and physical) state of the player, the location of the stars, and many other factors, we would like to warn the player against blindly following anyone's recommendations. Of course, we cannot give any guarantees of winning, and, moreover, we do not accept any material claims regarding possible losses. We just took the trouble to calculate exactly under what circumstances a particular game decision gives the best chances of winning from the point of view of probability theory, and we hope that our study will be of some use to you.

Aristocratic background

Punto Banco- the Spanish name for one of the oldest European gambling games, also known as baccarat, chmen de fer or piece of iron, and in addition - macao and nine. Today it is a very popular game in casinos around the world, notable for the fact that the biggest money is played in it. Thanks to its aristocratic origin, the game has retained its special ritual, stiffness and mannerisms that impress real players so much.

"And you are passionate, Paramosha!" - says General Charnota to the rich Korzukhin in the film "Running" based on the play of the same name by M. A. Bulgakov (Mikhail Ulyanov - Evgeny Evstigneev). Arriving in Paris to a banker-compatriot in lemon-colored underpants and a Circassian coat without a silver belt and without a dagger, the general put Khludov's medallion for $10 and won $20,000 by morning. They played at Punto Banco, calling this game the nine.

James Bond, a British MI5 secret agent with a license to kill, preferred baccarat to all card games. In this game, which required composure and endurance, he instantly gained the psychological advantage over his opponents necessary for victory.

Until recently, in Russia, the game shmen was very popular - fast gambling on banknotes. "Charge in a piece of iron" after the shift was a favorite pastime of waiters and taxi drivers. This simple and familiar game is almost an exact copy of the card game baccarat or Punto Banco.

Rules of the game

Props

Cosmos Casino has two types of Punto Banco tables - large and small. Tables have special markings. The game on the small table involves 6 decks of cards of 52 sheets from deuce to ace, which form a "big deck" of 312 cards. The large table uses 8 decks - 416 cards. A large table is usually served by 3 dealers: one gives out winnings and exchanges chips, the other shuffles cards and collects lost chips from the table, the third moves the dealt cards around the table using a special spatula called a palette. The third dealer has a special name - "caller". it is he who loudly announces combinations of cards and names the winner.

The game begins with the fact that one of the dealers shuffles the cards, gives the player to remove (cut) using a special plastic separator - cutting card, which, after cutting, is used to separate several cards big deck so that it does not play out to the end - when you can accurately calculate the remaining cards or in order to avoid the fact that there are not enough cards to finish the change. Shuffled decks are placed in a clog - a special box, a block for distributing cards. The played cards during the game are discarded into a special cylinder located in the center of the table.

In the further description of the procedure of the game and marking playing field the authors have in mind a large table for Punto Banco. On the small table, the same rules apply, only slightly simplified.

Card Value

Aces are valued at 1 point, kings, queens, jacks and tens - at 0 points, the rest of the cards - in accordance with their rank (for example, eight - 8 points, deuce - 2 points). The suits of the cards don't matter.

Card combinations

The sum of points on several cards is calculated, as mathematicians say, modulo 10. In other words, only the last digit of the sum is taken into account, and tens are discarded: for example, cards 9-8 give 7 points, T-6-3 - 0 points. The maximum possible amount is 9 points. Minimum - 0.

Number of players

There are usually several players at the table: for a small one - up to 7, for a large one - up to 16. New player can take any free position at the table. The place occupied at the table has absolutely no effect on the game, unless, of course, we take into account Fortune, which, as you know, can also nest in chairs.

Each place at the table corresponds to a certain box (outlined area) on the playing field of the table numbered from 1 to 16. If the player sits, for example, in position 7, he bets on box number 7, so that it would be easier for the dealer to identify the player and the bet he made when issuing a prize.

No matter how many players are at the table, there are only two opposing sides in each hand. One is called Punto (punter, player), the other is called Banco (banker, bank). Cards are dealt only in two hands - on Punto and on Banco. The side with the most points wins.

Bets and payouts on bets

Despite all its mannerisms and apparent complexity, the game is extremely simple. Each player can bet either that Banco will win (the pot), or that Punto will win (punter), or that there will be a draw (Egalite) - i.e. that Punto and Banco points will be equal.

The range of bets - minimum and maximum - is indicated on each table on a special plate. Usually bets are accepted on Punto and Banco from $50 to $2000, on Egalite - from $20 to $200.

The bet on Punto pays one to one. The bet on Banco is also paid one to one, but from this bet the institution keeps 5 percent in its favor. A bet on Egalite pays 8:1. It is understandable - equality of points does not happen often.

If desired, all three possibilities can be arbitrarily combined, i.e. play, for example, both Banco and Egalite.

If a player wants to bet on Banco, he must place a chip or chips inside the box marked on the playing field with the same number as the player's seat. Sitting in seat 7 puts in box number 7. If a player wants to bet on Punto, he places chips in front of the box under his number. A bet on the equality of points is placed on a special marked field with the inscription Egalite - naturally, on the sector with the corresponding number.

Game progress

When the bets are placed, both sides (Punto and Banco) first receive two cards, and then in some cases one new card can be added to any of these pairs. Thus, 4, 5 or 6 cards are involved in the distribution. The side with the most points wins.

In the event of a tie, the players who bet on Egalite win, but the other players do not lose their bets.

In the event that Punto wins, the dealer takes all bets placed on Banco and Egalite and pays bets placed on Punto at a ratio of 1:1.

In case Banco wins, the dealer takes all bets placed on Punto and Egalite and pays bets placed on Banco at a ratio of 95:100.

Dealing cards

In this game, the players themselves distribute cards from clogs. Each player in turn receives a clog, which moves in a clockwise circle from deal to deal. The player to the left of the dealer has the privilege to deal first. The dealer must bet on Banco. If he wants to bet on Punto or Egalite, the change goes to the next one. If no player bets on Banco, the dealer deals. If the player who bet on Banco and dealt loses, the deal goes to the next one. If the banker wins, the right to change remains with him. Any player has the right to refuse surrender.

There is no advantage in the fact of surrender. This is nothing more than a formality, a tribute to tradition, adherence to which gives the game a certain charm and attractiveness.

Having received a clog from the dealer, the player begins to deal cards. The dealer deals two Punto and Banco cards. The deal begins with Punto, the cards are dealt one at a time. The cards are placed face down.

Pallet - a special spatula

The dealer transfers two Punto cards with a pallet to the player who bets on Punto. He opens them with his own hands and puts them on the table. The banker, in turn, opens Banco cards. The dealer again takes the Punto and Banco cards with the spatula and places them next to him - the Punto cards to his right, and the Banco cards to his left. Having laid them out so that they are visible to the whole table, he loudly announces the points of the combinations that have fallen out.

Then he names the winner, either declares a draw, or asks to deal one more card, if the immutable rules of the game require it. After the winner is declared, the other two dealers collect the losing bets and pay the winners.

Dealing a third card

Whether the winner will be announced immediately after the two cards are dealt, or whether the third card will have to be opened depends on the amount of Punto points.

If two original cards give 8 or 9 points, these points are called natural or dumble. The term applies to both Punto and Banco (and zero-sum cards are commonly referred to as baccarat). If Punto has a natural 8 or 9, the game ends immediately: the dealer (or dealer) reveals the Banco cards. Punto and Banco points are compared, after which the reckoning takes place. The amount of the payout is not affected by whether the winnings are received at the expense of natural points or otherwise.

Note that the "algorithm" presented below is rather cumbersome and it is not easy to remember it the first time. In order to simplify perception, you can use Table 1, where the rules of the game are presented using a diagram. The first case, reflected in the table (for Punto - 8, 9), we have already considered.

If a pair of original Punto cards gives 6 or 7 points, Banco cards are opened and further actions depend on the sum of his points. If it is less than 6, Banco receives another card. After that, the total amount of Banco points (per three cards) is compared with Punto points (6 or 7). Otherwise (if Banco has 6 to 9 points) the comparison is immediate. In particular, with natural 8 or 9 points, Banco wins (this is the case in all other cases, which are discussed below). After the comparison, as always, there is a reckoning, and a new surrender begins.

