The Geometric Martingale

The geometric martingale is the most popular of all, as its principle is simple and, at first glance, infallible, it is THE martingale.

We start by betting K francs; if you lose, you double the bet, and you double it that way until you win. When that happens we lost

K + 2K + 4K +… + 2nKet we have gained 2n + 1K,

so we won Kfrancs. We then start all over again, with a stake of K francs.

Example: you bet 1 franc, you lose; you then 711kelab bet 2 francs, you lose; you then bet 4 francs, you win. In total, you won 4 francs and lost 3 francs, which gives a positive balance of 1 franc.

If we could thus always double, we would earn K francs in each series and, little by little, we would accumulate all the money we want. Find the mistake.

It is twofold. First, when you have nothing left, you can no longer bet; however, it happens that there are long sequences of identical draws (the record in a casino room is a series of 42 times the red).

Then, the authorized bets are limited (to 1000 times the weakest bet for a given table in French casinos) and therefore, even if you are very rich, you will not be able to apply the geometric martingale more than 10 steps.

Let’s make it practicable by specifying our choices in the event of a blockage. We double the previous bet if we lost, as long as nothing stands in the way, but if we can reach the goal of B francs by betting less than what the rule indicates, we do it, and if we do not not enough to bet according to the rule, we bet the maximum we have.

K is the initial bet. For each result, 50,000 tests were made. Here again, the results are given in Figure 2. If p is equal to 1/2, nothing allows to deviate from A / B; we verify, again, that American roulette is much more productive than French roulette (for the bank, of course!).

We discover that the geometric strategy is better than the two other game methods considered previously, and that it is better for K equal to 10 francs than for K equal to 5 francs or K equal to 1 franc.

It seems that not only does the money go to the rich, but it also goes (or stays, better!) To those who bet online casino malaysia bigger! The most violent strategies are the best. The bigger the value of K, the better it is, and the more violent the strategy, the better it is (the geometric is more violent than the d’Alembert, itself more violent than the constant bets). Is this rule general? If so, how to formulate it precisely?

The fact that, for ps greater than 1/2, we find that d’Alembert’s martingale with K equal to 1 is very slightly better to double its capital than the geometrical one with K equal to 1 (the only numerical exception to the general superiority of the geometric ) does not contradict our general remark, because, in d’Alembert with K equal to 1, the fall in stakes occurs more slowly than in geometry (also with K equal to 1) and therefore leads, on average, to a behavior more violent. The violence of the behavior seems in all general the good behavior in this game.