I simulated a very pessimistic scenario in which a high roller with an infinite bankroll places 10000 maxbets in a row (50% chance of winning each bet). Maxbet adjusts dynamically (to 1% of site BR) after each bet. Site's starting bankroll is 26500 btc.
See below the probability of the site's bankroll after 10000 bets (3600 iterations).
http://i.imgur.com/dKPeAQH.png
Site can't practically go broke, but BR can decrease substantially. Note the logarithmic x-axis. There is far more upward potential with this type of player....
See below the probability of the site's bankroll after 10000 bets (3600 iterations).
http://i.imgur.com/dKPeAQH.png
Site can't practically go broke, but BR can decrease substantially. Note the logarithmic x-axis. There is far more upward potential with this type of player....
Site will never go broke, because it is not possible with a maximum bet equals to 1% of the invested amount...
But basically, with your simulation, the expected value is 26.5k btc, like it was in the beginning. And it has the same chance to win or lose xxx btc.
But now, if you make your simulation with a martingale: the player is not always betting 1%, but he starts with 0.25%, then 0.5% if he lost, and finally 1% if he lost twice in a row. And also put a stop if the player win more than 0.5% of the capital at the beginning and start your simulation again... It will be unlikely that he lost everything he has, and he will always win 0.5% of the capital of the website
No, actually the expected value for the site is (starting BR + 0.01*total amount bet).
And if you really believe in Martingale I welcome you to play on JustDice and ruin the bank!