Are the observations independent - if not you are allowing A person to vote twice and their votes are likely correlated - that seems to be an issue for the normal or any dist right?
The observations are not
strictly independent as with a coin toss trial. The constant is the game. There are 52! possible deals. The total number of
unique games is substantially less than that because, for example, the order of the 24 cards in the draw pile is irrelevant, so the actual number is somewhat less than 52!/24!. And a fair number of games (about 15%, I believe) are unwinnable. Of those that are winnable, they vary in difficulty.
So we have three major variables: (1) The difficulty of the deal. (2) The skill of the player. (3) The mental state of the player.
I contend that if we have 1,000 people play a particular deal (constant difficulty), the number of moves they take would follow a normal curve. Smarter players would take fewer moves. I contend that if there were a way to have a particular player play a particular deal 1,000 times
without any memory of any previous tries, that would also follow a normal curve. Players have good days and bad days.
Each player will gain skill as they play more games. That can be thought of as a different player. I contend that a large number of players playing a large number of games will approach a normal curve. It may not be
perfect from a statistically theoretical perspective, but close enough to be useful. One of the ways that I believe it would be useful is to be able to compare a player's results against the curve.