pm plz

The shove is only 2.437x pot. As is, given the lines taken, our range is richer in Jx than is our opponent's, especially since we are holding a jack, which is quite important for card removal. Combine that with the fact that your opponent is value betting Jx himself some of the time and I don't see much cause for worry of risking 2.4x the pot to balance with bluffs.

To be clear, I definitely agree that the opponent should have some Jx when he checks, but that we should have a much larger proportion than he should when he is checking to us on the river to the point that moving in shows a profit until we are risking much more, especially if he's splitting that range of Jx by check-calling some Jx and by betting some Jx.

How is everyone else estimating Jx combinations, for both players? That's the crux of the problem. We need the right variables to account for the best play. For the pre-flop re-raiser, 4 AJ (discounted, given flop), 4 KJ (discounted given flop), 1 JJ, 4 QJ (if he checks all of them on flop) for 13 TOTAL possible hands. I'm sure people can argue the discounting methods up to this point for a few combinations one way or the other. After that, the total heretofore is split: betting some Jx and checking some Jx, 4 combinations that check to us? We have a lot more Jx that take our line than 4.

I highly doubt betting smaller with AJ makes sense unless your opponent check-shoves Jx, which doesn't make any sense to do unless for some reason it would fold out a chop, which means that the bettor (one checked to on the river) decided to play exploitively by betting smaller to induce a raise/call from worse and then fold when he could make more on average by shoving. I'm sure with 12x the pot effective stacks that betting AJ smaller makes more sense, but only because betting Jx smaller also makes sense.

PS - Link/quote other post?

Posting this here for you guys, too, so that points of view aren't confused.

...and a bit more. Looks like we're heading to calculating a correct answer. I'm showing here that we have about 3.2 times as many Jx in our range than our opponent.

Can we please get a link to this forum? Seems to be quite the discussion over there

http://www.runitonce.com/nlhe/mid/ RIO midstakes board.
That game theory cat is strong in GTO and quantitative analysis but shootaa is showing his deep understanding to a fine degree.
One of the most enjoyable threads in a long time even if across 2 boards.
Oh and i think for once in a long time i have learnt something from this board.

does indeed look like a very good thread, I feel like the problem just boils down to what people estimate both hero's and villain's river ranges to be. Could be very off track here, but this is what I was thinking. imagine two extreme examples ;

1) Villain bets turn super often. He loves bluffing this card, but is also not afraid to bet a set or even twopair for thin value. Once he gets to the river, he can therefore no longer just check/call Jx, if he does that his calling range becomes way too slim (since he bets a lot wider than Jx on the turn). He is forced to start calling a few worse hands, and our example goes towards the classical spot of nuts and air, and the fact that we want to betting a maximum in such spots. As his turn betting range x goes up, then so does our desired river betting size. The fact that he has AJ once in a blue moon is in this example just a paranthesis to our river betting size theory, it happens so seldom it's not enough to make alter our river sizing.

2) Villain bets turn super seldom, he only bets Jx/AJ and very seldom a bluff. On the river, he has enough Jx/AJ that he never has (or should) call less than Jx to a big bet. At this point, the theory does not apply, since we no longer have close to a "nuts or air" problem. Instead, we want to bet small, to reach the equibrilum where he becomes 0EV between calling and folding with his bluffcatchers (and since those are very few, we need to give him good odds, ie bet small). This is, of course, assuming that we even want to bet Jx at all in this scenario. In the very very extreme example, that he NEVER has a bluff on the turn, then GTO isolated on the river would of course be to check back Jx always, and instead create our river sizing from a range of AJ/bluffs instead. Anyways, don't wanna derail into how we should create our range (this is hard enough already!), just what our sizing should be depending on how wide he gets to the river.


If above statements are correct, then discussing the proper betsize without already having the estimated river range already established makes little sense, sinse the "gto betsize" will depend so much on what assumptions different posters make for earlier streets?


