Quote from: dooglus on September 25, 2013, 11:53:56 AM

Quote from: Deprived on September 25, 2013, 05:49:10 AM

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.

I didn't want to let this brilliant idea get missed.

Here are the numbers:

Quote

Bets >= 5 BTC at 49.5% for uid in (2548,9075,31791,46591,113828,118977,119016,136175,143341,145625,150486):

+----------+--------------+
| count(*) | sign(profit) |
+----------+--------------+
| 7209 | -1 |
| 7185 | 1 |
+----------+--------------+

49.9166% win

Bets of 0.01 BTC at 49.5% for the same uids:

+----------+--------------+
| count(*) | sign(profit) |
+----------+--------------+
| 10881 | -1 |
| 10558 | 1 |
+----------+--------------+

49.2467 win

So 49.25% of small bets win, when we expect 49.5% to win. Is that significant? It's not as far below average as the big bets are above average.

The expected amount of small bets won is 10612, the amount won is 10558, a difference of 54. Since this is a simple binomial distribution, we can easily find the standard deviation, which is 73.2. So the observed outcome is less than 1 sigma from the expected outcome. This is not significant in any way, shape or form.