Pair vs Overcards Question
Join Date: Mar 2008
Posts: 855
I know the traditional way of looking a pair vs two over cards all-in preflop in NLHE is 55/45 in the pocket pair's favor, assuming the over cards aren't suited. The odds change slightly depending on the over cards' connectedness and distance from the pocket pair as having close over cards could block outs to a straight, for example.
When we calculate these odds, we're assuming 48 unknown cards left in the deck and 5 draws at 6 outs for the over cards.
Why don't pocket pairs have a larger edge in the long run, because of the possibility of someone else mucking one of the over cards' outs preflop? Having one or more of six outs mucked is more devastating to the over cards than having one or both of the pocket pairs' 2 cards to hit a set out of the deck.
I can see how my thinking here is flawed, however, because if I think of a game where all the cards but the 5 for the flop turn and river are dealt, then it seems like it should still be a 45/55 situation.
Can someone help me sort out my confusion? Should we ignore the possibility that an out for the over cards could have been mucked when calculating these odds?
Join Date: Mar 2006
Posts: 555
i think the answer is that theres just as much of a chance that other cards from the deck have been mucked, reducing the amount of bad cards that can come, hence cancelling out the possibility of our outs being mucked.
Join Date: Mar 2008
Posts: 855
yea I think you're correct.
Join Date: Jul 2007
Posts: 8,391
The mucked cards are just as unknown as the remaining cards, so there is no reason to group them into another category.
If you actually do an exact mathematical analysis where you consider the probabilities of the cards being mucked, you will end up with the same answer as when you don't take it into account.
There might be some situations where this isn't true. For example in a really loose holdem game, if a lot of people fold, you can figure that the remaining cards probably have a higher proportion of face cards and especially aces. Similarly in a tight game if a lot of people enter the pot you can bank on most of them having high cards.
The effect is even more extreme in Omaha hi/lo, since a multiway pot in a tight game almost certainly indicates that most of the baby cards have been dealt out to the players.