Let's now assume that Punto has no more than 4 points. The Banco cards are revealed and if there are 8 or 9 natural points, Banco wins immediately. If it is not, Punto receives a third card. Further developments develop depending on the amount of Banco points.

1. Banco has 0 to 2 points. Banco receives a third card and the game ends (comparison of final scores and payback).

2. Banco has 3 points. If Punto's third card is not an 8, then Banco receives another card and the game ends. If Punto has an eight, the game ends immediately.

3. Banco has 4 points. If Punto's third card is a 2 through 7, then Banco receives an additional card and the game ends. In all other cases, the game ends immediately.

4. Banco has 5 points. If Punto's third card is a 4 through 7, then Banco receives another card and the game ends. Otherwise, the game ends immediately.

5. Banco has 6 points. If Punto's third card is a six or seven, then Banco receives an additional card and the game ends. In other cases, the game ends immediately.

6. Banco has 7 points. The game ends.

It remains to consider one more option: the original Punto cards give 5 points. This is the only time that Banco maps remain closed for now, and players are given the choice to get a third map for Punto (DRAW) or stop (STAND). The decision is made by the player who made the largest bet on Punto. If there are several such players, then they come to one or another agreed solution. And finally, if there were no players on Punto, Punto is forced to receive an additional card.

When the choice is made, the Banco cards are revealed. With 8 or 9 natural points, Banco wins as usual. In other cases, the course of the game depends on whether Punto has a third card. If yes, the game proceeds in accordance with points 1-6, which were discussed above. If Punto plays on the original cards (5 points), then if there are 6 or 7 points, Banco immediately wins. With 0 to 5 points, Banco gets an extra card, Punto and Banco's scores are compared, and the game ends.

That's all the basic rules of Punto Banco.

We add that the entrance to the game is possible before the start of any distribution. At the end of the deal, the used cards are set aside, and the remaining cards are not shuffled. Therefore, you can try to remember which cards are out of the game and which are left.

After the decks are shuffled, the notch is made again, the cards are placed in the clog, and the "burning" ritual begins: before the game begins, the dealer removes the top card from the clog. Its value will indicate how many subsequent cards should be "burned", i.e. remove from the game. Such a precautionary measure is taken to prevent possible abuses, such as: juggling cards, eating under desired card etc.

Strategy and Mathematics Punto Banco

In addition to intuition and luck, in Punto Banco the player needs some knowledge and skill. And although the game proceeds, basically, according to the knurled scheme, which requires almost no intervention from the player, two questions inevitably arise before him, requiring one solution or another:

1. What is better to bet on - Punto, Banco or Egalite?

2. What should I do if, after betting on Punto, the sum of points turned out to be 5? Which is better - take a card or stay?

The question "What to bet on?" - of paramount importance, the success or failure of the players depends on the correct decision. The second question seems to be "academic", but, as we will soon see, plays no less role than the previous one.

Below are some of the results obtained from the analysis of Punto Banco in the Cosmos casino using special computer programs.

We note in particular that the conclusions we have obtained are based on the smallest nuances of the rules of the game, adopted specifically at the Kosmos casino. Therefore, the strategy recommendations published below may not be applicable when playing at another casino.

We also want to make a special reservation: we considered only the mathematical aspect of the game, and all the others, such as mystical, psychological, astrological, sacred, were ignored. Assuming that the outcome of any game depends not only on the ratio of probabilities, but also on the state of the player, the location of the stars, and many other factors, we would like to warn the player against blindly following our recommendations. Of course, we cannot give any guarantees of winning, and, moreover, we do not accept any material claims regarding possible losses. We just took the trouble to calculate exactly under what circumstances a particular game decision gives the best chances of winning from the point of view of probability theory, and we hope that our study will be of some use to you.

When cards are evenly distributed

After a "big deck" shuffle, cards of different ranks can be expected to come out of the clog with the same frequency. Indeed, at this moment there are the same number of fours, nines or kings in the deck, so the probability of a card of a certain rank appearing is 1/13.

If the cards do indeed come out of the clog evenly, these probabilities remain virtually unchanged, and such a stable pattern may persist until the cutting card appears.

This, of course, does not always happen. These or those "distortions" are more common than is commonly thought. We will deal with this a little later, but now let's see what happens in the "base" case - with an even distribution of cards.

At the start of the game, both Punto cards are revealed. A card that gives 0 points is more common than others - the probability of its appearance from a clog is 4/13. Therefore, we can assume that the most probable sum of points on the two cards is zero. This is true: the probability of a zero sum is 25/169, any other (from 1 to 9) is 16/169. By seeing Punto points, each player can estimate the probability with which he will succeed. These probabilities are shown in Table 2, obtained using a computer; as for the "fatal" sum equal to 5, both options are considered in the table - DRAW (Punto receives a card) and STAND (Punto stops).

However, once you see the Punto cards, nothing can be changed: the bets have already been made. Probabilities of success are of interest earlier - when you are considering what to bet on. Based on Table 2 and the probabilities of one or another Punto score, it is not difficult to calculate the chances of success:

Punto- 0.4461 (DRAW) or 0.4463 (STAND);

Banco- 0.4584 (DRAW) or 0.4615 (STAND);

Egalite- 0.0954 (DRAW) or 0.0922 (STAND).

But this is not very revealing either. After all, the retribution with the winning players is carried out in different ratios: those who bet on Banco receive only 95% of their bet, but those who successfully play on Egalite are paid 8 times the bet. And in general, we are not interested in probabilities, but in money. There is nothing easier - in the case of DRAW we have:

Punto - 1,23%

Banco - 1,06%

Egalite - 14,12%

Before us are the expected losses of the players - as a percentage of the bet made. For example, a player who bets $100 on Punto loses an average of $1.23 per hand. The expected result of the players is a loss, winning strategy was not found, and there is nothing surprising in this - otherwise the casino would have gone bankrupt. For comparison: a roulette player loses on average 1/37 of his bet, i.e. 2.7%. Therefore, those who bet on Punto or Banco are in a better position.

So, with a uniform distribution of cards, two conclusions arise:

1. Playing on Egalite is extremely risky and the math gives a warning. Subsequently, we will see that the situation changes insignificantly on "oblique" distributions. Intuition, clairvoyance, inspiration are stronger than the model on which mathematics is based, but a dry representative of the "queen of sciences" will not bet on Egalite.

2. It is preferable to bet on Banco than on Punto. With distributions that are close to uniform, this is indeed the case, but when analyzing "skewed" probabilities, the conclusion often turns out to be the opposite.

But, perhaps, we hurried - after all, there was still a case of STAND? Let's see what kind of losses await the players here:

Punto - 1,51%;

Banco - 0,79%;

Egalite - 17,01%.

Recall that the choice between DRAW and STAND is made by the player who bet on Punto. So the solution is obvious. If he is not a hardened philanthropist, with 5 points on the original Punto cards, take new map necessary. The error is quite costly: the difference between Punto-draw and Punto-stand is much greater than between Punto and Banco in the case of a correct DRAW solution. And if there are no Punto players, then the rules are arranged in favor of the casino: the dealer opens the third card for Punto, and the chances of those who bet on Banco worsen.

As far as irregular allocations go, the "DRAW is better than STAND" rule isn't universal, but the exceptions are pretty rare. If a bet on Punto gives higher odds (with certain card distributions), then more often than not, the DRAW strategy is more effective. One of the possible exceptions will be discussed in the next section.

"Distortions" of probabilities

AT real game it is not uncommon to see distributions of cards that are far from uniform, and if you wish, you can extract some benefit from this. But in order to achieve this, it is necessary to carefully monitor the played cards and mentally adjust the likelihood of new cards appearing from clogs. In other words, to increase your own chances, you need to become a "counter".