Is this half correct? :s Just writing down what strikes me as logical, would appriciate if someone with better theoretical knowledge would correct any major faults in thinking here.

Optimal bet-size vs. your opponent depends on his range.

GTO betsize will depend entirely on what he SHOULD be doing, not what he IS doing.

Kind of semantics, but still true.

Fwiw, I'd imagine betting a sizing that makes QT a bluff catcher and not Jx would be better barring reads on your opponent.

X POST from other site
Fwiw, I've done a very similar analysis, but I gave Imfromsweden a 4-bet range preflop, and he defending a total of 45% of hands (instead of 40%). But it's still pretty close.

Beyond on that, I took the time to put together what I would think is some decent ranges for flop and turn from a GTO standpoint... I spent a fair bit of time doing this and I've had a lot of practice in the past, so I'm guessing that it's going to be better than the ranges that you guys are choosing. You can goto the end of the post where I give some of the major decisions I made on earlier streets.

RIVER RANGES BEFORE ANY ACTIONS:
http://gyazo.com/d2cb80ea2d13a01a4e9a32779d0e2194

FLOP ASSUMPTIONS:

Opponent:

- His frequency for checking AJ & AT is only proportion to balancing his check-raising range... in other words, contrary to what Imfromsweden said, AJ would not be used as a check-call. The gut shot is too strong to play as a check-call on the flop unless it's with the intention of ALWAYS check-raising the turn when bet into, in which case our opponent would have slightly less AJ in his checking range. AJ is one of our better nonmade hands, and it'll turn into the nuts quite a bit, so it should not be played for high card showdown value. This means that the Villain will have ~9.6 AJ in his flop checking range -- which actually seems very similar to what GTO thought.

- Opponent will be checking all his Qx type hands. I think this is a pretty fair assumption, I could see some arguments for betting flop and turn, and then checking river with AQ. Especially if we wanted to bet the flop small, and then the turn bigger with the intention of folding out some of the gut shot hands our opponent could have when the turn blanks. I didn't decide to do that, and it doesn't effect things much, but I'm just putting it out there.

- Opponent will be check-raising all his sets. I think this makes sense, since the opponent will want to have a check-raising range here and he can't cap his checking range too much (even though it is a 3-bet bot). Even though he'll be check raising into 16 combos of JT, Imfromswedends next best hands are going to be 99, KQ, so he's doing well against those type hands.

IMFROMSWEDEN:

- When checked to, Imfromsweden will bet ALL his AJ hands. I just can't really come up with a good reason why we'd need to check-back any AJ. The only reason that you'd want to check-back AJ is if we're going to have to bet-fold them to the check-raises. But this is not the case, they're going to be part of our bet-calling range. And they also don't have enough showdown equity to win with Ace high. This means that Hero has 0 combos of AJ on the river.

- If people totally disagree with me about the AJ above, I did have Imfromsweden checking back ALL his QJ hands. This is probably a stretch. I could see a very sensible argument for betting flop and betting turn and checking back river with our QJ hands. However, if we do start betting a lot of our QJ hands, then our flop betting range is going to be wider than our flop calling range, and the Opponent is going to have a large incentive to not have a betting range on this flop and just check-raise a ton. (fwiw, this flop hits Imfromswedens range pretty hard and there's an interesting side discussion about how often the Villain should be betting the flop anyways... but that's for a different thread).

- Imfromsweden will bet ~66% (pulled that out of the air) of his JT straights on the flop. Hero won't bet all his JT on the flop, otherwise is turn is going to be capped and Villian will start over-betting the turn large, until it's going to be higher EV for Hero to check back the nuts. I believe this would go back and forth until the EV of betting and checking JT will be the same, and GTO action will be a mixed strategy.

