co opens we defend bb a10o.

flop 875 two hearts, we have no hearts. ck.call.
turn black 4. ck bet call.
riv 3 fd bricks. ck bet we???

have been discussing this one w quite the range of friends-really only have 2 lhe peeps to have meaningful discussion with and this spot seemed and still seems fairly interesting

villain: gonna leave this pretty vague (would like it to be a fairly gto based discussion-will add some details in a few days). For now lets assume late 20s canadian pro. reg in this 2/4-3/6 game and on a decent heater in this game last 500 hours. value bets thin (as you're supposed to), and is extremely capable.

Hero-Young early 20s white kid. comes from an online background/not a regular in this game at all. expecting to get 3b even wider than normal by regs but doubt i'd be seen as scared $$$

Unless villian has specific reason to think you're nitty (which seems unlikely at 3/6) I dont think you're folding out anything we beat w. A raise.

Wide range vs. wide range situation, seems like pretty standard call to me.

I feel like there should be a hand or 2 that we are check-folding on river so the question for me is what is the worst hand that gets to the river with our line? I would think it is A9 unless people think we should be peeling turn with KQ? That seems pretty optimistic to me. As such, I think AT is probably close to a check-fold.

Maybe we are supposed to use this hand to bluff river some small percentage of the time but I don't think we should bluff with it every time. A2 and 33 are the only hands that really make sense to check raise for value so we don't need many bluffs to balance that out.

hmm, i play these games a lot, so if you gave name of the villain I could better suit (sounds like MGM).

So he should be barreling off his T9 combos, J9 combos, JT combos missed FD (some players in the pool would open T9o/J9o/JTo in the CO, and most open T9/J9/JT suited). We do block this combo, as well as the JT combos. From my experience in this game, if this is actually a good player who is playing a balanced/GTO strat, then we should be calling ATo otr given that we got here.

gonna let some more people give thoughts before i chime in myself-but yes good read ^^^ mgm is villain and he showed up with a hand i was pretty surprised he bet river with-- a4o

crazylond-can you justify your claim that we should have some combos that we fold otr here as well as combos we cr as a bluff (obv in any poker game this is almost always the case)

I was more curious your intuition behind "a hand or two" and coming up w a9 and a10 to potentially cf with whereas i would argue there are other parts of my range that may be better candidates

When I looked at it again, I agree there may be other candidates as I think it might be correct to get to river with some king high flush draws with this line.

One reason I think we should have some check folds on river is because if we don't, it follows that he should never bluff the river when we check. But then if he never bluffs, we should fold sometimes. To me, the only GTO solution is that he should bluff sometimes and we should fold sometimes.

The reason I think we should have some check raise bluffs is because we have some check raise value hands. To me, this river card seems innocuous enough that we should be check raising our strongest hands (a2 and 33) rather than donking them. So we need some small amount of bluffs so that he can't make exploitative folds when we check raise.

this is the THIRD time i'm writing this post lol.

hey chunkit. great to see you're enjoying your time in la.

first, i'd wanna look at your flop kr range. this would be in mine a good portion of the time, esp on a board like this since his range is chok'full'o hands like QTs/KJ etc. etc. and not many better aces or pairs at this point. a kr also makes the hand harder to play from his perspective and i dont want to give my opponents easy decisions at this limit.

here you've k/c'd 2 times and k'd the river, which really limits your range on this board from his perspective (and has given him an easy go of it. this kind of play will encourage him attacking your blinds and playing against you). since you didn't kr anywhere or bet anywhere it seems less likely that you have a strong draw like T9hh or a big heart draw where you'd be a favorite against much of his range. that means that when you get to the river you either have a busted draw like T9 or J9 or a heart draw w/ one over; or you have a decent/good ace that you're calling down with.

so when you're at the river, if you knew the guy pretty well and weren't playing with him forever, i'd lean towards folding when he bets b/c it's clear what you hold given how you got there. you're folding most of your draws and calling w/ your ace highs so he can value bet w/ impunity here.

that said, given that analysis, he then can't check his k/q highs b/c much of the time you have an ace that'll win, and so since he has to bet those hands to be closer to gto, you have to call more and ATo is a hand that fits that description: must call in order to prevent losing the pot to a worse hand.

overall, interesting hand and i'd fold in a vacuum, call here, and k/r when we "get there" w/ our monsters maybe 1/2 the time and bet out the other half.

re: crazylond bluffs-> i'd rather use T9 or J9 there vs. the ATo which can win by calling against K/Qhighs

PS - you have 3 lhe peeps to discuss hands with. i don't recall getting a text on this one

If the cutoff has a flop checking range, which I think is good on this board, then I'd check fold the turn.

