Is there a mathematician in the house?
How do I analyse the odds of this strategy working?
He bets at 66%, which pays out 1.5x. He starts at 0.06 BTC (this first bet is not shown in the screenshot), doubles on loss, halves on win, never halves below 0.06.
So it's a random walk, which makes a net profit of 0.03 BTC each time it gets back to betting 0.06. Steps down are about twice as likely as steps up, so it seems unlikely to reach max bet and bust very quickly.
But the question is how do I calculate the probability of such a progression busting, given that he can afford to go N steps up the random walk?
Is it a Markov Chain thing? Or how do I analyse it?
How do I analyse the odds of this strategy working?
He bets at 66%, which pays out 1.5x. He starts at 0.06 BTC (this first bet is not shown in the screenshot), doubles on loss, halves on win, never halves below 0.06.
So it's a random walk, which makes a net profit of 0.03 BTC each time it gets back to betting 0.06. Steps down are about twice as likely as steps up, so it seems unlikely to reach max bet and bust very quickly.
But the question is how do I calculate the probability of such a progression busting, given that he can afford to go N steps up the random walk?
Is it a Markov Chain thing? Or how do I analyse it?
You can make the following reasoning when you see a martingale that will show you that it is a gambler's fallacy:
- A martingale is a strategy with low probability (let's say it is 0.001%) of busting
- If you have two strategies with the same probability of busting, you should choose the one which plays less times, because the less you interact with the adversarial edge, the better
- You can always play the vanilla strategy of betting all your money at 99.999%.
- Thus the vanilla strategy must be better than the martingale
A martingale is just a way to hide a bad way to play with a low probability of busting strategy