- For both players, I'm having both of them bet ALL there back door flushdraws which aren't pairs. I think this makese sense because these will be the best bluffs which will have a chance to approve. I think they're probably better ideas than trying to make a small pocket pair a bluff. But I could see an argument for turning weak 9x into bluffs which I didn't do. My only point for really pointing this out is that I don't think either player will have many flushdraws on the turn because they both checked the flop.



TURN ASSUMPTIONS:

GENERALLY:

In the hand, the Opponent ends up betting the turn. The problem with this scenario is that the Hero's range is quite a bit stronger than the opponents on the turn, and while he can't have any AJ in his range, Hero's range is nothing like bluff catchers. I don't think there's a lot of incentive for the Villain to bet the turn to be frankly honest, but I'm going to go ahead and give him a betting range so there's a range for the river. This would usually mean just making it super polarized like straights and better, but then this makes for a super simple river situation and not a very interesting one. So with the goal of having an interesting river discussion I'm going to give the opponent a turn betting range which isn't super polarized.

Opponent:

- Similar to the flop for Imfromswedend, the opponent will both bet and check his AJ and Jx hands on the turn. The reason is the same, he'll have an incentive to not overly cap his checking range on the turn, since there's so much stack depth left with only two streets to go.

- Opponent will bet TopPair or better on the turn. Fwiw, more than 50% of Imfromswedens calling range on the turn will be weaker than TopPair, if that makes anyone feel better about the Opponent betting top pair on the turn.

IMFROMSWEDEN:

- I didn't give him a raising range. This could be open for discussion. The Hero doesn't have any AJ in his range, so that's not great. But I could see an argument for both raising and calling some % of Jx. In other words, from a GTO stanpoint, Hero probably would raise some Jx and call with some Jx. But I'm not giving him a raising range on the turn.

- The rest of his range is pretty normal.

I see what you're getting at, do you mean that we should take into consideration a GTO turn-betting range from him, regardless of what we believe he might do exploitavely on the turn. This opens up another problem though, if we want to estimate his turn betting range from a GTO perspective, we must also know how wide he gets to the turn in the first place... and for that we have to know GTO play for flop play.... and to know GTO play for flop we need to know how wide he gets to the flop... and then we need to figure out what GTO would be preflop, and it quickly becomes this massive massive problem that we have no chance of figuring out. Therefore I do think it's neccesary to instead make some assumption on his turn frequencies. Or?

Looks reasonable, except I'm wondering about this. I have a very hard time believing that we're calling less than top pair on the turn more than 50% of the time. Which are these hands, other than turned flushdraws?

Turn Ranges Before Action:
Opponent's:
http://gyazo.com/aa99e8dc4c80a268baaa9a2e8522a174

Hero's:
http://gyazo.com/43941a0975d2c5488a9cf0965066e037

You'll notice that the you, the Hero, has quite a bit more equity on the turn than the Villain. Similarly, if you look at the bottom of the Villain's range hans like 75o have 2% equity against the Hero's range. Therefore, we're going to want to defend AT LEAST enough where the Villain will be indifferent between betting and checking this hand, otherwise the Villain will likely be betting close to his entire range. But it's not hard to imagine that the true inflection point will be somewhat stronger hand. This just means that we're going to need to be defending ~61% or around there.

So how should the Hero construct his calling range? I like to think about having a couple different parts. There's the first part which is made up of strong hands which we plan on calling down with when the Villain bets the turn and river. Similarly, the first part will also be made up of some hands which will bet the river when checked to (ie straights). The second part of our range is made up of hands which will fold when the Villain's bet the river or bluff when the Villain checks the river. Now this type of hands are usually comprised of draws, as you mentioned in your post -- that you would call with flush draws but not much else. So below is how I'd contstruct those two parts of our turn calling range:

HERO'S TURN CALLING RANGE:

Part 1 - Calling down / maybe betting when Checked to:
Straights = 17.5%
2 Pair+ = 12%
Middle Pair (Q8 - Q2s) = 13.5%
1-Pair + GutShot (A9) = 7.5%

