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If the 'Banker' has an initial total of 7, the 'Banker' stands and draws no further cards. double-down restrictions: double-down allowed only on certain combinations. Doubles are permitted after splitting. Mathematically, the probability is equal to one that gains will eventually equal losses and a gambler will return to his starting point; however, the expected number of times he has to play is infinite, and so is the expected amount of capital he will need! A similar argument shows that the popular doubling strategy (start with $1, if you lose, bet $2, then $4 etc., until you win) does not work; see St. Petersburg paradox. Situations like these are investigated in the mathematical theory of random walks. This and similar strategies either trade many small wins for a few huge losses (as in this case) or vice versa. With an infinite amount of working capital, one would come out ahead using this strategy; as it stands, one is better off betting a constant amount if only because it makes it easier to estimate how much one stands to lose in an hour or day of play. SP = SPlit Resplitting Aces. Dice / Tiles A two-card hand of 21 (an ace plus a ten-value card) is called a "blackjack" or a "natural", and is an automatic winner. A player with a natural is usually paid 3:2 on his bet, although in 2003 some casinos started paying only 6:5 on blackjacks, a move decried by longtime blackjack players. Video Lottery Terminal Some common rules variations include: In the United States, Australia and Canada, a variation of baccarat is played in which the casino banks the game at all times. Punters may bet on either the player or the banker, which are merely designations for the two hands dealt in each game. Knock-Out Blackjack, Olaf Vancura and Ken Fuchs, 1998, ISBN 0929712315 Six full packs of cards of the same pattern are used, shuffled together. The players seat themselves round the table. In the centre is a basket for the reception of the used cards. If there is any question as to the relative positions of the players, it is decided by lot. The person who draws the first place seats himself next on the right hand of the croupier, and the rest follow in succession. Roulette Luck, Logic, and White Lies: The Mathematics of Games, Joerg Bewersdorff, 2004, ISBN 1568812108, 121-134

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