Hello,

I've made a conscious effort to fold more on the river lately vs good opponents, particularly with hands that I think would be slightly profitable as calls. This is due to my current understanding of indifference theory:

In order to make the in position player indifferent to checking or bluffing the river heads up, the out of position player should allow an immediate profit equal to the ev gained by the in position player when he or she holds his worst check back hand.

If I don't allow this immediate profit by folding hands that would be slightly profitable as calls, then the in position player may exploit me by never bluffing the river. In this scenario, checking back will be more profitable than bluffing.

If I take the idea too far and fold too much however, I will become exploitable by an opponent that bluffs even more.

There are too many factors to list here that will determine where the margin of bet/check for the in position player is. Instead of attempting to list these factors, I'll put forth my thought process for river play heads up out of position when facing off vs good opponents with a few examples that I'll post later.

I'm just gonna leave this here for now. Questions or comments are welcome of course as long as they somewhat pertain to the topic of river play.

You shouldn't ever fold a hand that is a profitable call. It doesn't make sense.

That's true, however most of the time the bluff hands have close to 0 EV for checking back, so you shouldn't be focusing on this too much.

This just means that there are some river spots in which it is optimal to fold a lot (let's say 70%) vs even a small bet. Those spots are pretty rare though, and pretty obvious when you see them.

Philip Newell is the author that you seek on how to divide up your ranges between check/call, bet/call, bet/fold, etc. He uses model poker to explain his conclusions.

I agree with this if you're referring to bad opponents, but I think that vs good opponents it's a necessity.

I've discussed this in depth with Phil in this thread:

https://forumserver.twoplustwo.com/3...ghlight=newall

which he seems to have abandoned. Oh well.

Note that the check folding frequency shown for the out of position player on page 54 of Further Limit Holdem allows the in position player to immediately profit a fraction that is equal to the value of checking or betting the hand on the check/bet margin.

Bob, it seems like you're advocating sacrificing short term EV in order to play a more GTOish, defensive style as opposed to exploitative poker. Obviously making a fold where a river call is +EV is just blasphemy to an exploitative style, but I'm not going to go as far as saying that its just plainly wrong.

The indifference principle has always been a bit messy IMO since you're almost always assuming fixed ranges which basically never happens in poker, especially on the river. I don't really see why that concept is really that important to what you're trying to convey here as long as its understood that your hand in question is some sort of bluff-catcher where a proper GTO strategy would use some sort of mixed strategy, say 60% call, 40% fold.

So your idea, I think, is that against a tough player you may have a read that a call is slightly profitable but if you take a 100% call frequency (because its just obviously profitable) your opponent eventually will adjust and at some point will just never bluff and then you're taking a huge loss with the auto check/call line which might surpass your previous gains with that line. So by folding right away *sometimes* you're preemptively preventing your opponent from making a move that will exploit you.

Again, I don't think the above idea is necessarily incorrect, but the obvious counter is that you time your mix-up to right about when your opponent will adjust. Take the small profit from the check-calls, and then once you think your opponent is sick of his bluffs getting caught you switch to check-fold. Its really just a leveling war, where you can easily get trapped into circular logic, as is much of poker.

Another problem is that you really have to be sure your hand is part of a mixed strategy in the first place. Really it should only come down to one or a few hands that are mixed, if your hand is 60% call/40% fold the next best hand is probably 100% call and the next worse hand is 100% fold (might not be exactly this because of blocker scenarios). If your folding a 100% call hand 40% of the time you open yourself up to some serious exploitation. And of course, how could you possibly know what the correct GTO solution is an actual game with real players?

Ok let's do an example:

no limit holdem tourney with 6/8 players remaining. Two spots pay. Blinds are 25/50 with no ante yet.

relevant stacks:

me: 15k after taking out two players
everyone else: 5k

a strong player opens on the button for 150, a strong player folds the small blind, I call in the big blind. Pot = 325

flop: 567r

checks through

turn: Jo

checks through

river J

I check, button bets 150 and I have a decision. Here's my thought process:

I'm getting 475:150. 150/625 = 24% equity needed to break even on a call.

Since my opponent is a strong player, there will be a number of hands with between 20% and 30% equity because of his polarized river betting range.

If he bluffs a bit too infrequently, my equity will run closer to 20%, while if he bluffs too frequently, my equity will run closer to 30%. Depending on metagame stuffs and human error, I think most strong players will have such a bluffing frequency here between 20% and 30%. The stronger they are, the closer to 24% this bluffing frequency will be.

I think the most important hands in my opponents range are these in particular order:

1) the very bottom of his range. Since the small blind was assumed to be a strong player, I don't think the button can get very out of line preflop. So I think the bottom of the buttons range on that river is (T8o), which should be in his flop and turn checking ranges at frequency >0% but <100%. My guess is that he should bet the flop with T8o at frequency ~90%. Then the 10% of the time that he doesn't, he should bet the turn with that hand at frequency again ~90%. So that leaves 1% of the time that he gets dealt T8o, will he end up with that hand heads up in position on the river.

