How do you play a pair + flush draw?

Here's how I played it (I'm favourite, just, against any overpair)

Seat 1: Bombjack - $37.79
Seat 2: Selem - $46.01
Seat 3: abdelsheva - $15.09
Seat 4: Jackal - $18.78
Seat 6: Lukaschenko - $4.80
Moving Button to seat 4
Lukaschenko posts small blind ($0.10)
Bombjack posts big blind ($0.20)
Shuffling Deck
Dealing Cards
Dealing [ ] to Bombjack
Selem folds
abdelsheva calls $0.20
Jackal raises to $0.80
Lukaschenko folds
Bombjack: better kicker
Bombjack calls $0.80
abdelsheva calls $0.80
Dealing Flop [ ]
Bombjack checks
abdelsheva checks
Jackal bets $0.80
Bombjack raises to $3
abdelsheva folds
Jackal raises to $17.98 (all-in)
Bombjack calls $17.98

Preflop is a bit meh without the bigstack involved and with an active player to act (albeit an EP limper). Flop is fine, without actually plugging numbers into PStove you're a favourite against his range so calling the push is fine and the c/r before it seems reasonable.

Yer looking at AA-TT often here, you could be in trouble vs 99 (77 is unlikely given he'd need the two case 7s, and does 22 raise pf?), or you could be ahead of something like AsKs or even the occasional silly bluff with overcards and no draw or something.

76 suited - Doyle Brunson's favourite hand! Especially against big pairs, or so he says.

Well, it's a little bit of a gamble. There's practically no hand he could conceivably hold that you're any better than a coinflip over, unless he's re-raising all-in on a total bluff, while there's some where you could be a decent-sized underdog.

Given his raise, the hands that seem conceivable are: set of 9s or 7s, overpair, or 2 spade overcards.

If he made any set you're about a 70/30 dog.
If he has an overpair, (most likely hand) you're at a coinflip.
If he has 2 spade overcards, you're at a coinflip (at most, you're ahead by 3%-4%).

Given that I know I'm not significantly ahead of anything, I don't know how I feel about the raise on the flop. You do have fold equity, so maybe it's a good move. But a lot of people will bet their set there, since otherwise they have to give a free card with 2 spades on board, and they'd get no money in the pot for that round by checking, so I couldn't rule the set out. Plus I know if he pushes back on my raise, I end up in this situation that I don't feel all that great about.

The thing is there's only one set we can be fearful of here unless villain is an identifiable LAG (in which case we can add 22). These hands make up such a small proportion of villain's range one can't get too concerned over them.

We should be more willing to get it in and push our edge on the flop rather than keeping the pot small and probably having to act against a big turn bet with our pot odds destroyed, less fold equity, and while still most likely drawing to the best hand.

If we look at it from his perspective, he probably puts you on a flush draw in which case his push after your raise means he isn't afraid of you having an over pair of an ace-9 kind of hand but is afraid of the flush. Looks like AA or KK to me. If you had AA or KK and bet the flop and was reraised with those cards out, what would you do? AA or KK almost requires a push here. If so you have 11 outs. Do you feel lucky? Well do ya punk?

More than 11. 9 spades, 2 7s and 3 6s = 14 outs. That's why I'm a favourite against AA or KK here.

Looks good to me.

Edit: And I check-raise for value, not for fold equity. Although you'll make some cents if he folds the A of spades, most of the time I'm still rooting for him to call.

And I check-raise for value, not for fold equity. Although you'll make some cents if he folds the A of spades, most of the time I'm still rooting for him to call.

Click to expand...

I think fold equity does have something going for it, even when you're a favourite. You have to look at how much of a favourite you are. In this case my opponent had [10c][10d] and although I'm technically a favourite, it's as close as you can get: 50.10% vs 49.90%. So if he calls, my long term net gain is 0.1% of the pot with us all-in. If he folds, my long term gain is the whole $4.10 that's in the pot already, which, for comparison, is about 11% of the pot above.

So in the case above I would need to be 61% to win the pot to prefer a call over a fold. You only get this kind of odds versus an overpair with a pair + straight flush draw, e.g. if the flop here were [4s][5s][7d].

Obviously it depends on the pot size - the bigger the pot, the more you prefer the fold. And... I'm making this up, so feel free to point out any flaws in my logic.

To put it mathematically, if
X = the amount initially in the pot
p = your chance of winning
S = the larger of your or your opponent's remaining stack

If you both go all-in, your expected return
Ea = p*(X+S) - (1-p)*(S)
= pX + 2pS - S

If you cause your opponent to fold, your expected return
Ef = 1*X

So getting your opponent to fold is better for you if
Ef > Ea
X > pX + 2pS - S
X + S > p(X + 2S)
p < (X + S)/(X + 2S)

So:
If there’s very little in the pot, or your stacks are very deep compared to the pot, the right hand side tends to 0.5: in other words, you want your opponent to fold whenever your probability of winning is less than half, and call when it’s more than half.

If the pot is large, or your stacks or short, the r.h.s. tends to 1, so getting your opponent to fold is better for you even when your probability of winning is very high.


In the above example, X = 4.10, S = 17.18
So getting my opponent to fold is advantageous is my chance of winning is less than (4.1 + 17.18)/(4.1 + 2*17.18) = 55.3%
(I was slightly out with the 61% above, but here it is worked out properly.)

A bit tricky to calculate on the fly, but maybe I’ll make a few more examples to practice working out what the best move is.

I maybe should have been more clear: I don't consider fold equity in my reasoning because no hand that I'd want to fold out will fold. I can't think of any hand that has a >44% chance of winning this pot that would fold on the flop. There's no way that he'd fold 10-10 (as you must have noticed) or any other combination of hands that I'd like to see mucked. There is some value in folding out high spades however, and a hand like KsTd might fold for instance. That way, you gain the benefit of fold equity for the small percentage of time that you would hit your flush on the turn but he would take it home on the river.