Quote from: cowbay on September 25, 2013, 05:36:12 AM

Quote from: Deprived on September 25, 2013, 05:03:43 AM

You still haven't explained why you chose to shift by 2 rather than by 1 or by 3.

Excellent point. It would be interesting to see the distribution of bet outcomes across different shift values to see if it is warrants looking into, or if this is simply the result of cherry-picking.

Correct or not, I appreciate the effort put into this analysis.

Well shifting it is fundamentally flawed for a (pretty obvious) reason.

Consider any significantly winning session of play which contains a mix of very high bets and very small bets. The result of the session are determined ONLY by the high bets - what happens on the very small bets is irrelevant. If you changed all the small bets to wins OR to losses the overall result would still be a significant win.

So we already know that a much higher percentage than average of the higher bets won - but if the results were genuinely random we know nothing at all about the results of the small bets as they're irrelevant to how we picked the sample.

If you take this session which has a much higher than average set of winning roll on BIG bets and an indeterminate set of tolls on SMALL bets and shift the results then, on average, the final result will be significantly lower. Because some of the lucky big bets will now be moved to small bets - and replace by rolls with an indeterminate lucky factor.

In short, not only is there no reason why shifting SHOULD produce the same results, there's actually a good reason why it should NOT : that being how the sample for analysis was picked. This is Bayes Theorem at its most basic.

It does, however, follow on from this that there IS an analysis which could be done to find a smoking gun. The means by which the sample was picked (i.e. why his rolls are being looked at all) DOES define what we should expect to see in big bets (more wins than expected) but says nothing about the very small ones. i.e. the small bets can be considered to be a genuinely independent sample not influenced by selection criteria.

IF he knows the seed OR has some means of otherwise predicting series then we'd expect to see a LOWER than usual win-rate on the small bets. Whilst if everything is genuinely random then the results of the small bets would be unrelated to him winning overall on the big ones.

IF a smoking gun exists then where you'd see it is in far more losses than expected on small rolls - where if there was no unfair advantage there'd be no reason for it to correlate with the opposite results in the big bets. We already know that his overall results on big bets are very significantly above average. By looking at the small bets seperately (we CAN legitimately treat it as a seperate data set) we can see if the results there are similarly significantly BELOW average. Such an analysis should be done by simply measuring his luck - not by factoring in varying bet size (as if a few small bets are much larger than the rest that would lead to no significant result).

I have no idea what the outcome of that would be.