I have been listening to The Poker Guys podcast for the past few weeks at work and they often talk about how many combos of a certain hand a player in question could have. I guess I am just wondering when this is to be used in a live game. And how to calculate if a check, call, raise or fold is correct?

Yeah, definitely. Usually it's a situation where you have a good idea of what your opponent's range looks like. Suppose you get raised on the river and figure that your opponent's value hands are either sets or JTs for a straight. You can be like: OK, JTs is 4 combos, each possible set is 3 combos. You add all that up, then you try to come up with bluff hands he could have, depending on how the rest of the hand has gone down. That lets you come up with a percentage of the time you're winning, then you can decide what to do.

Here is another simple example.

You open raise with TT. The button shoves for the rest of his stack. Based on your play with him, you think he is shoving AQ+ or JJ+.

There are 16 combinations of AK and 16 combinations of AQ. There are 6 combinations of AA, KK, QQ, and JJ. There are a total of 56 combinations in villains range.

Doing some quick math, you have 55% equity about 32/56 of the time(57% of the time), and 20% equity about 24/56 of the time (43% of the time). Doing some quick calculations, you discover that your TT has about 40% equity. You can then use that number to determine if you should call villains shove.

Using combinations, you can calculate your equity against his range by determining how likely each hand type is to occur in his range.

Unless you have a damn near photographic memory that allows you to remember what hands V opens with and shows down, I would advise you to use combinatorics when deciding how you you want to play your hand. i.e. bluffs vs value bets.

When trying to decide if you call/fold/raise, concentrate on pot odds, minimum defense frequency, and SPR to start. Then add in implied odds and fold equity ( I think was the 5th one.....I'll correct it later when I find it again)

I'm going to note you do this work off the table. Almost nobody is trying to add up the numbers while everyone is waiting for a decision. Anyone who is likely will get time called against them.

Yeah. Occasionally you can do it at the table but usually you do it later and that work improves your intuition and estimates at the table.

How did you come up with 55%, 20% & 40% for the TT


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I don't actually do the exact math in my head while playing, I just remember that it is approximately 2.5 times as common for an unpaired comba than a paired combo. i usually use this when trying to decide whether or not to call a short stacked shove (or whether or not to short stack shove).

As you mention, though, a lot of these scenarios can and should be worked out in advanced, as they are very common (for example, the number of times you will see a middle position, 5-10bb player shove into an unraised pot is pretty high, so you should already have your equity against the different ranges that player migt have worked out)

Using any equity calculator, you know that TT vs two overcards is approxiately 55% (not exactly, as it differs slightly based on card rank, suitedness, and connectedness...but you are really trying, at best, to estimate, not get exact numbers).

You will also see that TT vs an overpair has only a 20% chance of winning.

So, to calculate your equity against villains range, you average the equity against all possible hands in the range

This is where combinitorics comes in.

So, you first figure out how many combinations of overcards there are. The easiest way for me to visualize this is to say (to make AK, there are 8 cards (4 aces and 4 kings) that you can draw to make AK, and then if you draw one of those 8 cards, there are 4 other cards (either 4 aces if you drew a King, or 4 kings if you drew an Ace for your first card) to make AK. Therefore there are 32 (8*4) possible permutations that make AK or KA. Since order doesn't matter, and AK is equivalent to KA, we divide that number by 2, so there are 16 combinations that make AK).

You do the same for pocket pairs and see that for any specific rank, there are 6 combinations (take Aces for example. For your first card, there are 4 aces, for your second card, there are three aces. That means 12 possible permutations. Again, divide by 2, and you have 6 possible combinations)

Since we said that villains range was AQ+, JJ+, below is a table of possible holdings, and the number of combinations, and their approximate equity

Hand Combos Equity
AA 6 20%
KK 6 20%
QQ 6 20%
JJ 6 20%
AK 16 55%
AQ 16 55%
Total 56

Using the numbers above, you can do a weighted average (average=(# of instances*value of instance)/(total number of instances). This yields a value of 40%.

So, based using combinations, you estimate that the equity of your pocket tens versus his range of AK, AQ, AA, KK, QQ, and JJ is approximately 40%, and you make your calling decisions based on whether or not you have positive EV for your call based on that number.

As mentioned above, this is not terribly easy to do on the fly. It is best to do this calculation on paper (or with excel) a few times so you understand how it works and develop a feel for the mechanics. Then download an equity calculator and start modelling common situations.

Ahhh I knew that I see I was just over thinking that!


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Great stuff though!!!


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Pot odds, pot equity, minimum defense frequency,implied odds and fold equity. At least 2 of each of these concepts can/ should be applied when making a decision on every street. IMO these are easier to think through than combinations.

I mean realistically if a range is only 56 combos you can probably do the calculation in about a minute, which seems fine for a river decision in a live game.