Let's imagine that 260 cards of a "large" 416-card deck are played. The original deck contains 32 cards of each rank, so if they appeared evenly from the clogs, then 20 sixes, eights or queens have already left the game. And among the remaining 156 cards, there must be 12 cards of a certain rank (of which 48 cards are worth 0 points). But let's say you notice that there was a "skew" with the sevens: they came out not 20, but for example, 26. Only 6 of them remained in the clog, so the probability of the appearance of the seven is 6/156, i.e. about 0.038. This is markedly different from the "base" probability of a seven being rolled in a uniform distribution (1/13 - approximately 0.077). Assuming that the rest of the cards are in the clog more or less regularly, the expected losses of the players will look like this:

Punto- 1.07% (with right choice DRAW);

Banco - 1,22%;

Egalite - 15,56%.

Compared to the "base case", Punto and Banco seem to have swapped places - a bet on Punto turns out to be preferable. This is one of those additional chances that the "counter" enjoys: timely switching from Banco to Punto and vice versa leads to better results.

We will not dwell on the methods of counting played cards, but we will formulate general principle, underlying the "counter" strategy.

If there are relatively many fives, sixes, sevens, eights or nines in the clog, then this is in the hands of Banco. These maps can be called successful for Banco and unsuccessful for Punto. Conversely, an excess of other cards favors Punto and lowers Banco's chances. This can be put in another way: the more successful cards for Banco out of the game, the better for Punto (and vice versa).

Let's give a couple of examples.

1. Let's say that the count of the cards that came out shows that the probabilities of the appearance of fives and sixes (unsuccessful for Punto) are relatively small - 0.05. The rest of the cards are distributed approximately evenly.

Punto- 0.97% (with the right choice of DRAW);

Banco - 1,32%;

Egalite - 15,77%.

2. The same as before, but fives and sixes that are unsuccessful for Punto fall out with an increased probability - 0.11.

Punto- 1.53% (with the right choice of STAND);

Banco - 0,78%;

Egalite - 15,16%.

In this case, the optimal choice for Punto is the STAND strategy. But this example is not indicative: is it worth thinking about the strategy of the player playing Punto, if you need to bet on the opposite side?

Another illustration of the relationship between the odds of Punto and Banco can be found in Tables 3 and 4 on p.&. Table 3 shows the expected losses of players for various probabilities of a 4, a lucky card for Punto. It is assumed that the rest of the maps are evenly distributed, and the choice of DRAW and STAND options is optimal for Punto. Table 4 shows the expected results of the players depending on the probability of hitting a five - a card lucky for Banco.

There is one interesting problem with the choice of the DRAW-STAND strategy. If there were no such choice, and the DRAW decision was always made (which is what actually happens when there are no Punto players), then the general principle outlined earlier would have no exceptions. Fives, sixes, sevens, eights and nines would always be good for Banco and bad for Punto. But with the advent of choice in some exotic cases, the picture changes.

Let's imagine that there are too many cards that were successful for Banco in the clog. It turns out that in this "black" situation for himself, a Punto player can change his fate by choosing the STAND strategy. For concreteness, let's return to the examples with fives and sixes and assume that they appear with a probability of 0.2. In life, this happens extremely rarely, the "skew" is already too large (recall: the "base" probability is approximately 0.077). Nevertheless, due to the timely choice of STAND, the game is in favor of Punto:

Punto - 1,02%;

Banco - 1,25%;

Egalite - 9,38%.

With the wrong choice of DRAW, the result would have been depressing for Punto:

Punto - 2,14%;

Banco - 0,15%;

Egalite - 4,96%.

It can be confusing: after all, the right to choose is provided only on the condition that the original Punto cards give 5 points, and this does not happen very often. Why such a difference in expected losses? The fact is that with "skewed" probabilities, the influence of the choice of DRAW-STAND is so great that the wrong decision leads to a collapse even of the averaged indicators.

In general, we can say that with a competent card count, the player’s results, of course, increase. Dividends - albeit small - are evident, and they can be judged from the examples above. Although learning how to effectively switch from Banco to Punto (or vice versa) is a whole art that requires a lot of time. The odds of the "counter" increase as the "big deck" is exhausted, but an accurate count is impossible due to the presence of unknown cards: some are eliminated from the game with a cutting card, others are "burned" before the game begins.

Gaming systems

As you know, all people are different, and even more so the players. Some simply rely on luck, others carefully study astrological forecasts, others scrupulously count the cards that have left the game, and some try to ingratiate themselves with Fortune by using certain gaming systems.

Martingale

They began to think about game systems for a long time - probably since gambling appeared. As time went on, the systems were constantly modified, while new ones were developed. For example, gaming systems based on the principle of consecutive doubling of the bet have gained great popularity. Sometimes such systems are called "Martingale". Imagine that you are playing toss and betting on heads all the time. You bet $1, but it came up tails. Now you double your bet - $2. If you lose, the bet rises to $4 and then grows exponentially. When it finally comes up heads, you hit the jackpot: you can be sure that no matter how many previous failures, you won exactly $1. Now you again bet on heads (or, if you like, on tails), and the game starts all over again.

Obviously, if you have enough capital, you will win $1 in each series of tests. But the capital must be really big. After all, if a long losing streak begins, the stakes will have to be doubled all the time, and the budget may not be able to withstand the game according to the system. There is even a saying about such a situation: "The suit has gone, but there is nothing to bet!".

It's funny that the word "martingale" has four different meanings(often they say "martingale", but the inconsistency lies on the conscience of translators who treated the English word martingale quite freely). In the original sense, this is a part of the harness that prevents a frightened horse from throwing its head back. Also called the strap of a coat or overcoat. The gaming systems of the same name were also assigned "restraining" functions: they were supposed to save a confused player from a collapse. And finally, at the beginning of the twentieth century. the famous mathematician Paul Levy, who studied the paradoxes of gambling, introduced the strict and complex term "martingale" into probability theory.

"Martingale", so famously used in the toss, begs to be transferred to the game in the casino. When playing roulette, you can bet on red or black, when playing Punto Banco - on Punto or Banco, and in case of a loss, you can double your bet all the time. The difference from the toss is very insignificant: when tossing a coin, the chances of winning and losing are the same, and in the casino the rules are arranged in such a way that some small part of your bet goes to the house. For example, there is a zero in roulette, and the expected loss of the player is 1/37 of the bet made - approximately 2.7%. At Punto Banco, whichever side you bet on, the average loss is usually between 1% and 1.3%.

If the player has a significant initial capital, then the "Martingale" can cause huge damage to the casino. That is why in any casino in the world on every table, be it baccarat, blackjack or roulette, you will see signs that indicate the size of the minimum and maximum bets. The difference between them can be 10, 30 and even 100 times. But nowhere will you be allowed to raise the bet indefinitely.

Given this limitation of the casino, players began to develop systems, building a strategy for changing the bet within a relatively small range. A typical example is the system bearing the name of its author, Thomas Donald.

Thomas Donald system

The basic premise of the system sounds very simple. We make some initial bet (say, $100) on one side. After a loss, each time we increase the bet by $100, and if we win, on the contrary, we decrease it until it drops to the initial one.

Let's say we bet on Banco, but Punto won. Raise the bet to $200. If the victory is again for Punto, we bring it up to $300, if the points are equal (Egalite), we leave the bet unchanged. If we win, we lower it to $100, and if we win again, we don’t change the bet yet. Compared to the "Martingale", the geometric progression has been replaced by an arithmetic one.

Thomas Donald, who developed this system for roulette, had in mind the game for red-black or other "equal chances". At the same time, he was based on the assumption that at some certain period of time (day, month, year), the number of red and black fallouts will be approximately the same. Indeed, if this happens, and the player does not run out of money by then, he will usually win.

Let's see what this system gives in relation to Punto Banco.

Let's bet on Punto and play two hands. Since the chances of the sides are approximately equal, let's assume that Punto won the first hand, and Banco won the second hand. In both cases, we bet $ 100, so we stayed with our own.

And now it's the other way around: in the first hand, Banco wins, and then - Punto. At first we will lose $100, but according to the system, the bet is now increased to $200. As a result, the victory is plus $100. For starters, it seems not bad, but this, it turns out, is not the limit.

