originally posted in NL SS: set vs. overset

liucipher · #1 04-13-2006, 03:20 AM

A little off-topic. I've got a friend bemoaning his "bad" play becuase of a set vs. overset hand. I told him to not worry about it too much. I was trying to figure out how often it happens in a 6max game. Is this calculation right? (I know these are approximations.)

6% chance you get pocket pair
30% chance one of the other five has a pocket pair
11% chance you flop a set
11% chance he flops a set

so 6% * 30% * 11% * 11% ~ 0.02% chance or once per 5,000 hands or so?

I realize I'm ignoring the overlaps and chance of multiple pocket pairs, etc. but this is back of the envelope.

modnareno · #2 04-13-2006, 08:48 AM

HIs odds of flopping a set should be ~2/3 what you have listed. One of the chance he has to flop a set is taken away by the fact that it needs to match the card in your hand. I don't really know all the math, just wanted to toss that in there. Also, even if something happens once every 10k hands, if you lose 100 big blinds every time it happens, that is 1 big blind per 100 you're losing.

p-i · #3 04-13-2006, 04:43 PM

Roughly .000454 (odds 1 of 3 PP making set + odds of 1 of 2 PP making set 6 handed).

(.0032*(72/73)*.0102)+(.042*(72/73)*.0102)

Grabbed numbers from here and here.

Obviously the rank of your PP and whether you flop middle or bottom set would need to be factored in to give a more complete answer but I think this serves as a rough one.

Out of interest, is there anything "better" than the Math::Combinatorics Perl module for calculating stuff on *nix? Not that I have the knowledge to do so yet but I am interested in learning.