D’Alembert’s martingale: What is it?

You bet on a single chance, and if you win, you lower your bet by one, and if you lose, you increase your bet by one, and so on.

The name of the following gambling malaysia online casino process does not mean that d’Alembert believed it was a winning method. The Martingale of d’Alembert (or rising of d’Alembert): the initial stake is K francs; then, each time you win, you decrease your stake by K francs (because you think that the luck has just been favorable to you and that it is likely to be less so the next move), and each time that you lose you increase it by K francs (luck should now serve you better, do you think).

When the rule leads to betting 0 francs, the stake is not reduced, which remains Kfrancs. When we are close to the goal, we do not bet more than it is necessary to reach it: if, for example, when the objective is 100 francs, d’Alembert‘s rule leads us to 98 francs and we suggests betting 6 francs, we only play 2 francs. For each result, 50,000 tests were made; the results are given in Box 2.

Here again, the more p is favorable to the bank, the less often one succeeds. Then, in the case p equal to 1/2, the simulations find approximately the values ​​calculated for the constant bets (the variations compared to the theoretical values, 1/10, 1/2, and 10/11 are not significant).

This is deduced from a remarkable theoretical result, which indicates that, in the case p equal to 1/2, to go from A francs to B francs, all the strategies are equal.

If p is 1/2, whatever you do, you will succeed A times over B, neither more often nor less often.

Third result: as in the case of constant bets, we increase our chances of increasing K’s values.

For p equal to 18/38, for example, depending on whether you start from Kequal at 1 franc, K equal to 5 francs, or K equal to 10 francs, your probability of success drops from 3.56 percent to 3.72 percent. Then to 4.79 percent.

When p is less than 1/2, of the game strategies, tried so far, d’Alembert’s strategy with K equal to 10 is the best.

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