QUESTION: In Hold ’Em, what are the combined odds after the flop that at least one player at the table either has a pair in the hole or has flopped at least a pair, depending on the number of players?
I’ve seen the odds of flopping a pair with any two unpaired hole cards pegged at a little less than 1/3, at 32.5%.
I’ve also seen the odds of being dealt a pair pegged at 5.88%, or about 1 in every 17 hands.
So presumably my chance of having either a pocket pair or making a pair on the flop is a combined ~38.38%, or slightly worse than 2 out of 5 times.
It would be useful to have a rule of thumb to use at the table for the likelihood that if I missed the flop, the rest of the table did, too, according to how many people stayed in to see the flop. What are the odds that one of the players is either holding a pair or has flopped a pair (the board matches one of their hole cards), based on the number of players?
Secondarily, how about the chances of someone flopping top pair, based upon the number of players? (This may require leaving aside the fact that most players see flops with Broadway cards than lower ones; I would be more than happy with an answer that just dealt with random holdings.)
A simple chart would be great but my statistics skills are quite rusty. My inclination is to take the chances for one player, subtract it from 1, and multiply that by the number of players, then subtract for the possibility of cross-holdings. But with this speculation I am mainly just exposing my ignorance, no doubt.
Any help would be much appreciated. (NOTE: I mistakenly posted this in an existing thread some time ago, and only just got around to posting it as a separate question.)