[LearnedfromTV]

I was playing around with some five card draw math, and I was wondering how your kickers predraw affect what hands your opponents can have, and if there is any consequent effect on proper opening ranges.

I looked at JJxxx. I calculated the exact number of ways your opponents can have QQ+ based on the number of x's that are Q, K, A. For two pair+, I just prorated the number of combinations to adjust from 52C5 to 47C5. This isn't quite correct, but I actually think it understates the effect I found, since holding one pair slightly decreases your opponents' chance of having two pair, trips, and full house relative to if you held no pair (I think). Either way, it shouldn't matter much.

Anyway, here are the estimated probabilities of a particular opponent holding QQ+ (including all two pair+), based on how many of your kickers are > J

JJ234, etc - 24.1%
JJ23A, etc - 21.3%
JJ2KA, etc - 18.6%
JJQKA - 15.9%

This translates to the likelihood of holding the best hand predraw in each position as:

Position - JJ234/JJ23A/JJ2KA/JJQKA
UTG - 25.1/30.0/35.6/42.1
MP - 33.1/38.2/43.8/50.1
CO - 43.6/48.6/53.9/59.5
BN - 57.5/61.8/66.2/70.8
SB - 75.9/78.6/81.4/84.1

The key factor is that any card you hold cuts in half the number of ways your opponent can have a pair of that card.

Additionally, holding x's > J reduces the odds an opponent with two pair has queens up or better, giving us extra outs, and reduces the chance an opponent who is holding QQ will catch trips to beat us if we catch two pair or trips.

So I'm wondering how often people who play a lot of draw use this type of reasoning. Also, I'm curious if anyone has done a full study of card removal effects (even something as small as holding a three straight will reduce very slightly your opponents' chances of holding a straight, etc.)