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After the final value of the player and bank hand is declared, the high hand wins. If the hands are of the same value, a tie is declared, and both the player and banker bets are returned to the players. The payoff for a winning bet on the player is 1 to 1. The banker bet, which has a higher chance of success than the player bet, is paid at 1 to 0.95. This is because the casino takes a commission, or cagnotte, of 5 percent for all winning bets on the bank hand. Commissions on the bank hand are recorded by one of the dealers. The amount is usually settled once the shoe has been dealt out or the player leaves the table. Ties are paid off at 8 to 1. Casinos usually advertise this as 9 for l.

games of chance are run so that a small percentage favors the games operators at the expense of the players. In the short term, luck will shift back and forth between the house and its customers. Over the long term, however, the results will average out to give the house its percentage of every bet placed. Except in very unusual circumstances, the house always plays with this "edge" in its favor. This edge not only accounts for casinos' profits, but must also cover their expenses. Someone has to pay for all those chandeliers.

The best bet is to side with the banker. The banker bet has a house edge of 1.06 percent. This is one of the most favorable bets in the casino. Many players think that because of the commission, the bank is a bad bet. In fact, the bank has a slight informational advantage-the bank's third-card drawing decision is based on a logical assessment of the player hand. For example, it helps the bank to stand on a 3 when the player draws an 8 as his third card. Though normally a bad total, the banker's 3 will beat the player's total 3 to 2 (three out of five) occasions, giving him a substantial edge in this situation. The banker benefits from knowing that the player has probably worsened his hand by drawing an 8. The player's first two cards could total only 0 to 5, so an 8 will help only on 0 or 1 and hinder on 2, 3, 4, or 5. A banker's 3 will beat the player if his two-card score is 3 or 4 (+ 8= 0, l, or 2), lose against a player's two-card 0 or 1 (+ 8 = 8 or 9), and tie against the player's 5 (+8=3).

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Hand Strengths
So what does all this tabular data tell us? It is a matter of common sense that the fewer the number of opponents, the greater the chance that your hand will be best, which means that forcing opponents to fold always has a beneficial effect on \,-our odds of syinning. However, the degree to which fewer opponents helps you depends greatly on the strength of the hand you hold. Verify this for yourself by going to the table and comparing the winning chances of a straight flush and a pair of two's against increasing numbers of opponents:

• As we said, a pair of two's against one opponent wins about .50 percent of the time-not bad. But against seven players, it wins less than 1 percent of the time. As the number of opponents increases, the prospects of your little pair plummet dramatically.

Compare that to a straight flush. It has a greater than 99.99 percent chance of winning against one opponent. Against seven opponents, it .still has a chance of winning of more than 99.99 percent. In other words, no matter how many opponents are up against your straight flush, you are going to win. As opposed to a hand like paired 2's, the winning chances of a straight flush are virtually impervious to the number of opponents.

The eonclusion should now be obvious: The weaker a hand, the More it is hurt by the presence of inore opponents. Conversely, the stronger a hand, the less it is hurt by the presence of more opponents.
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