1 sat \ 6 replies \ @random_ 5 Mar 2023 \ on: #1 The Magic of Roulette - Martigale bitcoin
This reminds me of the St. Petersburg paradox.
Imagine a coin toss game where the prize starts at $1 and doubles each time you correctly predict the toss.
How much should one charge to play this game?
Critics of the St. Petersburg paradox attack in particular the assumption that the game can go on indefinitely. Perhaps because both the player and the banker are mortal and so the game must end at the latest with the death of one of them. Similarly, they question the size of the payoff for longer durations. That's because after just 35 rolls, the prize, if it were in US dollars, is equal to the value of the US gold state reserve deposited at Fort Knox, and after three more rolls it is already the amount of all US bank deposits. Thus, it cannot be expected that there would be a realistic possibility of a banker paying out even less than such a large prize.
With roulette, the criticism is simpler. Every casino has a betting limit, so the number of rounds is always finite.
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Analytically, the price to play should be inifinite.
I ran over 2 billion simulations of this game.
Empirically, I found that $200 was a pretty good price. $2 if the prize starts at $0.01
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Actually, in a coin toss, it's 50:50
In roulette, the odds are slightly less because 0 is neither red nor black, neither even nor odd, neither high nor low, so the probability of winning is only 48.65%.
With a coin flip, you can use the same game strategy, but you'll be hard pressed to find an opposing side that will play with you until you win :o)