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Betting progressions

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Theorem 1: If a gambler risks a finite capital over many plays in a game with constant single-trial probability of winning, losing, and tying, then any and all betting systems lead ultimately to the same value of mathematical expectation of gain per unit amount wagered. Some Horse racing betting systems can be based on pure statistical analysis of the odds, while others also analysis of physical factors e.

Common forms of betting systems for horse racing are:. From Wikipedia, the free encyclopedia. Strategy for wagering. Gulf Professional Publishing. Retrieved See: Gambling games. Gambling mathematics Mathematics of bookmaking Poker probability. See: Gambling terminology. Casino game Game of chance Game of skill List of bets Problem gambling. Thus, the expected profit per round is. Thus, for all games where a gambler is more likely to lose than to win any given bet, that gambler is expected to lose money, on average, each round.

Increasing the size of wager for each round per the martingale system only serves to increase the average loss. Suppose a gambler has a 63 unit gambling bankroll. The gambler might bet 1 unit on the first spin. On each loss, the bet is doubled. Thus, taking k as the number of preceding consecutive losses, the player will always bet 2 k units. With a win on any given spin, the gambler will net 1 unit over the total amount wagered to that point. Once this win is achieved, the gambler restarts the system with a 1 unit bet.

With losses on all of the first six spins, the gambler loses a total of 63 units. This exhausts the bankroll and the martingale cannot be continued. Thus, the total expected value for each application of the betting system is 0. In a unique circumstance, this strategy can make sense. Suppose the gambler possesses exactly 63 units but desperately needs a total of Eventually he either goes bust or reaches his target.

This strategy gives him a probability of The previous analysis calculates expected value , but we can ask another question: what is the chance that one can play a casino game using the martingale strategy, and avoid the losing streak long enough to double one's bankroll. Many gamblers believe that the chances of losing 6 in a row are remote, and that with a patient adherence to the strategy they will slowly increase their bankroll.

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.

When people are asked to invent data representing coin tosses, they often do not add streaks of more than 5 because they believe that these streaks are very unlikely. In a classic martingale betting style, gamblers increase bets after each loss in hopes that an eventual win will recover all previous losses.

The anti-martingale approach, also known as the reverse martingale, instead increases bets after wins, while reducing them after a loss. The perception is that the gambler will benefit from a winning streak or a "hot hand", while reducing losses while "cold" or otherwise having a losing streak.

As the single bets are independent from each other and from the gambler's expectations , the concept of winning "streaks" is merely an example of gambler's fallacy , and the anti-martingale strategy fails to make any money. If on the other hand, real-life stock returns are serially correlated for instance due to economic cycles and delayed reaction to news of larger market participants , "streaks" of wins or losses do happen more often and are longer than those under a purely random process, the anti-martingale strategy could theoretically apply and can be used in trading systems as trend-following or "doubling up".

But see also dollar cost averaging. From Wikipedia, the free encyclopedia. Betting strategy. For the generalised mathematical concept, see Martingale probability theory. This article needs additional citations for verification.

Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Mathematics portal. Dubins ; Leonard J. February Retrieved 31 March

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A simple way to. › Hobbies › Card Games & Gambling. The Paroli is a positive progression betting system, which means increasing your stakes after a win. You are not guaranteed to turn a profit with this system, but it.