Card-counting at Baccarat

Read on...I am going to offer you one of the most powerful systems in existence for an apparently unbeatable game.

Can you win at baccarat?

Baccarat is a simple game. It is a card game that is dealt from a shoe that holds 6 or 8 decks of cards. Two hands are dealt by the house dealer, the "banker" hand and the "player" hand. Before the hands are dealt, bets may be placed on the banker hand, on the player hand, or on a tie. Winning bets on banker or player are paid 1:1, but a commission of 5% is charged on bank bets making the net odds on such bets 0.95 to 1. If there is a tie, bets on the banker or player are returned. Once a bet has been placed, there are no opportunities for further decisions -- both the banker hand and the player hand are dealt according to fixed rules, resulting in final hands of either two or three cards for each.

It is a card game with one striking similarity to blackjack. The cards are dealt out and placed in a discard tray. They will not reenter play until the shuffle. In theory, knowledge of the undealt cards could be used to create practical winning strategies. Card-counting systems can be designed, much as they have been for blackjack. Is this practical?

No, says consensus opinion. Edward Thorp and Peter Griffin, the century's leading authorities on casino gambling, have both produced studies which show that it cannot be done. They both created card-counting systems for the game which showed the bank and player bets almost never favour the player, and which had great difficulty detecting advantages for the tie.

Griffin summed up his analysis by stating that a card-counter could earn no more than seven cents per day by using the strongest possible count system.

While the greater part of what these highly respected theorists say is true, it is not impossible to create a card-counting system which can win to a greater extent on the tie bet.

For example, say there are no odd cards remaining in the pack. There are only 5 possible totals:-0,2,4,6,8. The odds of a tie are doubled. You have an advantage of 62% on average.

You can detect such a situation by assigning a value of +1 to odd cards. When (and if) your count reaches 160, you know that the average distribution of cards will give you a huge 62% advantage.

The optimal bet (the bet which best balances risk with returns) is 7.8% of your bankroll. The optimal bet size is so high because the bet is so favourable.

So, given initial bankroll of $50,000 you ought to bet roughly $3800. You would expect to win an amazing $2,356 on average each time you made this bet.

Unfortunately this very favourable opportunity occurs rarely. Assuming we make our last wager having seen all but a generous 8-13 cards we can calculate the opportunity by the following methods: The chance of 8 even cards appearing on the bottom of the deck is mathematically the same as 8 cards off the top. This is given by dividing 416 by 256 (total number of even cards) to determine the chance of one even card appearing, then multiplying this figure by the result of 415 divided by 255, and so on until we reach 404/244. Then take the probabilities of having this extreme subset occur for 8 through to 13 cards, add them up, then divide by 6. It turns out we will encounter an all-even subset roughly once in every 10,000 hands!

This represents an earning per hundred hands of roughly $24. Subtracting the effects of making 10,000 $5 (roughly 1% house edge) table minimum bank wagers, we see that the system earns roughly $19 per hour. Not bad perhaps, but not a particularly good return on investment when we consider the alternative earnings from blackjack and poker.

Nevertheless, the evens system takes no more time to learn than it does to explain. Anybody who can count up to 160 can use it. You don't even need to understand the rules properly, let alone worry about playing your hands properly.

Of course, if you do not have $50,000 burning a hole in your pocket, you will not earn quite as much using this system. And the casino may be a little alarmed by a 1-760 bet spread, even if they don't know what you are doing (and they won't). But this is really just an example.

You can dramatically improve your expectation by making the system a little more complex. For example, some situations where the pack contains almost all even cards can also be favourable. The advantages are not in the 60% range, but such situations occur with more frequency. We can also keep a separate count of tens. When ten-valued cards are greater than 75% of the deck, you again can have a very favourable situation. Also, you can use your evens count to limit your losses somewhat on the bank and player wagers.

Most importantly, you can enter and leave a game of baccarat as much you want. In fact you can just sit and watch if you are not taking up space that could be occupied by another player. The effects can be quite dramatic. As an extreme example, if you enter the game with a deck to play and there 8 excess even cards to play, the odds of an all-even subset occurring are five times higher than at the start of the pack, and you have many fewer "waiting" hands to play. You would only need a 1-4 spread to make significant profits on a per-hand basis.

A player with a more modest $10,000 bankroll could easily make $50 an hour just counting odd cards if he chooses his games carefully. Of course, there are much more powerful methods dependent on the exact number of each denomination of remaining cards...but I had to save something for the book.

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