英语词汇“st petersburg problem”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

Also St Petersburg paradox, Petersburg problem, St Petersburg problem. A paradox associated with certain betting games, for which calculation shows the expected winnings to be unlimited, but which are nevertheless unattractive to players because of the high probability of only a small payout.In a typical game, a coin is tossed until a head appears, the player winning one pound if a head appears on the first toss, two pounds if two tosses are required, four pounds if three tosses are required, and so on. The expectation of the player's winnings is calculated by multiplying the amount won if n tosses are required (2ⁿ⁻¹) by the probability of winning that amount (1/2ⁿ) and taking the sum over all possible values of n. Since the multiplication gives a value of ½, and there are an infinite number of possible values of n, the expected winnings are infinite. Nevertheless most players would be deterred from paying to enter by the fact that the chance of the game ending on any throw is ½, and high payouts (more than the cost of entering the game) are very unlikely.

ΚΠ

1865 I. Todhunter Hist. Math. Theory of Probability xi. 220 Daniel Bernoulli now applies his theory to the problem which is known as the Petersburg Problem, probably from its first appearing here in the Commentarii of the Petersburg Academy.

1872 Chambers's Encycl. VII. 781/1 A very excellent example of moral as distinguished from mathematical probability is furnished by the famous ‘St Petersburg problem’.

1902 J. M. Baldwin Dict. Philos. & Psychol. II. 349 He [sc. Buffon] has a child toss a coin 4040 times to test the Petersburg paradox.

1924 Amer. Math. Monthly Apr. 184 Every day we see people take part in lotteries, insurances and other transactions in which ΔU < 0. On the other hand, as..Bernouilli has shown in the Petersburg paradox, there are cases in which the mathematical expectation ΔU is unlimited, and nevertheless nobody would engage in the corresponding transaction.

1961 F. Mosteller et al. Probability v. 180 Consider the expected payoff when the player tosses until he gets a tail. (This is the original St. Petersburg problem, and it is satisfactory to say that the expectation is infinite.)

1998 Isis 89 23 Menger..dealt with the use and limits of mathematics in modeling the St. Petersburg paradox. In the ‘Petersburg Game’, person A invites person B to place a bet with him in which a coin is flipped until a head appears for the first time.

单词	st petersburg problem
释义	> as lemmas St Petersburg problem Also St Petersburg paradox, Petersburg problem, St Petersburg problem. A paradox associated with certain betting games, for which calculation shows the expected winnings to be unlimited, but which are nevertheless unattractive to players because of the high probability of only a small payout.In a typical game, a coin is tossed until a head appears, the player winning one pound if a head appears on the first toss, two pounds if two tosses are required, four pounds if three tosses are required, and so on. The expectation of the player's winnings is calculated by multiplying the amount won if n tosses are required (2ⁿ⁻¹) by the probability of winning that amount (1/2ⁿ) and taking the sum over all possible values of n. Since the multiplication gives a value of ½, and there are an infinite number of possible values of n, the expected winnings are infinite. Nevertheless most players would be deterred from paying to enter by the fact that the chance of the game ending on any throw is ½, and high payouts (more than the cost of entering the game) are very unlikely. ΚΠ 1865 I. Todhunter Hist. Math. Theory of Probability xi. 220 Daniel Bernoulli now applies his theory to the problem which is known as the Petersburg Problem, probably from its first appearing here in the Commentarii of the Petersburg Academy. 1872 Chambers's Encycl. VII. 781/1 A very excellent example of moral as distinguished from mathematical probability is furnished by the famous ‘St Petersburg problem’. 1902 J. M. Baldwin Dict. Philos. & Psychol. II. 349 He [sc. Buffon] has a child toss a coin 4040 times to test the Petersburg paradox. 1924 Amer. Math. Monthly Apr. 184 Every day we see people take part in lotteries, insurances and other transactions in which ΔU < 0. On the other hand, as..Bernouilli has shown in the Petersburg paradox, there are cases in which the mathematical expectation ΔU is unlimited, and nevertheless nobody would engage in the corresponding transaction. 1961 F. Mosteller et al. Probability v. 180 Consider the expected payoff when the player tosses until he gets a tail. (This is the original St. Petersburg problem, and it is satisfactory to say that the expectation is infinite.) 1998 Isis 89 23 Menger..dealt with the use and limits of mathematics in modeling the St. Petersburg paradox. In the ‘Petersburg Game’, person A invites person B to place a bet with him in which a coin is flipped until a head appears for the first time. extracted from Petersburg paradoxn. < as lemmas
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