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?
I will try to give another way to see why any martingale cannot work. It is just a partial answer to the actual question and it is like discovering hot water, still it can be a benefit since the gambler's fallacy lurks behind.
Consider a martingale strategy which make a walk over a finite set of values {a,b,c,d, etc.} such that after the last value the martingale is busted. It does not matter the actual way of going from one value to the other. Now consider a huge list of all possible outcomes of this martingale (each outcome is a serie of played values), last ones being the busting ones. Then just collect all the reached values in columns and see that for every column, like for example the value "a", there is an expected loss of -0.001*a. This holds for "b" etc, so the final expected value must be negative.
The gambler's fallacy is thus in thinking that the "order" of plays would give a positive outcome, but of course it does not matter if I play my bets within an order or not.
Is it somehow clear?