I had forgotten that his bet size was only 1/2p. I think you're correct that a larger c/r size makes more sense, maybe to like 280-300. 450 might be reasonable in theory, but it's pretty absurd in practice, when laying a reasonable price on a bluff makes much more sense.


More theory vs practice. In theory, solvers very rarely slowplay JT/JJ/TT/66 here in equilibrium strategies. They tend to check-raise them >80% of the time, even allowing for IP to overbet in capped range spots vs OOP's c/c range. That is to say that the gain from having stronger hands in your c/c range is generally overstated. You're correct that the counterstrategy to a polarized betting range is simple: just call down often enough. "Often enough" generally means JT+ and good draws maximize their EV by fast-playing.

In practice, I don't see any necessity in slowplaying 98/sets/JT for board coverage purposes vs a described nitty player. As if to vindicate my point, he seemed to just half pot it with KQ on the turn. I just don't see any point in fretting over overbets unless you're certain villain is a tough player. I would, however, c/c KQ here pretty frequently, but that it strengthens my c/c range is an incidental benefit. We simply have a lot of combos of KQ (maybe all 16, depending on our 3-betting strategy) and they play really well as c/c's. They can call virtually every turn, unlike 98.

To address my point, having a BDFD just adds 4% of runouts that you're able to play a big pot on, you'd rather the pot were of maximal size when you get those runouts. In obvious words, 9d8d is a much more profitable c/r than 98o. It's also a more profitable c/c, and one could argue that 9d8d should sooner be a c/c because it has ~25% of turns that you don't have to fold your draw on. However, it's still considerable that c/c is the line that leads to an (on-average) smaller pot, and 4% added 100%/0% distributed equity encourages building a bigger pot from the beginning.

As far as your c/r vs c/c threshold, I'd eschew the term "bluff" when there are still two cards to come. Certainly c/ring a low-value draw like 87 has a big bluff component, but if you c/r that hand and get called, and the turn is a 9, your balanced betting range should recognize that some of your gutters have hit, and you will be able to bluff more often accordingly. A balanced c/r range on the flop should include all of the gutters and oesds (even KQ) in some frequency. Some of those draws would otherwise c/c and others would otherwise be forced to c/f. A solver would be playing mixed strategies with them all, with the nemesis playing exactly in such a way that makes the mixed choices equal in EV. Generally speaking, it prefers to take the more aggressive line with the highest and lowest value draws (for example, raising 9d8d and 87 but calling more often with 98o). It probably also tends to raise with KdQd.

Really shouldn't be check raising flop in this spot IMO, for a lot of reasons. Nor should you be donking. Check call is the only option IMO.

Flop: Check call>>>donk>check fold>>>>>check raise

I agree with rentons entire post

Perfect and /thread imo

Renton, I'm not sure which solvers you're using (screenshots or links would be appreciated), but I really think you're overlooking or at least prematurely assuming the invalidity of several key strategic options that are relevant only at deeper stacks. Indeed, I'm 100% on board with a check-raising range that includes 98s and 66,TJs at 100 BB stacks (I would re-raise TT and JJ preflop at those stacks). Please consider two points as I write these options out: (a) no part of the reasoning for your posts is sensitive to stack depths,* i.e. there's no apparent reason why the particular arguments you use to justify check-raise at 100 BB wouldn't hold to equal effect at any stack depth; (b) if there are situations in which optimal deep stack poker diverges from optimal 100 BB poker, you'd expect them to be in dynamic board situations precisely like this one (on dry textures blockers set a natural limit on how many bets go in). Those two points should be enough to suspect that something about your line of reasoning is incomplete.

* You did mention that on certain runouts (e.g. BDFD runouts) OOP would prefer the pot to be as large as possible. However you didn't acknowledge that there is a stack depth for each initial check-raise size for which that would start becoming untrue, namely the one at which implied odds would start incentivizing IP to play his range so as to either cooler OOP very often on those runouts (e.g. BDF over BDF or straight over straight) or make a large raise on the turn (specifically in the BDFD case).

1. For a fixed check-raise size, the deeper we become, the worse the EV of check-raising JJ on the flop. Another way of putting this: the minimum check-raise size that isn't dominated by check-call must increase with stack depth. This is true in part because deeper stacks allow better implied odds on poorer equity drawing hands.

2. Another reason is that JJ is no longer the nuts on >50% of turns (or even the effective nuts on many more rivers), which is a huge dent to EV(check-raise JJ) that isn't suffered to a proportional extent by EV(check-call JJ) simply due to the obvious differences between IP's bet-call and double barrel ranges, due to JJ being forced to bet-call turn and then check-call certain rivers on which it's <<50%, etc.

3. When OOP double barrels a semibluff as suggested, IP's power to reduce or even eliminate OOP's EV by raising the turn and firing river increases as SPR increases, both because IP's range widens and his raise sizing may increase. Of course, this effect has marginal returns past a certain depth point, due to blockers, but it's a strategic option that virtually doesn't exist at 100 BB.

