About how impossible mateo's winning were.. I made a few mistakes when
computing the prob and corrected it. Sorry ! Since it was discussed
here and
here, I thought I'd come back.
The approximation actually gives a probability of winning +600 btc like mateo did of about 1 in 1 to 10 millions... (for extreme values like here final result is highly influenced by the computers numerical methods and their accuracy).
See what a hundred thousand simulations of normal 60k bets looks like (histogram=simulations, curve=model), the max profit was 424.
Play with the numbers...
I do not think this is the correct model for computing the probability of mateo. It seems you assume that the player arrives and blindfolded bets for 60K times and at the end he just leaves the website with what is left in the pocket. But this is not like that, the players bets until there is money in the bankroll and for fun (I guess winning the bankroll is a lot of fun). If he just wins the bankroll in the middle of playing he just goes away, without extra rollings.
Also I cannot reproduce the result the 1 to 10 millions estimate, I run a simple script simulating a player betting 60K times at 0.5% of the bankroll (half-kelly as in the website) and on 10000 repetitions I get 4 times a final bankroll smaller than 15%.
I'm sorry, but you're using Dubious math. Kelly Betting is actually the amount the House "bets" which will increase their bankroll the quickest. The Player does not enjoy kelly bets as they are betting in a -EV situation. Kelly Betting is only for +EV (which in the case only pertains the House). Thus the formula you are using to determine the chances of bankroll going to a certain % is not correct. The correct % will be much much lower than 2%.
I do not follow your reasoning (maybe you can be clearer?) but I am using a very standard tool. If you run some simulations you can check by yourself that the formula you find in the link is correct.
