I wasn't sure how to formulate the question properly, so sorry. Anyway, let's say we're on the flop and it's:

8h10h2c

Villain who is super loose is on the btn, so he might have anything. But let's say he cbets only with draws (not with gutshots for a sake of an example) and when having a value hand.

Therefore, when he cbets we can say he has 32 combos of a straight draw (J9, 79); value hands (AA, KK, QQ, JJ, 1010, 88, 22, A10, K10, Q10) - 6+6+6+6+3+3+3+12+12+12 = 69 combos. How many combos should we give for a flush draw?

I'm trying to learn to use more of poker math cause when I started doing it more I started to feel more confident in my game. In the future I'd like to make decisions based on math only; so if you have any suggestions how I can become much better at poker math I'd appreciate it greatly.

And going back to the example above - if there were more combos of semi bluffs than value hands, would that mean we should raise huge where he wouldn't have correct odds to call?

Anyway the point is I wanna learn to use as much math in my game as possible.

Thank you!

Whale/Loose villain (high vpip) assume #30 FD combos

Nit/Tight villain-Avg assume #15-#20 FD combos, nits more like #10 they only play the suited Ax and some suited Kx

How loose is villain?

If he calls pre with AQs-A2s, KTs+, QTs+, J9s+, T8s+, 97s+, 86s+, 75s+, 65s, 54s (all suited aces except AKs, any two suited Broadways, some suited gappers, all SCs 54s+) then he has 18 flush draw combos on that board. If he's much looser he'll have more flush draws.

I used the pie-chart button Equilab to calculate/visualize this. Flopzilla has a similar function.

Note also that if you have a blocker in your hand (i.e. something in hearts) that can considerably reduce villain's FD combos.

Hey I was just looking into the same thing and came across this thread. How do we calculate this in PLO, where they can literally have any combination of hearts? I was always really bad with this stuff in math class. Is it just 11^2? Combination? Permutation?

Assuming someone is playing a very wide range, but they have two cards of the same suit, there are only 78 possible combos of suited hands in a particular suit, prior to the flop. (i.e. one of 32s in hearts, one of 42s, one of 52s etc).
You get to 78 because there are 12 combos of Axs (in a specific suit), 11 of Kxs, 10 of Qxs... down to 1 of 32s.
12+11+10+9+8+7+6+5+4+3+2+1 = 78.

If that player then sees a flop with 2 hearts in his hand and 2 hearts on the board, he has 55 combos of flush draws.

Bear in mind that even if you only play double-suited hands in PLO, when the flop contains a flush draw, over 50% of your hands do not have that draw, since they will be in the "wrong" suits. Also remember that in PLO, weak flush draws are usually quite bad hands that can get you into a lot of trouble. Even with 4 holecards, it's pretty hard to flop a draw to the nuts.

A perfect answer as usual, Arty. Who are you? Do you play full time? I feel like you're the only guy who takes the time to answer all these questions these days. And it's always so insightful. You're like, the guy. Anyhow know you're appreciated.

I've more or less retired from poker. This is just a stupid hobby for me. But thanks!

In PLO, one thinks that the opponent's range has a flush draw/flush at least one time in four (basically more often if he 3-bet, and generally more often when action has been taken), and as so it covers a big part of his range, as it does when one has a flush and one is thinking about bluff catching; and in some cases it would be two pair or better with a (significant) flush blocker, while in other cases based on action many flushes also find the muck. The combos are not the general way to think in PLO, as there are too many of them.

In NLH, the higher the flush the more combos there are and the board cards make some difference also. The high board cards can produce big pairs more easily, just like in PLO. Then it is about his missed draws vs. his value bets with a big pair of better, and from the Janda times, it might be 24 combos of pairs for value on the river (AA= 6, TPTK is like 12; 6-max; 1 on 1, one value bets more and bluffs more) and like half of that for missed flush draws, depending on bet size, and so one can't bluff all the missed draws on the river (A2s = 1).

Technically, the missed straight draw (or inside) combos are favoured to be picked as the missed draw bluff combos, and the ace-high draws might opt to check the river if any chance to win so (if not, it might be better to bluff them as they block ace kickers but that isn't all clear to me as one might see looking at the board).

In PLO, the flush blockers might be bluffed as well as used to vary GTO calling, and so being balanced but vs. a ton of players who don't bluff often enough on the river in most situations like they might not do in NLH either, depending on site and limit and format. The blocker might also have the opposite meaning as it is about what it makes more or less likely.