eldodo42

In fact, OP is not even on the top of his range in terms of hot and cold equity! His hand has 54%, while a Qxxx hand from your range has 63%, and even 2xxx has 56%! So we're in fact pretty close to the bottom of our range in terms of equity vs villain's whole range. I expect things to look similar against villain's continuing range.

ProPokerTools Omaha Hi Simulation
600,000 trials (Randomized)
board: Qh 9s 2c
Ad 7d Ac 4s 53.85% (311,523 wins, 23,143 ties)
15%6h 46.15% (265,334 wins, 23,143 ties)

ProPokerTools Omaha Hi Simulation
600,000 trials (Randomized)
board: Qh 9s 2c
15%6h:Q 63.89% (375,395 wins, 15,842 ties)
15%6h 36.11% (208,763 wins, 15,842 ties)

ProPokerTools Omaha Hi Simulation
600,000 trials (Randomized)
board: Qh 9s 2c
15%6h:2 55.59% (326,767 wins, 13,568 ties)
15%6h 44.41% (259,665 wins, 13,568 ties)

Even if we put villain on 10%6h rather than 15%6h, Qxxx still has 61%. So in terms of hot and cold equity our actual hand is maybe in the middle of our range. In terms of playability it's probably even lower, since when we have Qxxx we have more outs for making decent two-pair hands in future streets.

I think things would be different on, say, a 952r flop. But on Q92r you have plenty of hands to continue with, so I don't see any reason to put bare AA in our continuing range.

About the hand: I usually 4bet pre. But if OP decides to flat pre, then I think that on the flop x/f > b/f > x/c.

I happen to have a Ph.D. in math and I think I can shed some light on what Rubinstein is saying.

I'm pretty sure that when he says

"There are few insights from game theory that would improve one's game of chess or poker."

He it talking about the mathematical field of game theory, in its contemporary form. This field is far-reaching and deep, but indeed doesn't provide much help for poker players. The analysis that poker players do, that of finding minimax  strategies, solving toy games, etc, is so basic that I doubt Rubinstein is even considering it when he's talking about "game theory". For example, a probability theorist can correctly claim that 

"There are few insights from probability theory that would improve one's game of poker."

despite the fact that poker players discuss odds and calculate probabilities all day. That's because the nature of the field of probability theory is so far advanced beyond simple odds calculations, that probability calculations of that type are not even considered "probability theory" per-se.

Having said that, I should probably note that studying any sort of mathematical discipline should have a positive effect on a poker player, since studying mathematics trains one to study complex subjects in an organized, critical and rigorous way, a skill which is very useful for a poker player.

I think that it probably depends on how our and vilain's rangs look, for two reasons: firstly, we need to know how often they have the nuts (or a very strong hand) here, and secondly, we need to know how often they have a bluffcatcher. I think that depending on these factors, the answer is sometimes a and sometimes b, and will sometimes be anything in between.

But, having said that, I'd suspect that in most cases where villain's range is rather strong, and not at all capped, then the correct answer is to bet as small as we can while still being able to make a PSB on the river (i.e. option a). The reason is that in the cases where we're bluffing and villain's range is strong, we want our bluff to be as cheap as possible (compare to the case where villain's range is capped, where we want to take option a to allow us to bluff as much as possible while still being balanced).

Also, sometimes when our range is top-heavy and we don't have enough bluffs, then we want to take option c: bet say half pot on both turn and river, fully realizing that we can't get stacks in. There's no theoretical principle saying that the line that gets stacks in is the most +EV: if our range is too strong to give villain pot odds while still betting big, then villain would be correct in just folding to our big bets. We might have made a range-building error along the way that made our range so strong here as to not have a sufficient number of bluffs.

so, do we have a raising range at all on the flop? A lot of people like raising 55 and 9Axx here, which means we'll need a bluffing range, and the best hands to bluff with, except FD+wrap, seem to be NFD+overpair

well, I rather play against opponents who play passively against me than play against opponents who play aggressively against me. I think it's widely-agreed that the former is more profitable. Are you claiming that you'd rather play vs aggressive opponents?

As Zen said, limp pre. i actually even limp hand as strong as KKQ3ss or AA96ss here.

