# The Strategy Of Constant Bets

The strategy of constant bets is to play K francs at a time until you either have lost your capital of A francs or have reached the objective of B francs. This martingale is basic, yet many people use it.

The strategy of constant bets is to play K francs at a time until you either have lost your capital of A francs or have reached the objective of B francs. This martingale is basic, yet many people use it.

How to fix the value of K? Should we play jomcuci918 1 franc each time, or 5 francs, or 10 francs? To answer this question, two techniques are possible: computer simulation and mathematical study (we have excluded the test in a casino, because we are neither rich enoughâ€¦ nor patient enough).

It is only since we have powerful machines that are easy to program that we can carry out the simulations which were de facto forbidden to mathematicians before 1945, the date of the development of the first electronic computers. Since many complex problems could not be solved by reasoning, electronic computers were, from their conception, used to calculate the probability of success of certain patients.

In these simulations, where the rules of patience are included, the program randomly draws starting configurations and then counts successes and failures, and therefore the probability of winning.

Let us examine three concrete objectives: (a) to go from A = 10 francs to B = 100 francs (to increase tenfold his initial capital) (b) to go from A = 10 francs to B = 20 francs (to double his capital) (c) to go from A = 10 francs to B = 11 francs (increase your capital by 10 percent) The stakes played each time will be either 1 franc, or 5 francs, or 10 francs.

The results of the computer simulations are shown in the table in Box 2 for the coin toss game (or fair roulette), French roulette and American roulette. Each evaluation represents 50,000 tries (which, at the rate of one try every five minutes, 12 hours a day, corresponds to more than a year of indoor play for each box of the tables).

Here simulations are not essential, because this problem has a mathematical solution, discovered in a particular case by Huygens in 1657, generalized by Bernoulli in 1680, then clarified by Moivre in 1711.

When p is 1/2 and the bet is K, the probability of winning jomcuci918 e-wallet is A / B; when p is less than 1/2, it is [1 – (q / p) A / K] / [1 – (q / p) B / K]

So, the smaller p is, the less you will succeed; it is not a surprise !

The larger B / A (the more greedy you are), the less likely you are to succeed; it is not surprising either.

However, when p is set, you maximize your chances of success by taking K as large as possible. This result is not obvious! To increase your fortune tenfold and go from 10 to 100 francs using the constant bet strategy, it is better to bet 10 francs on each draw than 5 francs, and it is more advantageous to bet 5 francs than 1 franc.

If we compare the theoretical results given by the Huygens-Bernoulli-Moivre formula with those of our simulations carried out by carrying out 50,000 tests, we notice that only two figures given by the experiment are reliable.