Whenever someone goes on a streak I think we make the mistake of thinking about it in a successive way... i.e. "The probability of winning 50 out of 55 hands is 0.003% " therefore he must have cheated.
That isn't the right way to think about it. The right way to think about it is to think about each win being independent of the previous or future win. Then generate a profile or graph of said results.
So, if I create a program in which we are flipping coins but I give the house a 1.06% edge then we get the following chart.
Now, of course the overall trend is negative, however, there are plenty of positive variance runs.
So the proper mathematical way to think about Phil Ivey's situation is to think about where he is at on that curve. Sure, the probability of him being on the negative sliding parts of the curve is higher then him being on the positive uptrending parts of the curve but there are many positive uptrending parts thanks to the relatively low house edge.
So if we zoom in on a positive uptrend (the orange circle) we get
Now, each bet or flip was for 50 units. In this uptrend, we win 5,500 units over TWO THOUSANDS flips.
So, if Phil Ivey was betting $50,000 a shot then over this two thousand hand stretch he would have won $27,500,000
If he was betting $150k a shot then he would have won $82.5M
My point? It is easily possible the Phil Ivey playing at $50k - $150k per bet could hit a positive streak that would enable him to win $7.3M if he starts his game on the right part of the curve. Plus, the article said he played for 2 days.
60 hands an hour x ten hours of play is 600 hands. 600 is 30% of 2000 so
30% of $27.5M = $8.25M
30% of $82.5M = $24.75M
Basically, Phil Ivey going on a run is far from some statistical anomaly of 0.003% (or whatever). Its nothing unusual ESPECIALLY in a game with a house edge of only 1.06%. Hell, there are players that go on roulette runs that are an order of magnitude higher in probability/difficulty than Phil Ivey's run.
Last edited by dgiharris; 10-14-2012 at 11:15 PM.