Underpair vs Pair on Board

[arenaci]

Hi everyone!
So, I heard having a pair on board (E.G. J7 on Q73) board is much better than having an underpair (E.G. 77 on Q63 board). Why? Aren't they equal in strength?

 

[ph_il]

interesting question. i think, and i might be wrong, j7 > 77 because you have some blockers with the jack and you don't have any with the 7. so, you block some combinations of 10j, kj, and aj, meaning it's less likely to hit the turn. plus, if they did have a hand like those, the jack gives you 2 pair, so they're effectively drawing to 3 outs or more if they have a back door draw. ex: if they have kj and the turn is a 10, they pick some extra equity with an open-ended straight + k pair.

77 doesn't block anything and all over cards have the full equity to hit on the turn or river. and they also get full equity if they hit a back door draw on the turn. so, same example, lets say villain has kj and the turn is a 10. they have an full equity to hit their oesd + 2 over card pairs.

 

[arenaci]

interesting question. i think, and i might be wrong, j7 > 77 because you have some blockers with the jack and you don't have any with the 7. so, you block some combinations of 10j, kj, and aj, meaning it's less likely to hit the turn. plus, if they did have a hand like those, the jack gives you 2 pair, so they're effectively drawing to 3 outs or more if they have a back door draw. ex: if they have kj and the turn is a 10, they pick some extra equity with an open-ended straight + k pair.

77 doesn't block anything and all over cards have the full equity to hit on the turn or river. and they also get full equity if they hit a back door draw on the turn. so, same example, lets say villain has kj and the turn is a 10. they have an full equity to hit their oesd + 2 over card pairs.

What if it was 27 instead of J7? It is argumented that 27 is better than 77.

 

[ph_il]

What if it was 27 instead of J7? It is argumented that 27 is better than 77.

surprisingly, when i put up both situations against the same 16.4 range,
for 27 on a q37 flop, i got:

27o = 50.6% equity
27s = 53% equity w/ back door flush draw
27s = 67% equity w/ 4 to a flush on the flop

for 77 on a q63 flop, i got:

77 = 46.5% equity
77 = 47.1% equity w/ backdoor flush draw
77 = 53.8% equity w/ 4 to a flush on the flop

i suspect the reason why 27 > 77 in this this situation is 27 blocks 77 set combos. since you have a 7 and there is one on the flop, there is only 1 other combination of 77 for a set. with 77, it doesn't block any set combos on the flop.

so, while you still lose to 88+ over pairs in both situations, 27 is also behind q sets and 3 sets, while 77 is behind q sets, 3 sets, and 6 sets.

 

[fundiver199]

Hi everyone!
So, I heard having a pair on board (E.G. J7 on Q73) board is much better than having an underpair (E.G. 77 on Q63 board). Why? Aren't they equal in strength?

I am not sure, I agree with that statement either. If we look at raw equity against top pair or an overpair, then second pair tends to have more, since it has 5 outs to improve rather than 2, and maybe this is the main reason for the statement.

However there is a bit more to it than that. Assuming you are defending your blinds (J7 is usually a fold but never mind that for now), then your opponent does not always have top pair or an overpair, when he bet. Sometimes he might have second pair, and then you would rather than an overpair to that. 77 beat A6 on Q63, while J7 lose to A7 on Q73.

Implied odds also matter, and while J7 could turn a well disguesed two pair, this is still not nearly as good as turning a set. J7 would still lose to QJ, and a Q or 3 on the river would counterfeit it.

So I would not view these as totally different situations, and in general there is a limit to, how far you can potentially take these "two pair draws". This is even more true, if your hand is connected, as it often should be, because then two pair might give your opponent a straight, which can also end up being quite expensive for you.

 

[fundiver199]

To be a little more scientific about it I plugged in a Q73 rainbow board in equilap and assigned Villain a range, which I think, most people will C-bet as the preflop raiser. The range was 77+, 33, ATs+, A7s, KQs, Q9s+, 97s, 87s, ATo+, A7o, KQo, QTo+. This might seem wide, but if it was a late position open, I actually think, a lot of people would C-bet even more. And against this range 88 and J7 have an almost identical 36-37% equity. Folding either hand to a standard C-bet like half pot would therefore be a mathematical mistake.

 

[arenaci]

To be a little more scientific about it I plugged in a Q73 rainbow board in equilap and assigned Villain a range, which I think, most people will C-bet as the preflop raiser. The range was 77+, 33, ATs+, A7s, KQs, Q9s+, 97s, 87s, ATo+, A7o, KQo, QTo+. This might seem wide, but if it was a late position open, I actually think, a lot of people would C-bet even more. And against this range 88 and J7 have an almost identical 36-37% equity. Folding either hand to a standard C-bet like half pot would therefore be a mathematical mistake.

Let's flip the sides. If you were the preflop aggressor which one would you be more happy to c-bet? I would probably c-bet J7 because even when we are behind to some overpairs to 7, most of our 36% equity is realisible equity(about 20%) and we also can barrel turn also when we don't make our hand, whereas with 88 we only hope for an 8 to continue barreling.