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It's the probability of the door card being of a matched suit times three. Why? Because there are three ways to arrange door cards. So with 50 cards left, it's 2/50*3 percentage to flop a set. NOW, with the information that others have called, and the unlikelyhood that they have deuces in their hand, you can adjust it (w five callers) 2/42*3, which equals 1/21*3, which equals 3/21=1/7,or 6-to-1, so with 22, you are roughly getting odds to flop the set!.
This math is wrong cause A2, K2, Q2s, J2s, 22, 32s, 42s, 52s, etc. With 5 limpers the odds of a deuce in one of their hands is likely pretty good.
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Now, with sixes, it is not as clear how live they are, so you might not be getting odds, because people play 56,67, etc, but almost never 23. So in that circumstance you are not getting odds to flop a set.
But you don't play 66 solely for set expectation, you play it to make an overpair, a straight, or best second or third pair. All of those are much harder with 22 than 66. And 66 also has one substantial advantage over 22, it can overset 4 pairs, deuces can't overset anyone.
The easiest way to analysis this is the brute force way, run it against 6 limper ranges. When I do it, deuces is slightly above average equity (14.5% vs. 14.2%). 66 is well above average equity (17.6%).
Now this is hot/cold equity so in reality we know both hands have a lot of RIO. They have to fold lots of ugly boards where they still might be best and have good equity, so neither can really achieve it's equity in real world play. But we know that 66 has less RIO, because
a) it can continue on a some boards that deuces can't (55TT, A573) and every board deuces can.
b) it's significantly less likely to be over-setted and fewer of it's straights are dummy ends.
and 66 actually has more IO, it can win lots more extra bets than deuces because of it can over-set worse pairs, over-house worse full houses, and make higher/better straights.
When the more playable hand also has significantly more hot/cold equity than the less playable hand, you know the equity gap between them is even more substantial than raw equity is telling you, and even though the worse hand makes slightly more sets.
Last edited by DesertCat; 03-08-2017 at 01:30 PM.