See, you just proved my point. Knew your answer before you posted it. BTW, whenever anyone puts what is effectively a "demand for proof" on something, I tend to believe the burden of disproving that same thing lies with the person making the demands. Believe me, I've been down this path dozens of times over the last twenty years and have heard it both ways from some of the sharpest mathematical minds in the casino industry. Those who believe generally do not need further proof. However, there is plenty of roll tracking software out there one can use to validate whether or not they have an edge. I've been using BoneTracker for around ten years now - and I tracked with pen and paper before that. For those who do not believe, no proof will ever suffice. They always fall back on the same arguments regarding the validity of the recorded results and suggest that the person recording the rolls is "only tracking the good ones" or using a "that roll didn't count" approach to tracking. Same stuff. Different day. I will say this. I agree with you that the math of the game is irrefutable. Assuming your inputs are correct - which they are not. Whenever you start lumping all the play of all the players for all time together you'll get something very near (but not exactly) the statistical norm. But take any one player who has some measurable skills and look at his play over 200 sessions a year for ten or fifteen years and you may be surprised. I'll leave the last word to you - since I know you'll insist.