Quote from: Joecker on September 12, 2014, 06:53:14 AM

Now about dooglus' simulation, the probability he finds is the answer (I think) to this question :

III) Given that
- all bets are continuously updated at the maximum bet size (which is 0.5% of bankroll) all the time at most 60k times,
- betting stops if bankroll reaches 15% of initial BR,
what is the probability to win 85% of the initial bankroll ?

I don't think so. I didn't include the 60k bets limit at all. First, I don't know where it came from, or whether it's really how many bets he made, and second I don't know that it matters. If it would have taken twice as many bets as it did, wouldn't he have still taken 84% of the bank? I doubt *he* had a 60k bet count limit in mind. Much more likely his goal was to win as much as possible without caring how many bets it took.

When asking "how likely is it that what happened was for real?", we need to decide what aspects of "what happened" are significant. The fact that he rolled a 70.2 (made up number) on his first bet isn't significant. If we include all his rolled numbers in our analysis we will find it truly remarkable that he rolled exactly that sequence of numbers. His "feat" is that he won 84% of the bank, and so that's what we have to look at. If he did it by betting substantially less than the max bet, that too is part of the "feat" and needs to be taken into account, since that makes it less likely to happen without cheating.

Quote from: Joecker on September 12, 2014, 06:53:14 AM

This formulation does not make use of the available information about matnl bets. So it'd be of interest to answer this question: betting at max bet at most 60k times, what is the prob to be as lucky as him (in other words, to win exactly what he won).

I think that's not a good way of looking at it.

If I make a single bet of 1 BTC at "< 49.5", roll 33.3231 and win, and you look at it to decide if I was cheating, do you:

a) see that there was a 49.5% chance of me winning, and so it's quite possible that I didn't cheat
b) see that there was a 0.0001% chance of me rolling exactly 33.3231, and so it's very likely that I cheated

My point is that "winning exactly what he won" is a random detail, like me happening to roll 33.3231. Looking it the probability of *exactly* that happening is to miss the point. We need to look at the probability of being at least as lucky as him - which is low enough already.