Like the Martingale, the Thomas Donald system has many modifications. One of them - the Donald-Nathanson system - is especially curious and is based on the use of "zero" and "negative" rates. Let's say we bet $100 on Banco and win. After winning, T. Donald recommends lowering the bet by $100, but in this case it seems to be impossible. And yet we will try: put zero on Banco. In other words, we skip the hand, but closely monitor its result. If the Banco chosen by us lost, then, as always, we raise the bet - $100 on Banco. But if he wins, we lower the bet again and bet on Banco minus $100. With a little imagination, everything becomes clear: the $100 bet is placed on Punto. And so on and so forth. If Punto wins the next hand, we will be back to zero.

Now we'll bet Punto again and play two hands with opposite results. See for yourself that we will win $100 regardless of the order of hands won and lost. True, things will not come to a negative rate, but zero will come in handy.

What if you bet on Banco? Let's look at the same two deals. Let's say Punto wins the first time, Banco wins the second. Having lost $100 first, then we will win 200. Including "commissions", our winnings will be $90. If you swap hands, the winnings will increase to $95.

Banco seems to be a little offended. But we believed that the chances of the parties are approximately the same, and the chances are nothing more than the expected dividends (cash gains or losses). With this assumption, Banco should win a little more than Punto. Those who play on Banco receive a winning ratio of 95:100; it can be calculated that with equal chances of the parties, 39 Punto wins should account for 40 Banco wins. This is his compensation.

We only looked at two hands with different results. But we can also prove a more general position: if at some time interval the number of wins of Punto and Banco is approximately the same (with a slight bias towards Banco), then the Donald-Nathanson system will bring success to the player, no matter which side he bets on. This is its main concept. But we repeat: there is a danger that the player's money may run out long before the onset of "balance". And in the presence of large capital, it is quite possible to “rest against” the upper limit of bets set at the gaming table in the casino. "Martingale" is not alone in this sense.

What is the meaning of gaming systems?

From mathematics to philosophy

The main objection of mathematicians to any system of play sounds very simple. Casino players lose on average, and there's no getting around it. The mathematical expectation of your winnings is always negative, and the longer the game goes on, the deeper you sink into the abyss.

But let's look at another mathematical characteristic - the probability of retaining leadership. Most game systems are designed in such a way that in the initial phase of the game this probability significantly exceeds 50%. Leadership is a positive cash balance, so it's likely that you'll be winning at first, and possibly for quite some time. The most striking example is "Martingale": with a significant initial capital, the probability of retaining leadership "at the start" is so high that a negative mathematical expectation remains ... just an expectation.

But less aggressive systems, such as Thomas Donald, follow a similar principle. Indeed, this system is based on the position of a sufficient proximity of the frequencies with which two opposite events occur. On the initial stage games, this assumption is likely to be justified, i.e. we are again faced with a system that provides a high probability of leadership "from the start." Even more effective in this sense is the Donald-Nathanson system with zero and negative rates.

A natural question arises: how long does the player's leadership last in such systems and what kind of picture emerges after a sufficiently large number of trials? In order not to tire the reader with cumbersome calculations, let's forget about the realities of the casino for now and consider completely simple game. "Banker" tosses dice, i.e. a die numbered from 1 to 6. If a "1" is rolled, you pay $5, otherwise you get $1 from the banker. As mathematicians say, this is a zero-sum game: the mathematical expectations of the player's and the banker's winnings are 0. But unlike the usual toss, the "starting" probability of the player's leadership is higher than 50%. Here it is quite possible to do without tricky systems: the rules of the game themselves treat you "caringly". Now, please take a look at Table 5. It shows the probabilities of your successes (to the nearest hundredth) after each of the first 20 rolls of the die.

If you imagine a graph of the probability of maintaining leadership depending on the number of throws, then it would look like a damped sinusoid. It fluctuates around the 50% mark, and the "peaks" fall on the 1st, 7th, 13th trials and then alternate after 6 (the number of faces of the cube). It is easy to imagine what would happen if the cube had not 6, but, say, several thousand faces. (To play such a cube, you do not have to part with your native 3-dimensional space, it is very easy to simulate it on a computer.) The "period" of oscillations of our sinusoid would become huge, and the initial phase of the game, in which the player would most likely win , would be extremely long. This picture is very similar to what happens when using systems such as "Martingale". Needless to say, a tempting game...

We've got a pretty good illustration of the principle. The fact is that this or that damped sinusoid is characteristic of all gaming systems that provide a high "starting" probability of leadership. "Thomas Donald" is no exception, although the quantitative characteristics here, of course, are different.

If we return to a real casino and remember the negative mathematical expectation, then the form of the sinusoid will change. (Recall that in Punto Banco, players lose from 1 to 1.3% of the bet in each "average" distribution.) The expected loss will put pressure on our sinusoid from above, it will no longer fluctuate around the 50% mark and sooner or later , wriggling, will go down - into the very abyss that we have already talked about.

To avoid defeat experienced players apply the so-called "jump" theory, i.e. trying to stop the game at exactly the right time. In the circle of acquaintances or friends, interrupting the game at the moment of winning is considered unethical - you run the risk of being branded as a "piece cutter" and losing partners. It is generally accepted that playing in a friendly circle does not pursue pragmatic goals, but is a way of communication. Among professionals, and even more so in casinos, quitting the game at any time is considered absolutely normal.

If the game is 50% or close to it, and the win or loss graph is in the form of a sinusoid, then any professional player tries to stop the game at the moment of a positive peak. The only problem to be solved is to determine the magnitude of the maximum fluctuation, i.e. the largest deviation from zero in one direction or another. Sometimes, in case of bad luck, the point of "dismount" has to wait a long time. In another case, the optimal result is achieved after a few minutes of play.

A high-quality picture has been obtained, but what's next? What do gaming systems give us anyway? Firstly, there is a positive psychological factor: the player gets the feeling that he is not acting at random, but "systematically". But taking the lead early in the game has another invaluable advantage: the winner gets a good mood. His attitude to money often becomes light, and lightness is exactly what Fortune loves. N.A. Nekrasov tried to use the mysterious connection between the attitude towards money and the favor of Fortune. Going to a big game, he put the money "intended" for losing in a separate pocket. "It is necessary," he said, "to treat this money as if it no longer exists."

Of course, you can cultivate a light attitude towards money in yourself, you can even be born with it, but this does not always work out. Game systems serve as an indispensable assistant here, and this is their main and absolutely real meaning. Fortune often goes towards the "easy" player, and for some reason the terrible moment of retribution with the "banker" is pushed back. This unknown yet law was noted by many prominent players. They know that this law exists, and in this aspect they are practically unanimous.

Players are players, but what do professional mathematicians think about this? Our blitz survey showed that they are divided into several categories. Some consider all this to be a complete mysticism, but these are not at all the majority. Others believe that all this is good, but mathematics is powerless here. Still others say that modern mathematics is powerless. But one of the answers we liked the most: "Mathematics simply works with the wrong model. Some kind of natural science should give it a more adequate model. And then mathematics can do everything."

Suicide system

It is often asked if a player needs math skills? Not necessarily. Game systems come in different genres. Often other talents come to the rescue - for example, criminal ones.

This funny story is taken from Alexander Willcott's novel "The Bets Are Out", based on a true story. A young man who lost his money at the Monte Carlo casino committed suicide. His body was found on the seashore: a gun was clamped in his hand, and his shirt was covered in blood. An employee of the casino, under the cover of darkness, hurriedly descends to the sea and imperceptibly puts 10 bills of 1000 francs into the pocket of the unfortunate. The reputation of the casino should not suffer! Suicide because of a big loss is impossible.

But the imaginary dead man did not even think of taking his own life. There was only tomato juice on the shirt. And then a happy end follows: the hero returns to the casino and, inspired by good luck, increases his capital by 10 times!

Greek Syndicate

This story is described in Alan Wykes' Encyclopedia of Gambling. "Greek Syndicate" was born in Paris in 1919. Shortly before that, two Greeks arrived there - Nicholas Zografos and Eli Eliopulo, who wanted to try their hand at gambling. They quickly became widely known as bookies and regulars. gambling establishments French capital. In one of the clubs, they met Zoret Kuyomdzhan from Armenia, who earned his living by playing professionally. Since none of the trinity was inferior to the rest in skill, they decided to combine efforts and funds, creating the so-called "Greek Syndicate". Later, the Greek Atanase Vagliano joined the syndicate, investing his fortune acquired in the transportation of goods, and then the Frenchman Francois Andre joined the syndicate.