As played, I think turn is a bet (around 2/3 pot will be best IMO; you can go slightly smaller). The reasons are:
1. we still have a bunch of equity and we like neither c/c nor c/f, and someone will often bet after we check
2. It's hard to value-raise us since we have two blockers to the nuts so we expect to be value raised rarely if ever; and it's hard to bluff-raise us since we have the nuts in our range pretty often, and will be b/c or b/gii various draws and made hands pretty often
3. we have blockers to the nuts and the board just became more static, so overall we have a bunch of fold equity.

If I get raised OTT I mostly fold, but I expect this to happen rarely. If the river bricks out we fire again (I personally fire full pot here since villains have a pretty capped range) and I expect to get all made hands weaker than 86 to fold, and sometimes even 86 folds. If I had particular reads on villain (e.g. that they tend to station rivers) then I would bluff river much less often (but still fire turn unless both are passive).

Now, once you checked the turn I think you have to c/f. Your OOP, you have bad visibility, and your overpair will not do you much good. You simply don't have the implied odds to call this.

About flop sizing, I think you should bet around 5$. You write "I thought I should bet bigger too, but my 3Bet range doesn't connect with this flop a ton," but I think you're actually thinking of this wrong: remember that your cbet% in 3bet pots is 50%. Maybe even less on this flop. So your whole 3bet range doesn't necessarily connect well here, but your cbetting range, being much smaller, does. So you want to bet bigger.

In general, in spots where our range is noticeably strong because of the line we take then we want to bet bigger, and when our range is weak we want to bet smaller (assuming we choose a uniform bet sizing). Here our range is strong, so might as well bomb it IMO.

Turn and river I like your thinking, assuming you know he'll fire turn with naked NFD. (FWIW, I think it's a mistake for him to fire turn with naked NFD 100% of the time.) If we don't think he'll fire so often I'd bet/call or bet/fold this sometimes.

Ugh. On the table I shrug/call, but I don't know if we're good the required amount of the time. Also, if BB was on the passive side I think flatting the turn would have been better than raising, since it's hard to put villain on a bluff here. But seeing as villain is aggressive, I think rivers would be difficult to play and he shows up with dominated draws a bunch of the time or hands that would fold at some point, so raising is probably better.

If he checked the river I'm never betting. Sometimes he'll have a missed draw plus weak two pairs that he'll find a fold with, but I think it doesn't make up for all the times he has two pairs+ and calls.

Can't fold. I wouldn't raise either, though I wouldn't fault anyone for raising. People ITT don't like check/calling because of reasons that seem weak/tight to me: they think they're going to be easily readable on future streets so they don't have implied odds, but have a little RIO. This is patently false: If you think you don't have implied odds, it means villains are folding too much in future streets, which means you have to decide on some bluff-outs and bluff on them. For example, we can jam when a Ts hits, and maybe other T's as well.

Do we really prefer betting on the smaller side (16-17) and checking back blank turns as opposed to potting flop and shipping turn? My instinct is to jam flop as we have bad visibility for the rest of the hand but I'm not sure.

Viktor: some PPTing shows that if villains' continuing ranges (vs a pot-sized bet from us) are :JT,Q9,Q8,QQ,88,99, then BB continues around 15% of the time and SB continues around 23% of the time. This makes betting nicely +EV even with air. Considering our equity vs strong hands means that not only is betting greatly +EV, but if villains call wider then that doesn't hurt us since we have excellent equity vs pretty much any other hand. That's why, for me, 22% vs sets and straights is "decent equity" in this low-SPR case: because villains have those hands rarely enough that 22% is still very fine.

In other words, we expect to have the best equity here vs villains' ranges, and we have decent fold equity, and. in addition, playing future streets is difficult because we don;t know which outs are clean. This all points to a shove IMO.

I think I slightly prefer jamming over checking because our two-pair outs are murky. If our two-pair outs were clean (i.e. wouldn't complete straights) then checking is great since we can play accurately on further streets. But as things are, we don't know what our true outs are, and stand to make mistakes on further streets. Seeing as our equity is great vs AA and two-pairs, and is decent even against sets and straights, I'd be happy just sticking the money in now.

Of course, if villains play very face-up then checking and realizing our equity is probably best, since we're almost never ahead when the money goes in here, and the equity we get villains to fold when we jam probably doesn't make up for the money we lose when we're behind.

Very interesting hand. It strongly depends on villains' VPIPs, to determine how often they have nut flush draws and such. After all, we're ahead of a naked set and probably way ahead of most two pairs type hands (even if they have some weakish draw. In fact, as long as no one has the NFD, we should get the money to the middle as soon as possible.