Yes this. Op says he wants to discuss the hand from a GTO viewpoint. GTO is a turn fold and it's close on the flop. The bots never do anything 100% of the time but I am quite confident they fold ATo on the turn a huge % here.

Calling down here is fine vs tag fish who never value bet thinly enough and barrel off all their queen highs and **** but look how owned you got vs someone good. Why should he check A4o ever here it looks like the nuts every street.

I think CR flop is just horrible btw. Like I can't even comprehend that as an option. Now I think I could maybe make an argument for flop donk. But this hand just doesn't really fit into any bucket other than peel and hate life that he didn't check back this flop texture.

Close spot.

Biggest factors to consider:
Does CO cbet close to 100%
Do we have a donk range?
If yes, does villain know this.

It's MGM, just fold and be thankful you only lost 2.5 Big Bets with a 14% equity advantage vs. his preflop cutoff range.

Compliment his beard after the hand as well. He may value bet slightly narrower in the future.

appreciate the responses-pretty much agree w everything DD had to say. flop cr seems like the worst ever

Was really frustrated w my turn peel in game and then just puke called river.

tpir-lol all around

phunkphish-cbet is def nowhere near 100%. i def have no donk range in both live lhe and the bovada 30 streets these days.

"bots never do anything 100% of the time but I am quite confident they fold ATo on the turn a huge % here. "

If the solution is to check call the turn sometimes and fold sometimes, that would mean that calling the turn is exactly 0 ev. Thus the river is a clear fold because the turn call is dependent on the ev gained from the cutoff checking back the river sometimes. If the river is ever a call, that would imply that the ev of a call is equal to or greater than zero. Therefore the turn would be a profitable call as well. If the turn call is profitable then we must call 100% since folding has an ev of zero. This is true no matter how slight the profitability of a call is. This is why I would fold this hand 100% on the turn and if it's in fact a profitable call on the turn, we must call 100%.

Bob I don't disagree with your logic but it opens a question I don't know the answer to: can a mixed strategy ever have higher EV than a stratified strategy considering you can make an argument for the profitability or lack thereof of any individual hand within our range? When GTO approximations are reached they always seem to have a mixed strategy for individual hands, is it your contention this is not truly optimal? I think I am having a hard time making generalized conclusions from your post because it is logical but goes against what I have seen previously from the bots.

this seems easy enough. u wanna donk ATo ~65% of the time and check the rest, vs the flop bet you wanna cr about 53% of your ATo and call the rest. as played, on the turn you want to donk ~43% and check the rest, folding to a bet 15% of the time, calling the rest. as played, c-c 39%, c-r 7% and fold the rest.

This is getting sidetracked a bit but I definitely think GTO can mean a mixed strategy.

Think about a 1 card poker game where you have a 1/3 chance each of an ace, a king or a queen against an opponent who always has a king and it is face up. To bet costs a dollar and there is a dollar already in the pot. You act first. No raising is allowed and he will never bet when checked to because his hand is face up and we'd only call with equal or better.

First, let's restrict both of us to having to play the same way every time (no mixed strategy). If he folds every time, it is clear we should bet every time for a net gain of $1 every time (and his breaking even).

If he calls every time, it is clear we should bet when we have an ace and it doesn't matter whether we bet when we have a king. We will win 50c when we have a king (chopping what's already in the pot), win $2 when we have an ace and break even when we have a queen for a net gain of 83c per hand. He, on the other hand, will win $1 when we have a queen (because it will go check-check), win 50c when he has a king and lose $1 when we have an ace, resulting in winning 17c per hand. So his best fixed strategy is to call every time which will result in a 17c win per hand.

Now let's imagine he instead does a mixed strategy where he calls 45% of the time.

Now, it is clear we should bet if we have a queen. Because the bluff will lose us $1 45% of the time but win us $1 55% of the time.

And it is just as clear we should also be betting our kings and aces. The kings gain fold equity and the aces are hoping to get paid off.

How does he do?

When we have a queen, he breaks even 55% of the time and wins $2 45% of the time for an average win of 90c.