In the 20s and 30s of this century, the syndicate set the tone in a number of the largest casinos in Western Europe - in Monte Carlo, Deauville, Cannes. Over the years of their turbulent activity, the members of the syndicate have amassed a considerable fortune and significantly increased their capital. They owed much of this to the exceptional playing talent and uncanny intuition of Niko Zografos.

While still a 20-year-old boy, Zografos directed his considerable mathematical abilities to improve his skills in calculating various gambling games - especially baccarat. At first, he carefully studied the slightest subtleties of this game, then he trained hard and after a while reached the pinnacle of skill. He began to be rightfully considered one of the leading baccarat experts.

In many ways, Zografos' gambling talent was due to his amazing memory. He could unmistakably name any card played throughout a game of baccarat. By the end of the game, Zografos invariably knew the exact value of the last few cards left in the deck. Therefore, he easily determined the probabilities of receiving certain cards, calculating the amount of bets in advance.

During the heyday of Zografos's gambling activity, he was firmly entrenched in the reputation of a successful player who almost never suffers defeats. Therefore, he also possessed a purely psychological superiority over most of his potential opponents. Thanks to his phenomenal memory, he could easily name the sums of winnings and losses of his opponents during the evening, as well as the maximum amount they could afford to play. This data, plus an almost unmistakable gaming instinct, allowed Zografos to accurately determine the strategy and tactics of partners, the value of their bets in various game situations. Of course, such skills are necessary for any professional player, but in fact, only a few have reached the heights of skill that Zografos submitted to. In addition, it is significant that in relation to the "Greek Syndicate" there has never been even a shadow of doubt about the honesty and decency of its members.

In those days, the French Riviera casinos favored the baccarat variant, where players play against each other. One leads the game and acts as a banker, the others ponte (see footnote & on pg. &). And in 1922, the members of the "Greek Syndicate", thanks to their remarkable gaming abilities and the combined capital, managed to impress the entire gaming world by taking a step never seen before. It was officially announced that in the case when a member of the syndicate acts as a banker, restrictions on the maximum bet sizes are removed.

The idea belonged to Zografos, and the main part of the necessary capital (about $2 million) was provided by Vagliano. At the opening of the season in Deauville, Zografos, taking the place of the banker, simply and casually announced: "There are no restrictions." The stakes could be raised even to the skies. The syndicate's brightest hopes quickly turned into reality. Wealthy gamblers flocked from all over the world to the casinos where the syndicate settled, ready to risk large sums and ruin the challenging bankers. But those who counted on huge winnings were forced to make big bets. And it was not easy to play against Zagrafos: the capital of the syndicate not only did not decrease, but grew by leaps and bounds.

But no one is immune from failure: Zagrafos also had breakdowns. For example, in 1926 in Cannes, he lost $672,000 during a week. One evening, after several unsuccessful games, he got up from the table, left the playing hall, and some time later returned with 1 million francs ($168,000). . Apparently, this was his last money. But Zagrafos sat down to play without hesitation and immediately bet the entire amount. Feeling the approaching denouement, the opponents made maximum bets. Zagrafos calmly dealt his cards. The opponents got a seven and an eight, and the turn was passed to Zagrafos. His first two cards turned out to be pictures (0 points), and then he took the third. It was a nine of diamonds - an unconditional victory! He still won. And a streak of success began: victories followed one after another, not only that evening, but also in all subsequent ones. And the nine of diamonds became the talisman of Zagrafos. Her image flaunted on many of his things - a cigarette case, cufflinks and even on a yacht pennant.

This episode was a turning point in the activities of the Greek Syndicate. Despite some setbacks and defeats, he never found himself close to the edge of the abyss. And for a long time, the syndicate remained the all-powerful ruler of a gambling empire that covered almost all of Western Europe.

Baccarat scam

Is it possible to use cheating techniques when playing baccarat?

Of course, in principle, it is possible - as in any other card game. But before we look at a couple of cases, let's ask ourselves the question "Who benefits from this?". Respectable casinos that value their reputation do not resort to cheating either for playing baccarat or for any other, because it is unprofitable. The loss of good name and customers, not to mention the loss of a license, will cost significantly more.

In baccarat, as we remember, players traditionally fought each other, the institution itself did not participate in the game, but only received an insurance premium from the banker, being its authorized representative, beneficiary. In this situation, the dealer, the representative of the casino, has no economic motives for dishonest play.

In today's practical situation, the advantage that the casino has over the player in the form of a small percentage, in the long run, leads to the fact that all the money found in the game will sooner or later end up where it should go - in accordance with the laws of mathematics. It would be unacceptable stupidity for a casino to jeopardize the reputation of the institution and resort to fraud. All he needs is for the gambling table to be surrounded by a crowd of worthy players and for the bets to be as large and numerous as possible. An advantage of 1-1.3 percent is practically a guarantee that in the end all the money will be "on base".

However, cheating while playing baccarat does happen. This sometimes happens for the reason that some operators simply cannot force themselves to play honestly (Shura Balaganov's syndrome: "Commander, Ochakov, I didn't want to, I'm mechanically), while others are not able to protect their clients from "dashing people". The game of baccarat itself is a delicacy for cheaters all over the world, because the biggest money is played in this game, and the stakes are exceptionally high. the players are constantly under the supervision of three croupiers, who are carefully watching what is happening from three different points.

John Scarne tells how he once managed to convince a doubter that cheating at the baccarat table is possible in principle.

It happened in 1958 when Mike McLaney, the owner of the Habana Nacional casino, and 19 other Cuban casino operators decided to establish uniform regulations and create the Cuban Gaming Control Board. Scarne was invited as an expert and was even asked to head the Commission, but he turned down the offer for personal reasons. During the meeting, Scarne argued that any establishment that has a baccarat table, be it Cuban, American or Monte Carlo, is doomed from time to time to become the prey of international cheaters.

The owner of Sevilla Biltmore casino named Analito Batisti allowed himself to doubt:

I doubt any thief would be able to steal anything from my baccarat table! Everyone knows that I have the best croupiers in all of Cuba, so no fraud is possible in my casino!

Scarne just smiled back. But after three weeks, he went to Batisti and privately offered him a friendly bet:

There is no doubt that the best croupiers in Cuba will immediately expose the cheater playing baccarat. Let's check them out. I'm betting $500 that I can "shove" them something they can't "buy back". I will play until I win or lose $10,000. This money is not included in the bet: You will give me a loan, and I will play "do not pay - do not receive." If I lose or get caught by the hand, I'm 500. If I win 10 "pieces" - by cheating - 500 from you.

Batisti was a player. He thought: "What, in the end," Pyatikatka "is not lying on the road." The bet took place.

It was early evening, and the baccarat table had not yet begun to operate. There were only casino employees at the table. Batisti told the croupier that Scarne could get a $10,000 loan while he sat down to watch the game on the dais for the inspector. The game has begun. For about 20 minutes, Skarne bet $100, and all this time Batisti had a riddle written on his face that he was trying to solve: “How is this guy going to win $10,000 playing $100?”.

John was on his own when he suddenly said, "I'll bet $10,000 on a player." The croupier looked at Batisti, who nodded in agreement. The croupier placed the 10,000th marker on the "Player" (Punto) position and said to the dealer: "Cards, please." When two of the player's cards and two of the banker's cards were dealt face down, the croupier brought the player's cards with his "palette" and placed them directly in front of Skarne. He took them with his left hand and, holding them in the closed position for a fraction of a second, quickly turned them over onto the table and cried out: "Nine!" Indeed, beautiful 9 points in the form of a jack and nine of spades lay on the table. The croupier turned to the dealing dealer and asked to open the cards of the bank. The banker has 6 points. "The player won," stated the croupier. He collected all four cards from the table and dropped them into the drawer through a special slot in the center of the table. Having received the prize, Scarne got up from the table.

The casino staff behaved as if nothing had happened: indeed, a bet of $10,000 was not something out of the ordinary in this casino. However, Batista's face showed bewilderment. He climbed down from his dais and approached Skarna, "But where is your fraud!? You're just lucky!"