My instinct on the table is to look at VPIPs, see how wide they are, and then raise the donk bet and get it in (assuming we're against the two small stacks; can't figure out villains' stack depths). I think that should be nicely +EV and good for your overall game, but this very well might not be as +EV as calling. Overall flatting is nice, but I don't see myself folding even facing the c/r: I think we're not up against the NFD often enough for it to make this a fold, but I'm not sure: it really depends on villains' aggression.

PFR is whatever.

On the flop I cbet this pot-size (70% pot is also fine; against fish smaller is good as well), and the reason is our back doors and two-pair outs, as well as the fact a Q63 flop is hard to hit. When we cbet this villains must either fold a lot (good outcome) or call a bunch. The most natural hands to call are FDs (which we dominate) and Qxxx (which we have amazing equity against). We don't expect villains to have two-pair+ particularly often on this board. Betting merges our range and allows us to keep it uncapped, which is important because we're going to make a fair bit of medium-value two-pair type hands and don't want to be bluffed off them in later streets. Our backdoors and various outs guarantee that we can keep aggression on a good number of turn cards.

The only problem with betting is that we're not thrilled about getting raised, but that doesn't happen often enough to change my opinion: villains can't raise with impunity since be have overpair+FD here quite a bit, and have QBBB a lot, and a fair share of QQ. But because of our backdoors and pair we actually can play decently well when we get raised, so it's not that big a deal.

Hand format is atrocious. Villain I assume is BB, not BTN: he's OOP postflop.

Don't fold the turn IMO. I'd call the turn and then call any river that gives us two-pairs+.

I don't think we can play like this vs a villain who just keeps jamming whatever piece for pot-sized bets: when we're this tight we'd end up folding too much.

I think 4betting pre would be +EV but flatting is better, and that OTF raising is fine but calling is better.

I think that usually there are many ways to play a poker hand. This hand is not one of these cases. Flop is always a call, and turn is always a jam, and I believe this is the only correct way to play the hand vs described villain. Here's why:

Some PPTing will show that on the flop after villain raises we have the best made hand like 80% of the time, maybe more. This is simply because of our blockers, which decrease the chance that villain has a set to ridiculously small proportions, while all of villain's semibluffs are still in his range. The knowledge of our blockers make almost any reasonable-aggressive villain very unbalanced here. However, our equity vs villain's range is not that great, since he has a bunch of combo draws and draw+pair which we flip against or are even dogs against, so we're a little ahead or way behind. So we flat and wait for a safe turn (not that there are many of those).

Luckily enough, a safe turn indeed comes, and now all of a sudden we're doing really well vs villain's range (we even picked up a gutshot, but the analysis doesn't change if we hadn't). Villain has to keep firing with his draws most of the time in order to be able to win the hand on the river if he misses. So he bets with the vast majority of his range. Now we get to jam. We don't mind much if villain folds or calls: either he puts money when he's significantly behind, or he folds his considerable equity. In either case, folding is out of the question, and flatting is out of the question since we let villain's realize his equity.

Bet the turn. We have nut blockers and no reason to think we're behind. You're rarely getting raised, and we have great visibility for the river.

As played, I can't find a fold OTR vs this guy unless we have pretty good reads, but I can't say the fold is incorrect: might very well be correct. He shouldn't be getting here with KJ, after all, and people rarely bluff this big when your range is uncapped and rather strong.

I really dislike flatting this pre. There's no point to playing deception games in PLO with SPR 5: we'll just end up playing guessing games on flops since we'll almost always have a bare one-pair hand on the flop and will have to play guessing games against a range that has decent equity against us. If our hand was hit-or-miss that would be fine, but you're actually planning to rely on the showdown value that a one-pair hand gives you, which will cause you trouble. Villain is presumably 3betting a decent hand which flops well, which means you want to minimize the flop SPR as much as you can.

There's some theory behind this as well: what you're doing here is setting yourself up for a bluffcatching spot. I'm not sure if you know this, but assuming both players play well, bluffcatching is inherebtly worse for the bluffcatcher than for the bluffer due to game-theoretic reasons (this is essentially the RIO effect). Therefore we want to avoid as much as possible situations where we'll be bluffcatching.

As played, I raise flop. We have a blocker to top set, he should rarely have J2 or J4, and we don't want to see any more cards from all the above reasons.On the river it's an ok call, but I hate how we got here.