Suppose you have a casino with n poker players. Each player has a win rate - the amount of money he wins or loses per hand. We assume that these win rates are normally distributed with a mean of 0. (We also assume that the players don't pay the casino any money.) Our goal is to estimate the variance V of the distribution.
For each player x, we have observed a number of hands; we know how much money x has won or lost on each of these hands.
How would you go about estimating V? Can we get a better estimate if we add some empirical assumptions (in the vein of "in the long run, no-one can sustain a win rate of more than 1$/hand")?
EDIT: Let me try to clarify what I mean by "win rate". If a player wins 500.000$ by playing a million hands then his observed win rate is 0.5$/hand. With a million hands it's also likely that his actual win rate is close to 0.5$/hand. The idea is that a player has an actual win rate which cannot be observed directly, but which is a function of the player's skill. For example, if all players are equally skilled they will all have an actual win rate of 0; in this case, we also have V=0. The question above is concerned with actual win rates.
EDIT: My motivation for asking this question was to estimate how many players have an actual win rate of, say, more than 0.3$/hand. If you disagree with the assumptions made above, feel free to base your estimate on other assumptions.