This is what you think! And I advise you to take out the box for played cards and take a closer look at the last four cards.

Two of them, upon closer examination, turned out to be with a different shirt - a jack and a nine of spades.

You changed cards!?

Well, yes. You prefer Bicycle cards, I prefer Tally-Ho.

Having received his "honestly acquired" $ 500, Skarne left the casino to the sounds of finding out the owner of the relationship with "the best croupiers in Cuba." Batisti preferred to express his dissatisfaction with them in Spanish.

John Scarne's Advice for a Baccarat Player

1. The middle-class player has little chance of surviving if he misses any cheating from the croupier. Therefore, the first and best advice: Bet closer to the minimum than the maximum if you are not playing at an establishment with a long established reputation for excellence.

2. The most common and most "killer" trick is to insert a pack of cards prepared in advance, folded in a certain order, into the clog. Some even manage to replace the entire clog containing 8 decks, carefully laid in advance. In order not to become easy prey, keep your eyes open - follow the process of shuffling cards and placing them in clogs carefully.

3. Some unscrupulous casinos use clogs with a secret when playing baccarat. Such a clog has a secret pocket in which eight cards are usually hidden: 9-10-9-10-9-10-9-10. The pocket is located next to the hole through which the cards are fed during the deal. By squeezing the clog with his left hand, the fraudulent dealer opens the slot with the help of a built-in mechanism. secret pocket, through which he draws the desired card with the thumb of his right hand. As soon as a large bet appears, the swindler deals to his accomplice player a combination that gives an immediate win (9 points).

To eliminate the possibility of such a swindle, Scarne recommends using clogs made of transparent plastic materials to make sure that there are no secrets in the drawer.

Entire books have been written about the advantage that marked cards give when playing baccarat, considering not only the question of how to use this advantage, but also how to neutralize it.

Scene from M.A. Bulgakov

M. Bulgakov "Running"

A play in four acts

<...>

Charnot. Well, you know, Paramon, I'm a sinful person, I would sign up with the Bolsheviks on purpose, just to shoot you. I would have shot and instantly signed out would be back. Wait, why do you have these cards? You play?

Korzukhin. I don't see anything surprising in this. I play and love it.

Charnot. You play! What game are you playing?

Korzukhin. Imagine, at nine, and I love you very much.

Charnot. So let's play with me.

Korzukhin. I'd love to but, you see, I only like to play for cash.

Golubkov. Will you stop humiliating yourself, Gregory, or not? Let's go to!

Charnot. There is no humiliation in this. (Whispers.) What did you say? Last resort? This will not be the last case. Come on Khludov's medallion!

Golubkov. Please, I don't care now. And I'm leaving.

Charnot. No, we'll go out together. I won't let you go with that face. You will dive into the Seine. (Holds the medallion to Korzukhin.) How much?

Korzukhin. Hm... a decent thing... Well, ten dollars.

Charnot. However, Paramon! This thing costs a lot more, but you don't seem to understand it. Well, let's go! (Hands the medallion to Korzukhin, he gives him ten dollars. Sits down at the card table, rolls back the sleeves of his Circassian coat, breaks open the pack.) What is your slave's name?

Korzukhin. Um... Antoine.

Charnota (loudly). Antoine!

Antoine appears.

Bring me, my dear, a bite to eat.

Antoine (with a surprised but respectful smile). Listen, sir... A lanstan! (Disappears.)

Charnot. How much?

Korzukhin. Well, for those ten dollars. I'll ask for a map.

Charnot. Nine.

Korzukhin (paying). I'll ask for a ticket.

Charnota (mosque). Nine.

Korzukhin. Quit again.

Charnot. Do you want a card?

Korzukhin. Yes. Seven.

Charnot. And I have eight.

Korzukhin (smiling). Well, so be it, to quit.

Golubkov (suddenly). Charnota! What are you doing? After all, he doubles and, of course, now he will take everything back from you!

Charnot. If you understand the game better than me, then you sit down for me.

Golubkov. I can not.

Charnot. So don't block the light for me! Map?

Korzukhin. Yes please. Oh damn fat!

Charnot. I have three points.

Korzukhin. You don't buy into threes?

Charnot. Sometimes, like when...

Antoine brings in a snack.

(Drinking.) Golubkov, a glass?

Golubkov. I do not wish.

Charnot. What about you, Paramon?

Korzukhin. Mercy, I've already had breakfast.

Charnot. Yeah... Would you like a card?

Korzukhin. Yes. One hundred and sixty dollars.

Charnot. Goes. Countess, at the price of one rendezvous... Nine.

Korzukhin. An unheard of thing! Three hundred and twenty coming!

Charnot. Please send cash.

Golubkov. Come on, Charnota, I beg you! Now drop it!

Charnot. Kindly do something. Well, look at the album. (To Korzukhin.) Cash, please!

Korzukhin. Now. (Opens the cash register, bells immediately ring out in it, ringing is heard everywhere.)

The light goes out and immediately comes back. Antoine appears from the anteroom with a revolver in his hand.

Golubkov. What it is?

Korzukhin. It's a thief alarm. Antoine, you are free, I opened it.

Antoine exits.

Charnot. A very good thing. Let's go! Eight!

Korzukhin. Is it six hundred and forty dollars?

Charnot. Will not go. This rate is not accepted by the bank.

Korzukhin. You play well. How much will you take?

Charnot. Fifty.

Korzukhin. Let's go! Nine!

Charnot. I have fat.

Korzukhin. Send.

Charnot. Please.

Korzukhin. Five hundred and ninety!

Charnot. Eh, Paramosha, you are gambling! That's where your weak string is!

Golubkov. Charnota, I beg you, let's go!

Korzukhin. Map! I have seven!

Charnot. Seven and a half! Just kidding, eight.

Golubkov suddenly covers his ears with a groan and lies down on the sofa. Korzukhin opens the cash register with the key. Again ringing, darkness, again light.

And it's already night on stage. Candles in pink caps are burning on the card table. Korzukhin is already without a jacket, his hair is tousled. The lights of Paris are in the windows, music is heard somewhere. In front of Korzukhin and in front of Charnota - piles of currency. Golubkov lies on the sofa and sleeps.

Charnota (sings). You get the death blow... three cards, three cards, three cards... Fat.

Korzukhin. Send four hundred! Send three thousand!

Charnot. There is. Cash!

Korzukhin rushes to the checkout. Again darkness with ringing and music. Then light. In Paris - a blue dawn. Quiet. No music is heard. Korzukhin, Charnota and Golubkov are like shadows. Champagne bottles are scattered on the floor.

Golubkov, crumpled, hides the money in his pockets.

Charnota (Korzukhin). Do you have the newspapers to wrap?

Korzukhin. There is not. You know what, hand me the cash, I'll give you a check!

Charnot. What are you, Paramon? Would any bank give out twenty thousand dollars to a man who showed up in underpants? No thanks!

Golubkov. Charnota, redeem my locket, I want it back!

Korzukhin. Three hundred dollars!

Golubkov. On the! (Throws money.)

Korzukhin throws the medallion in response.

Charnot. Well, goodbye, Paramosha. We sat up with you, it's time for us.

tables

Table 1

The scheme of a set of cards in the game Punto Banco (P - Punto, B - Banco)

table 2

Probabilities of winning Punto, Banco and Egalite after opening a pair of Punto cards

Table 3

Expected losses for Punto and Banco with different probabilities of a FOUR

Table 4

Expected losses for Punto and Banco with different probabilities of FIVE

Table 5

Cube game. The probabilities of the player's results depending on the number of dice rolls

Baccarat Mystery

Do you know the secret of baccarat?
You need to know it:
This loud game
Like crystal is a friend of smoke.
The same restrained frenzy,
The same nonsense half-dressed
And crushed cigars
Delicate ash on the cuffs.
Told us a long time ago
Don Juan's honest code
What's up with the participation of ladies
Refinement is undesirable.
What then will only come out good,
If at once Donna Anna
Backwards will burst across
Immaculate sofa.
The dumber the smarter
The straighter the better
With surprise, "with a prisoner, with her",
You pass the spring evening.
And gambling
Shares the same tastes:
This bitch, baccarat,
Only impudently inferior.
For those who are timid, thoughtful, strict, -
Forever tricks brings,
And rows a stack of paper
Who is better suited to her.

