Testing advantage, prob Q for David and Mason

[bisognor]

David and Mason,

If a card counter at BJ wanted to know if he was playing at an advantage about how many hands would he need to play in a test run to know that his win was not typical variance from the house percentage, and that his skills were rendering an advantage over the game? 10k, 100k more? Also how is this nminimum # of hands determined?

This is a question I ponder in several gambling persuits Whether I am testing sports betting skills, horse handicapping,or a casino game or poker for that matter. What number of desicions or hours of play are required before I know my profits are from skill verses typical variance. Please help me in figuring out these questions.

Robert

[David Sklansky]

The answer depends on how well you are doing. For instance after 10,000 bets the Standard deviation is 50. That means that a result of 5100 wins would occur about 2 1/2 percent of the time if you had no edge. I'll let others elaborate.

[doormat]

To elaborate on David's post, the standard deviation is derived from the formula SQRT(npq) where n is the number of trials, p is the probability of success and q the probability of failure. So the SQRT(10000 * .5 * .5) = 50, which is only approximate for blackjack because of added variance for doubling down, splitting, blackjacks, etc. But it is close enough. If you think you have a 2% advantage, your expected return would be 1.02 times your average bet - if you could achieve this advantage by flat betting one dollar per hand (good luck!) you would expect to be 200 dollars ahead after 10,000 hands. Since one standard deviation is 50, 2/3 of the time your result should be between 10,150 and 10,250. Hope that helps-

doormat