very basic question

[RydenStoompala]

Sounds like you've been to school? Just a guess.

[RydenStoompala]

FYI, I liked your post. For us mathidiots, it works.

[BruceZ]

I just noticed that in the series of Poker Digest articles, I'm In...No I'm Out, Brian Alspach has solved this problem using inclusion-exclusion for 1-11 players. He solves it over the course of two separate articles, and and his results appear at the bottom of article 28. His line for 8 players agrees with the value I got here (1 minus the value for 0 players or add the other columns).

The method I described here can also be easily modified to generate data for different numbers of players. His method is much more complicated in that he is considering all arrangements of hands among distinguishable players, and he handles the problem of different players having the same pair in a closed form way. His method may become easier for the cases where you want the tiny probabilities of having 4-5 players holding a pair.

This is an advanced problem, and should not be the first example of the inclusion-exclusion principle that you study. See this post for a simpler explanation and examples of the inclusion-exclusion principle.