2) the top of his bluffing range and the bottom of his checking range. Depending on his value betting strategy, this may be as strong as QT or as weak as T9. Most players will go for the thin value vs me because I'm a showdown monkey. So let's assume that he will bluff QT and anything worse on the river because he has the number of value hands to back up such a wide bluffing range.

3) his value range. Going with the above assumptions, I think a strong value betting range on the river may include hands as weak as 86s, again because I'm a showdown monkey. Some players will be stronger when they value bet the river there, but I think that in order to fulfill the assumption that this opponent is strong, we must assume that he can value bet with 87s or anything better. The more frequently the opponent checks such strong hands on the flop and turn, the more value bets he will have in his range on this river, naturally. I don't know what's right as far as these frequencies go, but I think anywhere between 40% to 60% is good both in practice and in theory. Any less will result in a capped river betting range on too many runouts, imo. Any more will result in a loss of flop and turn value.

4) his slowplay range. Due to the nature of the board, I think it's good to slowplay here in the buttons shoes at a relatively high frequency because of the strength of my range in the big blind. If my range in the big blind is strong on this board, then slowplaying as the button here should be quite profitable and necessary to prevent me from overbetting turns and rivers. This is why I'd check many strong hands at relatively high frequency as the button here. Maybe this is wrong, but that's my understanding of the situation. Because of all that, my guess is that the buttons value range can include all strong hands at frequency leading into the river, where these hands will be bet at 100% frequency.

5) his checking range. These are all of the hands leftover from building a polarized betting range as the button. Depending on the button's value betting strategy and resulting bluffing strategy, this checking range will include hands between Q2s and A6, or hands between KQ and A5.

At game speed, this is all too much to consider of course, but I'll think about the above as much as I can with the time I'm given, that is if I find myself with a hand that I think is close. In this case that means I think that the bottom of my bluffcatchers will be Q2 through KQ. I think this group of hands may be profitable as calls on the river, but I also think that if I called with these hands 100% of the time, then the button could exploit that tendency by never bluffing. This is why I'll fold these hands even though calling may be breakeven or slightly profitable. I'll allow a slight profit for the button's bluffs to avoid exploitation.

We could come at it from the opposite angle and look at my range and decide based on the pot odds how often I should call, but due to the mixing of my frequencies on the flop and turn, my river range is a discounted mathematical mess of hands that I can't really begin to account for.

Sorry tourney's going on now I gotta go concentrate.

So villain is close to balanced, but not quite, so you can make some slightly +EV exploitative calls against him. If you show down a really light river call villain may adjust by being more imabalanced in the future and never bluffing. How is this a bad thing? Why do you say this will lead to you being exploited in the future if you can guess how he's adjusting? After you show down a river call that reveals your exploitable strategy you can either attempt to beat his adjustment when he makes it or play balanced yourself and render his adjustment futile.

See I feel like you’re wasting too much time and mental energy in just setting up your hypothetical. A river spot where we have bluff catchers and should be calling *some percentage of the time* is pretty common in poker. Calling 100% might be too much while calling 0% would be too little. Proper gto would be a mix. So when you say “I’ll fold sometimes” it makes sense since you’re just adhering to the mix. When you say “this hand is a profitable call but I’ll fold”, it’s a little different though since you're acknowledging an avenue for exploitation but deciding not to take it. If a hand is supposed to be a mix of strats, it’s value neutral against other gto strats. So just saying “this is a profitable call” implies either that your opponent is making a mistake by bluffing too much, or that you have a 100% call hand to begin with.

You *can* mix in some folds to keep your opponent in that mistake zone and prevent him from correcting himself but again that’s just one option. You can just disregard your opponent and play as close to gto as possible, or you can go the max exploitative route and just start folding when your opponent is about to shut down with his bluffs.

You guys are right. If I knew that calling is profitable, then I should call 100% of the time. I was mixing up (allowing immediate profit) with (folding profitable calling hands).

If we can forget that I said that, I think there is still stuff to discuss here regarding (allowing immediate profit), which is what I really wanted to talk about.

----

I was having an issue visualizing the ev of river bluffcatchers, which now I see is clearly (0ev), or breakeven as calls or folds.

So there is no need to fold profitable calling hands.

Going back to the example:

Nice. I like this. Notice that when we're closing the action on the river there's no room for counter exploitation.

If you have a pure bluff catcher and you are playing against a balanced player, then they are always ev = 0 calls.

If you have a pure bluff catcher and you are profiting from calling, then the player is just unbalanced and no hell reason to fold.

If you have a pure bluff catcher and you are loosing money from calling, then you have no reason to call and should fold it.

If you have a bluff catcher that gets some value against a balanced player, then your bluff catcher is not pure and you are beating some part of his value betting range, no reason to fold neither.

You never sacrifice any ev with a single hand in GTO for any reason.

