I understand that in the classic Martingale, the slight chance to lose all the starting tokens counters the high chance of net winning that is brought by doubling up the gamble amount after each loss.
I'm now having trouble with the following variation :
- It is a one player game.
- Each minute, the player gains one free token.
- Each five minutes, the player can gamble any amount of the tokens they own to a coin flip.
- If they win, they double up, the net gain is the amount of bet tokens.
- If they lose, they lose the bet tokens.
- The coin is weighted in favor of the player with a 60% chance to win
I'm unsatisfied with my attempts at finding a strategy that is the safest AND fastest to increase my token count.
At first I thought that the safest was to not play, but considering the coin is weighted in my favor, it is for instance strictly better to bet at least 5 coins every time. Using expectancy of an All-In bet doesn't take into account the 40% chance to lose the bet tokens.