Part 2 - Folding on River or Bluffing when checked to:
Flush Draws (9xs) = 3%
Gutshots (A8 - A2 type hands) = 8%

So we don't have many flushdraws in our turn range because we bet most of our backdoor flushdraws on the flop. So when deciding what hands we want to put in this part of our range, it doesn't really matter what the hand will be when the Villain bets the river and we fold. But we do want to pick a hand which will do well when it hits. Ideally we will want a hand who's equity does well against the Villain's betting range (ie a flushdraw). So if we don't have anymore flushdraws, Ax type hands equity do pretty well if the J falls on the river because we'll have the nuts -- unless the flushdraw got there. And when your hand doesn't hit on the river, you want a hand which does well as a bluff for when your opponent checks to. Hands which do well as a bluff on the river, are hands which blocks your opponents defending range. As we have seen our opponent will be check-raising us with some AJ type hands on the river, so by having Ax hands as our bluff on the river, we'll block the Villain's check-raising range, and maybe even some of his river check-calling range.

So our total turn defending range = ~61% of hands

If we're betting all of our straights when checked to on the river, our ratio of value to bluff hands on blank rivers will be somewhere around 2 to 1 which seems pretty reasonable if we'd be betting pot on the river -- but that's still up in the air. If this seems a little bit high for our bluff ratio on the river, there's a combo os 9A in there which could check-back, and sometimes our Ax will hit on the river and we can check them back OR the J will fall on the river, and our bluffs will suddenly be the nuts. In other words, I think it's a fine ratio of turn float type hands.

EDIT: fwiw, the Villain's weakest hands on the turn have ~8% equity, not 2%. The 2% assumed that the river was always the 4 spades. However, I don't think this changes our turn calling range, and I'm still very comfortable with how much we're calling the turn. Even when the Villain has a hand like 75o and the turn goes check and check and he hits one of his 7 or 5, he's not going to be able to bet it, and at best will be able to check-call a river bet. Similary, if he bets the turn and hits his 7 or 5, we already know that he won't be able to bet it for value, and when he checks, he's gonig to be losing to all of our check-back range cause all of our high card hands are being bluffed in which his EV will be very close to 0. In other words, I just don't think it'll be easy for the Villain to realize his entire 8% of equity.

fwiw, with my ranges i did my best to come up with good ranges from a GTO perspective. There almost certainly off in a myriad of ways, but as you can see from my posts, I had a strong theoretical reason for all the decisions.

geeks itt, we has a straight!

qft

You run into this problem any time you're trying to crack GTO from an applied point of view. In order to solve for GTO... you need to know GTO :P

I'd assume my opponent is not going to be so trivially bad so as to only bet straights on the turn. It would be fairly easy for him to increase his EV by betting a wider range on the turn, even just by betting some random airballs.

I havent seen this mentioned yet so I'll chime in, but should we be using a mixed strategy on this river?

I say this because if we always bet Jx then our opponent can always check raise AJ, and maximize his AJ value, so we never force our opponent to bet AJ thus minimizing AJ value, plus the more he bets AJ the more he needs to bluff into our strange range here so that is also a + I think.

So I would think you want to check back a % to make his AJ strategy mixed and counter him being able to take a very easy very high ev strategy with his AJs, then you would want to bet a proportion of your Jx X size relative to how many fds/ other bluffs you show up here with.

It is possible you want to have mixed sizings too, like maybe if you have AJ you want an overbet and maybe Ax fd hanbs to overbet bluff (or a portion of) and then you should have another bet sizing which makes him indifferent to check calling the weaker parts of his range (assuming he bets 2 pair+ on the turn x %)

Just my opinion, but I do not claim to know nada, Im a foreigner to heads up

O yeah also I would think that his strategy has a lot of checks with Jx, therefore your bluff size should be very small on the river, and therefore Id think your most common value bet size on river would also be small