Pair vs Overcards in NHLE?

Question

Ok, after doing more research, I have a question about two over cards vs a pocket pair.

The usual wisdom is that the pocket pair has a 52% vs 48% advantage to win the hand at worst. However, after some research, it seems that the over cards only have about a 32% chance to pair.

In other words, how does that 16% break down? How much of this would be a tie?

Answer 1

the 16 percent could be a straight... or a flush.... or a full house... that 32 percent is just a plain pair

Answer 2

No, your 32% is off.

The winning percentage of 2 overs v pocket pair DOES vary, but not by that much.  It varies if the overcards are suited, the pair covers suits, the pair interferes with straight draws, the pair can be counterfeited, etc.

For example a 2h2d vs a 9s10s is a 45% - 53%, but a QsQh vs a KsAh is a 56% - 43%.

The only way you can get to a 32-68% is if you know some of the folded cards or if you use some Greenstein-Malmuth style analysis to determine the 'likelihood' that those other cards would have been folded.

Hope this helps.

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Unless I answered the wrong question.  Were you referring to a 32% WINNING percentage, or a 32% PAIRING percentage?

Because the odds of PAIRING your overcards is always the same (again assuming you don't know or analyze the values of the discards) but the odds of WINNING with your overcards changes quite a bit.

Answer 3

When folks are talking about a race, it is generally with over cards that are connectors too, that is where it is virtually 50/50 (example a/k v. j/j )  I would imagine it would be a little bit different if you are talking like a/8 vs. 6/6, heck, it would have to bee different.