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Related links Now suppose that we have just tossed four heads in a row. A believer in the gambler's fallacy might say, "If the next coin flipped were to come up heads, it would generate a run of five successive heads. The probability of a run of five successive heads is 0.55 = 0.03125; therefore, the next coin flipped only has a 1 in 32 chance of coming up heads." Notice that the gambler's fallacy is quite different from the following path of reasoning (which comes to the opposite conclusion): the coin comes up heads more often than tails, so it is not a fair coin, so I will bet that the next toss will be heads also. This is not fallacious, though the first step - the argument from a finite number of observations to a statement of likelihood - is a very delicate matter, and is itself prone to fallacies of its own peculiar kind. Dealer hits on soft seventeen (ace, six)
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References Slot machine 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. Insurance is statistically a bad bet for the player who has no direct knowledge nor estimation (e.g. through card counting) of the dealer's 'hole card' because Insurance has a negative expected value for the player. Even for the player who has been dealt a natural (a two-card 21) it is unwise to take Insurance. In such a case, the dealer usually asks the player "Even money?" This means that instead of 3:2, the player with the natural accepts to be paid off at 2:2. Thus it is exactly the same thing as buying Insurance, losing the Insurance bet and getting paid 3:2 on the natural. (If the player with the natural refuses "even money", and the dealer turns over a natural, it is a tie.) A couple already has two daughters. What is the probability that the next child is a son? (Answer: 0.5) [if we assume the gender of a child is completely random, and that a male or female child is equally likely, either or both of which may be incorrect.] The Theory of Blackjack, Peter Griffin, 1996 (1979), ISBN 0929712129 Spanish 21 The above is a basic strategy table for the most common 6- to 8-deck, Las Vegas Strip rules. Specifically: dealer hits on soft 17, double after split allowed, multiple split aces, one card to split aces, blackjack pays 3:2, and (optionally) late surrender. Big Wheel / Big Six
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