4. Those 'capped range spot overbets' that your solvers found on later streets start looking increasingly enticing with more of your range if you're able to make polarized check-raises over them for increasing amounts of money. Likewise, not having certain hands in your range as OOP (in sufficient frequency) allows IP to bet wider and wider on a wider variety of runouts - so it's not just about lacking JJ on blank runouts, but also being light on straights when a Q or 7 hits (are you really calling 98o OOP? who is the BB here again?)

1~3 make a case for a fixed check-raise size becoming increasingly unattractive as stacks deepen, or alternatively, the minimum competitive check-raise size becoming larger and larger. 4 makes a case for check-calling becoming increasingly attractive as stacks deepen. All of this is congruent with the opposite observation that in shallow stack poker there is more check-raising on the flop and 3-betting preflop. If correct flop check-raise frequency goes down as stacks go up, it's situations like these that we should expect to be affected most.

Comments in BLUE.


I didn't have time to address all of it (or the need, you explained yourself very well and its hard to disagree with most of it). I have a few scattered thoughts about exploitative strategy in this spot, though.

1) I don't think we have the information required to assume that BU is going to attempt to exploit our check/calling range with the bet sizing and bet frequency necessary to make check/calling a dominant play with JJ or TT. I would guess that the percentage of the live poker-playing population for which this is true is less than 5.

2) He bet 60 into 140, I think that already indicates that his range is weaker than usual and it's a bet size I would like to attack with a fairly wide range. I think it also indicates that a turn bet is less likely than if he had bet 80-100.

3) In my experience, decent nitty live players cbet the flop way too often, betting with hands like 88 and Tx with high frequency to "take the pot down." Again, it makes sense to punish this tendency. An equilibrium player would be betting less than 40% of his range here, but the average player in villain's shoes is betting 60-80%. All of the theory we've been babbling about goes out the window when a player is betting 60 into 140 with the majority of their range on a board where he is quite significantly range-disadvantaged.

I accidentally put 255 for OOP's c/r size. I'll run it again with a larger size to see if anything changes. I did have to simplify a few things to make the tree more tractable. For one, IP only bets 60 on the flop or checks, and equilibrium has him doing so with about 40% of his range. For each turn and river, I gave IP the options of betting 75% pot or 200% pot. I could add 300% pot but that would make the sim take longer. I gave each player the option of raising to 75% pot facing any bet at any point.

I showed on the side pane how it differentiates play with 98s, as I suspected it prefers to c/c more often with the non-bdfd variant. If you want to see any specific street spots I'll screen them, just let me know.

Renton



How I view myself as a poker player




How I actually am as a poker player

Also in case I didn't say so directly, the data sort of proves us both right and wrong. I said earlier in the thread that I thought equilibrium would "rarely" slowplay the nutted combos here. In actuality it mixes it up more and more with deeper stacks, but still fast playing them a majority. The draws follow suit, ascribing more and more value to passive lines but still raising them all quite a bit to balance the raising range.

Pre depends on a lot of variables. All three options are close given the info you provided. Flop is good. Turn is a clear c/f. After getting to the river like this, there is merit to donking, but if you go for c/r it should be small.

His shove is hilarious (even though you almost never have KQ). Fold fast.

You know how I get around the never having KQ thing here? By sometimes having KQ.

I'm not sure the smug satisfaction of being able to call here to chop is worth all the value you give up by playing KQ suboptimally up to this point. Especially considering that outside of slowplayed KQ, we should have no raising range at all on this river. No 98 combos are callable on the turn, AA should virtually always be 3-bet pre and JJ is probably too thin to c/r river.

Pre is fine. I'd prefer to 3bet but calling obv can't be bad. Agreed w most that turn is a fold as played.

Also, not sure why everyone is heavily discounting KQ from our range. Obv pre 3bet would be super std but it's deep live poker calling here and there seems fine if not at the very least possible in villain's eyes.

I feel like if I was villain and was faced with this raise on the river, value raise only makes sense to be KQ and nothing else. Calling with KK/QQ seems way better than bluffing on riv since it beats random spaz/turned bluffs by us. In fact it's suicidal to bluff in such polar spot esp w an all in bet. Pretty trivial fold imo.

I think it's more that we only c/ced the less than 1/2p turn bet with a huge amount of stack behind...

even against villains with a history of bluffing and playing position very aggressively, a 3b ship on the river is usually nutted. Well played by him if his objective was to make you fold, because you should almost always fold in this spot.

I fold; you will get a better spot in a 4 handed game to get stacks in. And I would pay attention to his future river play to see if he jumps out the window again. Also, when you fold here (given you didn't show) you may have given off the perception you're capable of making moves on the river, which could be useful in future pots when you you're OOP.

Just curious as to people's reasoning for 3 betting pre here? Purely for initiative?

Generally this is a hand that will retain much of its equity even if you narrow someone's range. I.e. it will achieve a similar EV postflop in terms of percentage of the pot whether you flat or 3-bet, but 3-betting results in you winning the pot immediately sometimes. It's also good for your 3-betting range, being strong on boards that are bad for AK, weak on boards that are good for AK.

Very concise, very right on. Well done Renton.

the turn and preflop should both be folds. even the flop is not so hot with only 4 nut outs