The other day I was in a NLH cash game, somewhat short stacked. I have QQ in late position and 3 bet. Another player who has been rather tight in the BB 4 bets and puts me all in, everyone else folds leaving dead money in the pot. I feel rather confident that this player would only make this move with AKo, AKs, KK or AA. In this sort of heads-up situation, where I am heads up with one other opponent preflop for the rest of my stack and have a good idea of their range, how do I determine if I am getting the correct price/pot odds against a range of hands (i.e. not against a specific hand)?

Hypothetically, if my remaining opponent showed me their cards, I could easily compare my true odds to my pot odds and determine if I am getting the correct price to call or not. But let's say someone else saw their cards, and came over and whispered in my ear that they have one of the hands in the range listed in my example above, but would not specify the exact hole cards. In theory, there should be some formula I could use to determine the exact probability of having each of those hands (ex. 16 combos of AK, 6 combos of AA/KK each) and the expected value of each combo compared to my hold cards to then determine the overall correct price as whether I should call or fold.

What would this formula look like?

Eventually, I would like to use this same formula to determine the correct odds for other hole card/range combos in this spot. Another example would be JJ against a range of QQ+ & AK, etc.

You can use equilab for this among other various free softwares. In a HU scenario you also could do it by hand if you know your equity vs. each combo of his range.

QQ vs AKs, AKo, KK, AA

AKs = 4 combos, QQ vs AKs ~53.95% equity
AKo = 12 combos, QQ vs AKo ~56.76% equity
KK = 6 combos, QQ vs KK ~18.06% equity
AA = 6 combos, QQ vs AA ~18.46% equity

QQ vs (AKs, AKo, KK, AA) = (4/28)*53.95 + (12/28)*(56.76) + (6/28)*18.06 + (6/28)*18.46 = 39.86%

https://www.pokerstrategy.com/poker-...quilab-holdem/

Thank you, this is exactly what I was looking for. I tried googling before posting, but apparently my google-fu is weak. I assumed there was already some software that did this, but didn't know where to find it. It's also nice to know how to do the calculation manually.

Also if anyone is interested, I did end up making the call with QQ, and my opponent had AKs, which was in the suspected range. Luckily the queens held up. Now next time I'm in a similar spot I can make a more informed decision as to whether to call or fold.

Brokenstars calculation is right on the money, but probably more math than one could handle doing in your head at the table (at least it would be for me). At the table I would do some approximation and say that there are 12 combos of AA and KK, 16 combos of AK for 28 total. 16/28 = 4/7 so he will have AK 4/7 of the time and we win about 50%, adding 2/7 to our equity. We are up against the bigger pair 3/7 and win 20% of the time, which adds 0.6/7 to our 2/7 from the AK case for a total of 2.6/7. 2.1/7 is 30%, 2.8/7 is 40%, so that 2.6/7 is somewhere in the high 30s, in approximate agreement with the more exact 39.86. If you are capable of mentally dividing 2.6/7 you would get 37.14% - not too shabby for a simpler approximation.

You do this work away from the table, but it's pretty easy to work out "12 combos I'm 20/80 against, 16 combos I'm flipping against, got slightly more flips than owned so it's maybe 37% or so?"

As stated, you should have these ~memorized.

And you don't even need to be able to do that to get pretty close, plenty of simpler shortcuts to get something in the correct ballpark

Memorization is fine, but limited. What if you think villains range is TT+, AK? Having memorized the equity for KK+, AK won’t help. What if you have KK or JJ instead of QQ? The possibilities quickly multiply, probably giving more spots than most people can easily memorize. It still is helpful to be able to do an approximate equity at the table.

Sure, but basic ones should be approximately memorized:

AK vs Pocket pair

AK vs AQ

KQ vs AJ

KQ vs 65s

Pocket pair vs over pair

Pocket pair vs QQ+, AK

vs JJ+ AK

vs TT+ AK

This is like 10 things and you can have it memorized with minimal effort. Would take a marginally intelligent person ~5 minutes of study a day for a week to have it roughly memorized. Even if you did not do studying in a structured way with the intent to have it memorized you would probably memorize approximations for these values/situations by just passively playing/studying on your own. The situations arise pretty frequently and especially frequently for SNG/MTT scenarios.

great thread