Georgy Shengeli (Printed by autograph)

1. From fr. baccara. Communication with fr. baccarat - crystal of the highest quality, whose name comes from the city of Baccarat, where it was produced. Possibly also derived from Italian. baccara - zero. ()

2. From fr. chemin de fer - railway. ()

3. Named after the Portuguese colony in East Asia off the coast of the South China Sea. ()

4. This was the name given to this game by Koreans living in the Caucasus and Central Asia during the Soviet era. They played it very big after harvesting rice and onions, traditional Korean crops. ()

5. Palette (fr.) - shoulder blade ()

6. From English. call - call, call ()

7. Cutting card (English) - a card for cutting ()

8. Sabot (fr.) - shoe, block ()

9. The word baccarat just means zero points; compare tank - zero in the game shmen, in the pre-revolutionary games of macao and baccarat, a combination that gives zero points was called fat ()

10. In the oldest version of this game, still practiced in many gambling houses, players played against each other. One acted as a banker, the rest ponted. The institution did not take anything from the punters, and the banker for each bank that was successful for him "unfastened" the institution a percentage of the winnings. It is logical when a banker throws a bank with his own hands. ()

11. If there are several players betting on Punto, they decide for themselves which of them opens the cards. If there is no consent, this right belongs to the one whose rate is higher. If there are no bets on Punto at all, the dealer opens the cards. ()

12. Except one case - when Punto has 5 points. ()

13. From fr. d "emblee - gives a win. Mayakovsky has "A sharp verse about roulette and a piece of iron", in which this term is used "at once":

I propose somehow on a gloomy evening
come GPU and remove the "dumble" -
half of those who play themselves
and the other - MUR. ()

14. Tens and pictures as the first card are worth 10 points. ()

15. "Redempt" in cheating jargon means "recognize" ()

16. "Five" - ​​500 rubles. From 5 "kat" - on a hundred-ruble note from the time of Catherine II there was a portrait of the Empress. ()

17. It's about o baccarat, in which players play among themselves, and the institution has only its own legal percentage of the banker's winnings ()

18. A l "instant! - This minute (fr.) ()

Baccarat (game) Baccarat (game)

BAKKARA (fr. baccara), gambling card game from the category of banking games (cm. BANK GAMES).
An unlimited number of players can participate in the game, which are divided into punters (cm. PUNTER) and banker (cm. BANKER). Play with a full deck of 52 cards. Cards (two each) are dealt into two hands: one - to the punter, the other - to the banker. In some cases, due to the rules of the game, the player can buy a third card to his combination. The sum of points on each hand is calculated, and only the last digit of the sum is taken into account, and tens are discarded: for example, nine and eight give 7 points. The maximum possible amount is 9 points. Minimum - 0.
The player with the most points wins. Aces in baccarat are valued at 1 point, kings, queens, jacks and tens - at 0 points (the word baccarat just means zero points; in Russia until 1917, a combination that gives zero points was also called fat), the rest of the cards - in accordance with their rank (for example, eight - 8 points, deuce - 2 points). The suits of the cards don't matter.
The game of baccarat came to Russia in the 19th century. from France, where for a long time she was an indispensable accessory of salons and aristocratic clubs in high society. Other names for the game of baccarat: chemin de fer (fr. chemin de fer - railway), or piece of iron; macau (cm. MACAO)(after the Portuguese colony in East Asia off the coast of the South China Sea), punto banco (Spanish Punto Banco) and nine. A variation of the game of baccarat on the numbers of banknotes is called shmen.
Baccarat is currently very popular in casinos. (cm. CASINO) all over the world. It is believed that the biggest money is played in it. The casino is usually played by mixing 6 or 8 decks. The indispensable accessories of this casino game are: a special table in the form of a bean, a clog (a special box for distributing cards), a palette (a special long spatula, with which the croupier (cm. croupier) moves cards and chips).
A variety of baccarat, the nine, is played by the heroes of the play "Running" by M. A. Bulgakov - General Charnota and Paramon Korzukhin.

encyclopedic Dictionary. 2009 .

See what "BAKKARA (game)" is in other dictionaries:

- (Vassarat) a gambling card game very common among the French ...

- (Baccarat) a gambling card game very common among the French ... Encyclopedic Dictionary F.A. Brockhaus and I.A. Efron

- ... Wikipedia

- (fr.). 1) a gambling card game beloved by the French. 2) (from own name). A type of crystal made in Baccarat, France. Dictionary of foreign words included in the Russian language. Chudinov A.N., 1910. BACCAR 1) gambling French ... ... Dictionary of foreign words of the Russian language

1. BAKKARA, unchanged; cf. [French] baccarat]. One of the most valuable varieties of crystal. ● Named after the city of Baccarat in France, where such crystal has been produced since 1816. 2. BAKKARA, unchanged; m. and w. [French] baccara]. An old gambling card game in… encyclopedic Dictionary

In the picture of Paul Cezanne Card game game with application playing cards, is characterized by a random initial state, which is determined using a set (deck) of cards. There are also many sets of cards created under ... ... Wikipedia Wikipedia

In September this year, Russian Railways will celebrate its 15th anniversary. For the past three five years, the state corporation has been carrying out a structural reform, trying to adapt to the realities of a market economy.

Among the priority tasks is the separation of rail transportation from infrastructure services, the formation of a competitive environment. Since 2008, Russian Railways has been transforming into a vertically oriented holding. The book value of the company, its current head Oleg Belozerov, a couple of years ago, estimated from 2 trillion to 4.5 trillion rubles.

The problem of Russian Railways is its gigantic size and geography of presence. Today, the natural monopoly has 85.2 thousand km of railways, thousands of stations and train stations, depots and dispatch centers on its balance sheet. Half of the steel lines - 43 thousand km - are electrified. According to this indicator, Russia ranks first in the world. Russian Railways has a fleet of 20,000 locomotives and 230,000 freight and passenger cars. The company accounts for almost half of the volume of cargo transportation and 26% of passengers.

The company is the largest employer. There are currently 751,000 employees on staff. It should be noted that at the start of the reform there were almost 2 times more of them. Optimization will continue - by 2025, according to the plan, 709 thousand people will remain in Russian Railways. The management promises to make this process "natural" and help those laid off with employment in new places. It was decided to compensate for the reduction in staffing by increasing labor productivity - by 1.5 times over 8 years. At the same time, the average salary in a state-owned company should be 80 thousand rubles.

Shrinkage and shrinkage

Experts ambiguously evaluate the results of the 15-year reform of Russian Railways. The Institute for Natural Monopoly Problems (IPEM), in particular, notes that in recent years, road and pipeline transport has strengthened its position in competition with respect to rail transport. As a result, Russian Railways is losing highly profitable cargo, compensating for the “shortage” mainly through low-profit transportation. In particular, the loading of oil on the networks of Russian Railways decreased by more than 2 times: from 55 million tons in 2010 to 22 million tons in 2017. This year, market participants predict a further 2.3% reduction in the loading of oil cargo on the railroad.

In the risk zone is another highly profitable cargo - oil products. Gasoline, diesel fuel, fuel oil are also gradually “leaving” in pipelines. According to IPEM estimates, in the coming years, due to the commissioning of new pipelines, as well as the conversion of existing oil pipelines to oil products, railway transport will lose 3.6 million tons of cargo, respectively, Russian Railways will miss about 3.6 billion rubles in annual income.

Railroad workers cannot hold bulk cargoes such as cement. Here is a disappointing statistic for Russian Railways – cement production in Russia increased by 5 million tons in the period from 2010 to 2017, while railway loading decreased by 6.6 million tons. According to IPEM, no less influence on the flow of goods is exerted by the structure of pricing for different types transport. Services from competitors, such as car companies, are not subject to government regulation or are partially regulated.

