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Descubra o melhor curso de 4bet: aprimore suas habilidades de poker agora
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A martingale is a class of betting strategies that originated from and were popular in 18th-century France. The simplest of 😄 these strategies was designed for a game in which the gambler wins the stake if a coin comes up heads 😄 and loses if it comes up tails. The strategy had the gambler double the bet after every loss, so that 😄 the first win would recover all previous losses plus win a profit equal to the original stake. Thus the strategy 😄 is an instantiation of the St. Petersburg paradox.
Let one round be defined as a sequence of consecutive losses followed by 😄 either a win, or bankruptcy of the gambler. After a win, the gambler "resets" and is considered to have started 😄 a new round. A continuous sequence of martingale bets can thus be partitioned into a sequence of independent rounds. Following 😄 is an analysis of the expected value of one round.
Let q be the probability of losing (e.g. for American double-zero 😄 roulette, it is 20/38 for a bet on black or red). Let B be the amount of the initial bet. 😄 Let n be the finite number of bets the gambler can afford to lose.
In a unique circumstance, this strategy can 😄 make sense. Suppose the gambler possesses exactly 63 units but desperately needs a total of 64. Assuming q > 1/2 😄 (it is a real casino) and he may only place bets at even odds, his best strategy is bold play: 😄 at each spin, he should bet the smallest amount such that if he wins he reaches his target immediately, and 😄 if he does not have enough for this, he should simply bet everything. Eventually he either goes bust or reaches 😄 his target. This strategy gives him a probability of 97.8744% of achieving the goal of winning one unit vs. a 😄 2.1256% chance of losing all 63 units, and that is the best probability possible in this circumstance.[2] However, bold play 😄 is not always the optimal strategy for having the biggest possible chance to increase an initial capital to some desired 😄 higher amount. If the gambler can bet arbitrarily small amounts at arbitrarily long odds (but still with the same expected 😄 loss of 10/19 of the stake at each bet), and can only place one bet at each spin, then there 😄 are strategies with above 98% chance of attaining his goal, and these use very timid play unless the gambler is 😄 close to losing all his capital, in which case he does switch to extremely bold play.[3]
In reality, the odds of 😄 a streak of 6 losses in a row are much higher than many people intuitively believe. Psychological studies have shown 😄 that since people know that the odds of losing 6 times in a row out of 6 plays are low, 😄 they incorrectly assume that in a longer string of plays the odds are also very low. In fact, while the 😄 chance of losing 6 times in a row in 6 plays is a relatively low 1.8% on a single-zero wheel, 😄 the probability of losing 6 times in a row (i.e. encountering a streak of 6 losses) at some point during 😄 a string of 200 plays is approximately 84%. Even if the gambler can tolerate betting ~1,000 times their original bet, 😄 a streak of 10 losses in a row has an ~11% chance of occurring in a string of 200 plays. 😄 Such a loss streak would likely wipe out the bettor, as 10 consecutive losses using the martingale strategy means a 😄 loss of 1,023x the original bet.
