The bold game theorem
August 12, 2021
This general result that everyone should know will be called the Bold Game malaysia casino online Theorem or Law of Dubins and Savage (they were the first to establish it, in 1956). The precept is moral, we must spend as little time as possible in front of the green carpet mmc996 malaysia.
The best way to play in a game with two options of probabilities p and 1 – p with p less than 1/2, to go from A to B, is to always bet what brings the desired goal the closest.
All game methods, as we have seen from experience, are not equal. My friend was right on one point: to achieve a given goal, there are better strategies than others (which does not mean that you can win against the casino).
The Bold Game Theorem leads us to better strategies than those considered so far to increase tenfold, or increase by 10 percent, our capital.
If your objective is to increase your nest egg tenfold (go from A to 10A), you must bet A the first time (that’s the most you can do); if you won, bet 2A, then, if you won, bet 4A; then finally bet 3A (because that is enough for you to reach 10A). If you lose on the last move, you find yourself with 7A, you are missing 4A, so you bet 4A. Etc.
This strategy resembles the geometric martingale in the case where we take K equal to A, but it is not completely equivalent to it, because when you have just lost, rather than starting again from K (geometric martingale), here you play what is necessary to achieve the goal in one shot, if possible.
In the case of the objective of doubling the capital from 10 francs to 20 francs, the strategy of constant bets with K equal to 10 francs and the geometric martingale with K equal to 10 francs are identical to the strategy of the Bold Game, which is then reduced to betting once 10 francs (the probability of success is obviously p). The experimental results obtained by carrying out 200,000 tests for each case (the experiment being faster, the number of tests was increased to have better precision) are shown in the table in box 2.
Note that, if you are ready to risk 10 francs to win 1 franc (or 10,000 francs to win 1,000 francs), by applying the game rule given by the diagram, you will succeed in France with a probability of 0.9042656 … ( see below for the optimal strategy for winning 10%), which is quite reasonable. Let’s not rejoice too much: if you apply this method of play every night on a regular basis, the nights you win (over 90 percent of cases) do not make up for, in the long run, the ones you lose, because when you lose, you lose ten times more than when you don’t win.