Buzz, thank you for yet another great article.

So clear and well written... who would believe percentages can be so unscary?

I liked the last part, emphasizing the importance of trying to scoop.
I'd add: looking for spots to 3/4 an opponent (by promoting the high) instead of worrying about getting quartered...

The most interesting thing for me was actually the open question at the end: when DO we push?

Here's a quick hand from last night at the Venetian, playing against a rock-solid frequent poster on 2+2:

a very loose player limped, 2+2er limped, hero limped BTN with A247ds OTB (for deception purposes and because I don't like building pots when half the limpers in front of me should have similar type hands), SB folded, and a loose BB checked.

Flop (4 players, 4 small bets): 367r
(made nut low with counterfeit protection, tptk, one card 7-high straight draw and backdoor nut flush draw on a rainbow board)

BB checks, 2+2er bets...

2+2er should have A2 here a ton, in which case my high prospects are pretty good if I get it HU...

Do I pull the loose players in? Do I push them out to promote? Do I simply raise, hoping they call but not minding them folding? When do I push to promote? Do I make my move on the flop, turn or river? Which turn/river cards am I looking to make my move on?

delicate spot... very complicated indeed...

some tiny boring editing stuff:

-hero indeed flopped the seventh nut low in the A36K hand from your article. the question mark is unnecessary.

-hero can also improve to fourth nut low with a 5.

some strategy:

After the flop, I wouldn't normally give the A6 for low much value at all, especially if there's action (for example, a bet and a call) in front of me. In which case i'd have to wonder if drawing to the K-high flush when the low is already out (and my low prospects are unrealistic) is worth it. In an unraised pot, my answer would be clear: no.

I'm surprised that simulations show that A6 has above average chance to win the low by the river. I guess that's the difference between hot/cold equity and playability right there. with a marginal hand that can't really force the action (BTW, If it's checked to me on the flop, I would often bet this hand. otherwise, i'd check/fold), hero will often be forced to fold at some point during the hand, not allowing his equity to materialize.

Also, hero doesn't need to continue after the given flop in order to justify playing this hand. this hand can hit the flop much harder in many different ways. AK63ns is very playable in my opinion and it doesn't even have a single flush draw possibility to begin with...

QJT, AK2, 45K, 24T, 25J, 56K, are all much better flops. besides, flopped trips and hero automatically has the best kicker, thanks to the AK. with the suited K, hero can obviously flop a flush, nut flush draw, nut low draw+2nd nut flush draw, etc.

You're welcome. Thank you for the compliment.

Good addition. Well put.

If we make Hero's hand A, 4, 7, 2 and the flop
3, 6, 7, so that Hero has the nut back-door flush draw:
• Heads-up, as simulated against random cards, Hero wins the equivalent of about 74% of the time and loses the equivalent of about 26%. When Hero loses, he loses X bets. When Hero wins, he wins X bets.
Hero's net is 1*0.74X-1*0.26X=+0.48X

• Three handed, as simulated against random cards, Hero wins the equivalent of about 63% of the time and loses the equivalent of about 37%. When Hero loses, he loses X bets. When Hero wins, if both opponents come along, he wins 2X bets.
Hero's net is 2*0.63X-1*0.37X=+0.89X

• Four handed, as simulated against random cards, Hero wins the equivalent of about 57% of the time and loses the equivalent of about 43%. When Hero loses, he loses X bets. When Hero wins, if all three opponents come along, he wins 3X bets.
Hero's net is 3*0.57X-0.43X=+1.28X

If we keep Hero's hand the same,
A, 4, 7, 2 but change the flop to
3, 6, 7, so that Hero doesn't have the nut back-door flush draw, Hero's equity drops, but not much. Indeed, as simulated, whether Hero has the back-door nut flush draw or a back-door baby flush draw doesn't seem to matter that much.

But in either case, although Hero doesn't win as often with more opponents, when he does win, since he has more opponents paying him off, he nets more with more opponents. Of course you have to temper that by taking into account how your opponents will play, whether or not they're likely to pay you off. Some will. Some won't.

In general, it looks to me like Hero nets more against more opponents. Depending on how likely they are to pay off, although Hero doesn't win as often, when he does win, he more than makes up for having a lower win frequency.

But now comes the question of whether to push or not. And the answer depends on how his various opponents are expected to act when pushed. If a raise won't have any effect on them, then sure, go ahead and raise. But if anyone is more likely to fold a non-nut low when Hero raises, then Hero should pull rather than push. In other words if a raise might cause an opponent who would otherwise continue to fold, then Hero should call rather than raise.

No. You do mind them folding. You don't want someone with an inferior low folding. Note that Hero probably will not be successful pushing anyone out who has the same nut low. (However he might push out someone with a worse low).

Excellent question. The answer depends on how your various opponents think and play and also on the cards involved.

Let's see what the turn brings before we make a decision. With this hand and these opponents, we might push on the turn, we might push on the river, or we might not push at all.

Not on the flop. You're pulling on the flop. Keep any weak lows in the hand.

If the turn gives you a one card draw for the flush and if it's the nut flush draw, do you want to push out the non-nut draws? No? (Me neither). But how about if the turn gives you a one card draw for the flush and it's a baby flush... do you want to push out better non-nut draws? Yes? (Me too). But if you have the nut flush draw and a push won't push out non-nut draws, then if you have favorable fresh money odds, go ahead and jam on the turn.

On the river if you miss a high and if you sense no opponent has the nut high and anyone still in the hand is skitterish, go ahead and push hoping to scoop or 3/4 an opponent with the same nut low but no high better than your pair of sevens.

Lots of possibilities here, depending on your opponents and the particular cards involved. Basically you have to "play poker."

Thanks.

I agree. But it's not nothing and can improve.

I think it depends a lot on whom is responsible for the action.

When there are two wheel cards on the board, the A6 low becomes roughly the same as an A4 low with no deuce or trey on the board. Without those two low cards on the board, the A6 low doesn't look nearly as good.

I'd generally see the flop with it in a cash game too. (Tournament play has other considerations).

Buzz

yes excellent article

a side question though

how come you play such low limit poker especially since you seem like a well rounded great player in OE

i believe you mentioned you played at hp 20/40 60 OE but why devote so much time and effort into playing lower limits?

"rock-solid frequent poster on 2+2 at 8/16"

there are several 15/30 40 games everyday with half the rake and a much better game

why would he/she play lower and pay more rake with a much better game a table away?

@Buzz and str8 or better

Very good posts by both of you! Keep 'em coming.