Re: Winners and Losers?
First, let me say that all these estimates are provisional and depend on what fraction of the players play each limit.
One could reasonably estimate that the house (plus tips) makes about 0.5-1 BB/hr. on each player. Let's use .5 for this calculation. Considering that 1BB/hr is a good rate to make, we can estimate that the SD of the EV distribution at this time is 1 BB/hr. (about 7% of player will make 1 BB/hr or better). The mean is -0.5.
If all these people play an infinite amount of time, 30.85% will be ahead. However, in a real situation, most of the losers will leave, and many of the winners will move to limits where they can't win or will go broke from fluctuations. Thus the actual percentage of lifetime winners will be much lower (probably about 5%).
If we suppose that we keep the same players (reasonably valid for a one hour time period, loses accuracy as people leave because of bankroll considerations):
On a given night (let's say a 4 hour session) with luck SD of 20 BB in 4 hours, ~46% of players will be winners.
After 100 hours ~35% of players will be up and as time passes we closely approach the 30.85% that would be expected winners in the normal distribution with mean -.5, SD 1.
Regardless, the lifetime percentage of winners must be smaller than the nightly percentage of winners due to fluctuation affects, unless something bizarre occurs, like more winners quitting poker forever than losers.
Craig
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