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The Mathematics

If both the player hand and bank hand followed the same rules to determine whether or not an additional card is to be drawn, baccarat would be an even game with no advantage on either side. It would be no different form flipping a coin and betting on either heads or tails. However, because the rules for drawing to the bank hand are slightly more advantageous than those for drawing to the player hand, the bank hand will win slightly more often than the player hand. Determining the exact percentage against the player hand is a complex process that involves isolating each of the differences in drawing rules and determining the impact it has on each hand's chances of winning. The calculation reveals that the player hand wins 49.32 percent of the time and the bank wins 50.68 percent of the time. If you subtract the first figure from the second, you will find that the player hand faces a 1.36 percent disadvantage. Since player-hand bets are booked by the house, when someone bets on the player hand, he is giving the casino a 1.36 percent edge. We have already seen that when someone bets on the bank hand, the casino gives itself an edge by charging a 5 percent commission on any winnings paid on the bet. Don't make the very common mistake of assuming that this means that the house has a 5 percent edge on the bet. First, you must keep in mind that the 5 percent is charged only on winnings. It is not charged on the wager itself, like the 5 percent charge the house makes on buy bets at craps. This, in effect, means that the 5 percent is only charged on halt the money involved in the transaction. This cuts the casino edge in half, from 5 percent to only 2.5 percent.

However, even this figure does not tell the whole story. You must remember that, without the commission charge, the bank hand would enjoy and advantage of 1.36 percent over the player hand. This figure has to be subtracted from the 2.5 percent cut the house in giving itself to arrive at a net house advantage of 1.14 percent. This figure is very close to the actual house percentage, but one more adjustment has to be made. In converting the 5 percent commission to a 2.5 percent edge, we assumed that the bank hand would win half the time. Yet we have already seen that it wins very slightly more than half the time due to the difference in drawing rules. This means that the 5 percent commission is charged very slightly more than half the time, increasing the house edge very slightly. When this factor is taken into account, we find that, instead of 1.14 percent, the casino ends up with an advantage on the bank-hand bet of 1.17 percent. This can be calculated as follows. The bank-hand bettor wins 50.68 hands out of every one hundred played but receives only 95 cents for each dollar bet. Therefore, the gross profit from one hundred one-dollar wagers would be 50.68 x $95 = $48.15. Since the bank hand bettor loses 49.32 hands out of every one hundred played, the gross loss for one hundred one-dollar wagers is $49.32. If you subtract the profit of $48.15 from the loss of $49.32, you arrive at 1.17, which is the house P.C. on the bank-hand bet.

A disadvantage of 1.17 percent on the bank hand and 1.36 percent on the player hand makes baccarat one of the best games for the player to be found in the casino. It is a smaller percentage than that faced at line bets and 6 and 8 place bets at craps, far smaller than the edge at all other craps wagers and all wagers at roulette. Only pass-line craps bets with full odds and blackjack with proper strategy offer the player a better break than baccarat. Although the bank hand retains a very slight edge over the player hand, the two figures are so close that for all practical purposes it can be considered that the two bets offer virtually identical chances of winning. So if a baccarat player asks, "Which hand should I bet on, player or bank?" the answer is, "It doesn't much matter." One may as well ask whether it is better to bet heads or tails when flipping a coin. Baccarat is a game of pure chance. There is no element of strategy either in the play of the hands, which is dictated by the rules, or in deciding which hand to bet on. This is one situation in which you can safely rely on hunches, ESP, the I Ching, or any other arcane system you wish for deciding on which hand to bet next. I don't for a moment think these techniques will help you win, but they won't hurt either. As long as you don't make the mistake of thinking that your particular method of determining which hand to bet on offers an unbeatable system - a delusion that might lead you to wager money you can't afford to lose - there will be no harm done. Follow any whim you wish in deciding whether to place your money on the player hand or on the bank hand, because it is bound to be as good as any other method of deciding.

The opposite side of the card that the casino provides that lists the drawing rules for player and bank hands is a scorecard designed for the player to keep track of whether player or bank hand wins each round. This is for those players who like to look for trends or believe that eventually the wins and losses on the two hands have to even up. We have already discussed the fallacy of the maturity of chances enough for you to realize how silly this kind of scorekeeping is. It is trials process because, as the game process, the shoe become depleted of different value cards at different rates. Therefore, there is a sense in which what happened on previous hands can have an impact on what happens on subsequent hands. However, which hands have won earlier in the shoe, player or banker, does not act as any kind of an indicator of what is happening to the composition of the cards remaining in the shoe. In other words, previous hands have no predictive value for subsequent wins. Personally, I think following your hunches on what hand will win next is better than trying to detect any pattern from a scorecard. Both methods are equally unreliable, but at least the hunch method is less tedious and more fun when it does work.

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