I have done a couple more cases, so I'll add them to the table below.
Number of Players | Split Pot Pct |
---|
2 | 49.4% |
3 | 66.0% |
4 | 74.4% |
5 | 79.3% |
6 | 82.7% |
7 | 85.0% |
Yes, the above results do look a lot like 1-1/N.
To be perfectly honest, I was quite surprised by those results. I initially believed that "good hands" would win both boards a fair amount of the time. Say a high pocket pair or even AK.
I might be misinterpreting your comment, but it sounds like you are saying that if all players play the same range of hands, we would expect a result of nearly 1-1/N fraction of split pots.
I do not agree with that unless I am totally missing something. For example, to take an extreme case, if the rules of holdem were changed to rank hands solely according to cards' ranks (i.e., ignore flushes, straights, pairs, etc.), then I am quite confident that this variant of split holdem would see very few split pots. In such a game a high card in the hole would often win both boards.
Since these are simple to do, I just ran a simulation of this variant and got only 3% split pots in this heads-up variant (again, all deals going to showdown).
So there is something about how two hole cards interact with five board cards that is "causing" the very high prevalence of split pots.
Let me ask the audience, if I re-ran the simulations but restricted all players to play only top hands, would you expect the split pot percentages to change significantly?
In the 2-player simulations, I could restrict both players to play only Top 50% hands. Would we still expect to see around 49% of all pots that went to showdown be split?