When we have a king, he breaks even 55% of the time and wins 50c 45% of the time for an average win of 22.5c

When we have an ace, he breaks even 55% of the time and loses $1 45% of the time for an average loss of 45c.

So on average, he will win 22.5c per hand, which is better than the 17c per hand he was able to attain using his best fixed strategy.

I think the same concept holds true in the more complex poker games that we normally play. And it make sense when you think about it. For example, let's just say that in a given LHE hand, we decide we are supposed to bluff raise the river with A7 high but just call the river bet with A8 through AK. If we decided instead to use AJ as our river bluff and call with A7, it would cost us occasionally (when they hero call raise with AT or were making valueless bet with A9) but against a solid opponent, it's very rarely going to matter. Both hands are bluff catchers when we call or bluffs when we raise.

We just pick these parts of our range because of those rare situations it matters and because it helps us systematically figure out what part of our range we are in so we can try to apply the correct frequencies. What really matters is the frequency of our bluffs and calls. If we decided, for example, to turn every hand from A7 through AJ into a river bluff, this would be a large mistake that would be easily exploitable. Not because we are bluffing with the wrong part of our range, but because we are bluffing too much.

As humans, it is easiest for us to play different hands the same way and always play the same hands the same way in the same situations. And we can get fairly close to GTO doing this, simply because of the vast combinations of hands that there are in LHE. But a computer doesn't have the same mental restrictions and can play the same hand different ways and more accurately pin down the actual GTO solution by doing so.

I just woke up and am posting theory in the high stakes forum. 🙃

I think mixed strategies are necessary against an opponent that both plays a properly mixed strategy and has the ability to adjust to a pure strategy.

If this opponent can't adjust, then it doesn't really matter which line we choose as long as we make one of the most profitable plays instead of the less profitable plays.

If this opponent can adjust his frequencies in order to maximally exploit us due to our non optimal frequencies, then we must play a properly mixed strategy in order to maximize our expectation while minimizing our opponents expectation.

However, when most of a hands ev is derived from unimproved showdown value on the flop or turn, such as this ATo, bluff raising will always be inferior to either check calling or check folding. This last part is speculation stated as fact but I believe it's true.

The hands that I'd use mixed frequencies with here are those that derive most of their ev from draw equity or those that can be check called and check raised for a good profit. I don't think ATo fits into either category.

The whole point of GTO play is that it is unexploitable, even by an opponent capable of adjusting. A strategy that is profitable as long as our opponent doesn't adjust, but unprofitable if they make certain adjustments, is not GTO.

I don't disagree with your point that ATo is probably not a raise on the flop or turn in this hand. Both plays seem terrible to me and I wouldn't expect a GTO computer to make either play any percentage of the time. But I could believe they check call and check fold the turn with different frequencies.

I don't intentionally use mixed frequencies at all while playing. But I'm not a GTO computer.

"A strategy that is profitable as long as our opponent doesn't adjust, but unprofitable if they make certain adjustments, is not GTO."

I agree. The point is that if the opponent doesn't ever adjust then we can play a pure strategy without losing ev. We are indifferent and thus it doesn't matter what we do as long as we choose from the most profitable lines. Indifference then becomes a product of our opponents mixed strategy.

On the other hand, if our opponent could adjust, then it would be in our best interests to play a properly mixed strategy; we're still indifferent but we're exploitable if we play a pure strategy.

"I don't intentionally use mixed frequencies at all while playing. But I'm not a GTO computer."

I think you should vs good players, particularly with draws.

I think you are right about this. I think I actually just realized something about the way I play and why I sometimes lose too many bets in spots against players where they have a hand they "shouldn't" ever have. I think this is actually a really profound area to explore but not going to do it here.

As far as the rest, I feel like you may still be missing something. A player who is playing a "perfect" but non-mixed strategy will lose money to a GTO computer that is using a mixed strategy. So your assertion that we can play a "pure" strategy against an opponent who doesn't adjust and be profitable is only true if our opponent is not playing GTO. Against a GTO opponent, any strategy will lose money except for GTO and this includes all non-mixed strategies.

Your last sentence is incomplete. I made the same mistake in the past.

Any deviation from gto will result in a loss of ev equal to or greater than zero. I'll be right back with a link.

Some really good stuff here:

http://forumserver.twoplustwo.com/15...=bobf+equal+to