In rail transport, the costs for the consignor consist of the prices and tariffs of many participants in the transportation process, the main of which are Russian Railways and operators providing freight cars. If the cost of services of a state-owned company is regulated by the government, then market pricing applies to operators. As a result, Russian Railways services account for about 50% of the total costs of shippers.

At the end of 2017, the government approved the introduction of a long-term tariff system for the period 2019–2025. This will allow Russian Railways to plan its activities for the long term, including investment programs and contracts, which should become a competitive advantage of steel lines compared to alternative modes of transport. In general, in 2018, the economic situation should be in the hands of railway transport. IPEM predicts that not only coal, as it was in 2017, but also ferrous metals, timber, grain, mineral and chemical fertilizers will become the driver of cargo transportation growth.

The passenger went to the exit

In April this year, the government submitted to the State Duma a draft law "On the organization of regular passenger rail transportation and amendments to certain legislative acts of the Russian Federation." The document provides for the reform of the passenger transportation segment, which is going through hard times. better times. The reasons for the crisis are the aging of infrastructure and rolling stock, as well as the prohibitive cost of tickets, which is a direct consequence of the lack of competition in the market.

The decrease in the number of passengers was first recorded in 2014. At that time, 103.1 million people used long-distance trains, 7 million less than a year earlier. In 2015, the situation worsened even more: only 97.9 million passengers remained loyal to Russian Railways. The state corporation, represented by its “daughter”, the Federal Passenger Company (FPK), tried to take revenge, but did not succeed very much in this matter. In 2016, the figure was 101.4 million people, and in 2017 - 102.3 million (an increase of less than 1%).

The facts show that Russian Railways is losing the passenger transportation market to airlines. In 2016, 88.5 million Russians used the aircraft, in 2017 - already 105 million. The Analytical Credit Rating Agency (ACRA) published a forecast in March, according to which in 2018 it predicts an increase in air travel in Russia by another 5.5%. Russian airlines will transport 110.8 million people, and taking into account the contribution of foreign airlines, the result could be 130.9 million people. The reason for the change in passenger preferences is the high prices for railway tickets. The scandal that Russian Railways got involved in last November is a clear confirmation of this. The Federal Antimonopoly Service (FAS) published on the departmental website an analysis of the cost of air and railway tickets in reserved seat and compartment cars in one direction for one date.

It turned out that in some cases the prices of reserved seat tickets (subsidized by the state) were more expensive than compartment tickets for the plane. So, on October 30, 2017, it was possible to fly from Moscow to Yekaterinburg on a Pobeda low-cost airline in 2 hours and 20 minutes for only 2,499 rubles, although without luggage. A ticket for a compartment car of the branded train "Tomich" for that date cost 4457 rubles, for a reserved seat - 4767.3 rubles. Travel time is 26 hours 32 minutes.

The government expects that with the adoption of the new law in the segment of passenger transportation by rail, it will be possible to create a competitive environment. Logically, the fight for the client, who, as you know, is always right, should lead to lower ticket prices. The question is whether the sprouts of market relations will be able to survive in a natural monopoly environment that is unfavorable for them.

Along the tundra, by rail

In May 2018, the construction of a bridge across the Ob between the cities of Salekhard and Labytnangi was launched. This is a key element of the future railway - the Northern Latitudinal Railway (NLRT). A 707 km long highway will be built in the Yamalo-Nenets autonomous region(YNAO). It will connect the region with the Urals, the northwest and the center of Russia. In fact, the SSH is a return to the Stalinist project of the Transpolar Highway, which was supposed to stretch from the Barents Sea to Chukotka. Only small sections of the railway were built, which were abandoned and are now unusable.

They returned to the idea in 2003, but it has only now come to practical implementation. SHH is included in the Transport Strategy Russian Federation for the period up to 2030. Companies developing oil and gas fields in Western Siberia (Novatek and Gazprom) have confirmed their interest in directing cargo traffic along the Northern Latitudinal Railway.

Sergey Olenin, head of the integrated research department at IPEM, believes that the construction of this highway will allow unloading part of the existing Russian Railways infrastructure, which is operating at the limit of carrying capacity, as well as ensuring the development of territories, including the development of new hydrocarbon deposits.

However, the SSH is only a small part of the obligations of the state company for the construction of highways. The strategy for the development of railway transport in the Russian Federation provided that by 2030 at least 16 thousand km of new tracks should be put into operation. The task is relevant, given that the density of railways in Russia is 5 km per 1,000 sq. km. km, in Canada this figure is higher by a third, and in the USA - 5.5 times higher.

However, this point of the industry strategy did not become a guide to action. Here is the result - in 2012, Russian Railways reported on the completion of the construction of 104 km of tracks, in 2013 - about 67.8 km. Against this background, the commissioning last year of 140 km of the railway section bypassing Ukraine looks like a real record for the last decade. For comparison: in Russia, exhausted by the World War, in 1917, almost 2.5 thousand km of new tracks were built, during the Civil War - from 1918 to 1920 - 1.3 thousand km.

Need for Speed

Russian Railways is ready to bet on the creation of high-speed lines (HSR). Russia is not represented at all in the world rail transportation market in this area. Meanwhile, delivery of goods railway lines at speeds up to 300 km per hour - a new business segment, a kind of global trend. It is no coincidence that many EU countries, China, the United States are actively implementing high-speed rail projects, Morocco and Saudi Arabia are breathing down their backs.

The Transport Strategy of Russia currently includes 5 high-speed rail projects at once. The most developed is the Moscow-Vladimir-Nizhny Novgorod-Kazan expressway, which Oleg Belozerov, the head of Russian Railways, considers as constituent part high-speed transport corridor Moscow - Beijing. A Russian-Chinese consortium is completing the design of the highway, and construction could begin in 2019.

According to him, the task is "not only to connect the two capitals with an infrastructure of a qualitatively different level, but also to link together the two largest high-speed systems - the cargo EuroCarex and China's high-speed railway." As a result, the delivery time of goods along this route will be reduced to 3-5 days. Construction, as Belozerov promises, will begin in 2019. The need for investment is estimated at 7 trillion rubles, but experts do not exclude that the costs may significantly exceed the declared amount. Such is the property of a monopoly.

An order of magnitude less investment involves the project of connecting the Trans-Korean Railway and the Trans-Siberian Railway - only $ 3-4 billion. It can be implemented within 3-5 years, unless, of course, it once again violates the politician's plans. At the end of June, it became known that Russian Railways and Korail were ready to study the conditions for organizing transportation to Europe along this route with the participation of the DPRK. The memorandum was signed during the visit of South Korean President Moon Jae-in to Moscow. Seoul plans to deliver goods to Europe through Russia, which are now going by a roundabout sea route. For Russian Railways, which is losing cargo and passengers on the domestic transportation market, this is certainly a chance to improve its financial and economic performance.

Bargaining is inappropriate

One of the most problematic activities of RZD is the organization of purchases for the needs of a natural monopoly. Vedomosti found out that in 2017, 78 major suppliers received contracts from the state-owned company and its subsidiary RZDstroy for a total of 185 billion rubles.

Russian Railways leads among state-owned companies in terms of the number of complaints about purchases, Vedomosti writes, citing the words of the deputy head of the Federal Antimonopoly Service (FAS) Rachik Petrosyan. In particular, in 2016, out of 298 complaints considered by the department, 148 were found to be justified. For their part, the auditors of the Accounts Chamber, who checked the use of funds from the National Welfare Fund for the modernization of BAM and the Trans-Siberian Railway, came to the conclusion that the provision on the purchase of goods allows the state corporation to increase the scope of work and contract prices by 30% without competitive procedures, arbitrarily change suppliers and place orders from a single supplier. At most open auctions, according to the Accounts Chamber, in 2016 the decrease from the initial maximum price was only 0.5%, in rare cases - 1%. The winner is the bidder who made one move at the auction.

Russian Railways sees nothing wrong with purchasing from a single supplier, much less a violation of antitrust laws. Allegedly, such decisions are forced to be made when performing work at federal facilities, when deadlines are tight, and also when new contract becomes a logical continuation of the previous one. This, they assure the state-owned companies, is done solely to ensure succession.