At a table of 10 players, what are the odds that someone is dealt a pair, any pair? What are the odds that a particular person is dealt a pair?
Let me make sure I have the assumptions correct. At the beginning of the game, each player is dealt 2 cards, and you want to know what the odds are of at least one player having ANY pair?
You also want to know, if I choose player X and then the initial 2 cards are dealt, what are the odds of player X having ANY pair?
I know that your odds of getting a pocket pair is 6%, regardless of how many players are in the game.
One particular player: exactly 1 in 17 (or 5.9%)
One or more pairs among ten players: 45%
For completeness, if ten-handed:
0 pairs: 55%
1 pair: 34%
2 pairs: 9.6%
3 pairs: 1.6%
4 pairs: 0.19%
5 or more pairs: <1 in 6500 (or, < 0.015%)