Correct me anyone if I am wrong

Didn't see this, good you got it

By the way, the little profit that comes from bluffing for villain strategy is because we will be folding hands that can't beat his bluffs, and will be making him indiferent to bluff only with the hands that beat any of his bluffs. It would be their worst equity bluffs that would benefit the most from this little value gain, because the better ones will almost equal between bluffing and getting a little value and checking and gaining a little value.

Question:

When playing out of position, should the oop player employ a balanced donk bet range on the river? Or maybe the turn?

If all the oop player ever does to place balanced bets is a checkraise then control of the betting and the balance stays with the in position player.

If control of the hand is always left to the player in position, then any profit for the oop player (and reason for oop to participate) lies with mistakes from the in position player.

Yes I think the out of position player needs to bet the river with his hands in range that have the least showdown value. The exception being vs a very tight turn bettor that is value heavy and will not fold the river enough for the out of position player to profit with such hands.

I would guess that any time a player arrives at a point where they have the nuts and villain does not (probably due to chance more so than planning) you will see a player taking the lead some of the time. It probably depends on the expected mixture of hands in your opponent's range.

If it's less likely your opponent will bet due to having fewer value combos (and thus less ability to bluff and less ability to bet overall) then taking the lead makes sense.

Right. So middle set can be the nuts if given the right information.

I was having trouble visualizing the part about check folding those hands with no showdown value heads up out of position, but then I remembered that it's ok because if we assume that we got to that point on the river by making profitable decisions previously in the hand, there is no loss of value.

Let's look at a marginally profitable bluffcatcher imo, on the turn: I've been playing exclusively tourneys lately so here's a tourney example:

I raise 99 for 3x in the cutoff with about 100 big blinds average between the button and the blinds. Button calls, blinds fold.

45Tr

I bet 4 big blinds, button calls.

Ko

I check, button bets 8 big blinds and I have a pretty close decision:

getting about 3:1, I need to win just under 25% of the pot back on average to call. If calling is profitable then it's likely to be profitable by a small margin, depending mostly on how often the opponent will bluff this turn, which hands he bluffs with, and also how often the opponent will give up his bluff on the river.

Let's assume that calling is just slightly profitable vs this particular opponent. That probably means we're winning back about 25-35% of the pot back on average by calling the turn for an overlay of 1-10%. Sweet. However, then these rivers fall:

8/7/6/Q/J/3/2/A/5/4/K/T/9

think about that progression from bad river to good river. Of course it's debatable, but I still needed to estimate the progression to show that when bad rivers fall, our ev for calling again with a bluffcatcher is going to vary with these different river cards. The most debatable imo are 8-J, which may be backwards but oh well.

Depending on the size of the river bet we face, this is how I'd proceed:

1/2 pot on the 5 river? I'd call. I'd fold the A river though.

3/4 pot on the K river? I'd fold, but I'd call on a T river.

full pot on the T river? close decision imo. Probably only getting back 30-35% of the pot back in the long run vs good players.

But? Don't forget about the times it checks through on the river and we win. To make calling the turn profitable, then we need to include that ev in the calculation: (river checkthrough ev) + (river calling ev) = (turn calling ev).

Notice that as (river checkthrough ev) increases because our opponent makes one of these mistakes: (missing value) or (missing bluffs), then (river calling ev) may go up when they miss value, or down when they miss bluffs. If they make both mistakes of missing value and missing bluffs, there may or may not be a canceling out effect causing the illusion of indifference, but that is short lived when you remember that (river checkthrough ev) has increased.

Notice that as (river checkthrough ev) decreases because our opponent makes one of these mistakes: (value betting too thin) or (bluffing too much) then river calling ev goes up. Thus there is no loss of value.

Or maybe fold the turn idk.

Check the flop. I think 99 is among the worst hands to c-bet in that spot. Or maybe not "worst", as something like A9o would have a lower EV, but if I was to make a list of hands that make most sense as flop checks, 99 would be the very first hand I put on the list.
Villain can float (or raise) the flop with all kinds of stuff and cause you headaches on most runouts.

Interesting. I thought cutoff vs button it's a solid value bet, but I was only posting the hand to illustrate the profitability of bluffcatchers, which is a small value vs good opponents.

If you like, we can change the hand to T9s.

T9s makes a lot more sense as a bet and then a check-call on the turn. On most rivers, I think T9s is probably a fold vs a bet of 1/2p or more. You'll have better hands to bluff-catch with (QQ/JJ, better Tx), and villain will rarely have total air on a lot of runouts if he bets turn and river. I think he'd check back quite a lot of hands once you call on the king turn though, so you really need to have a good read that he's overbluffing. (e.g. He has to float hands like QJs/AJs that bet the SD on the turn and then almost always fire again if they don't make a pair).

What about the flopped straight draws that should call my flop bet sometimes like 76s, 86s, 87s? I think those should bet the turn at high frequency and then if they bet the turn, they should bet rivers that miss them as they should be the bottom of the buttons range, while the hands you listed should probably take the free showdown and expect to win occasionally. Also, when the low straights tend to pair up on the 2/3/6/7/8 rivers, I think that those now paired hands should check back the river as the bottom of the buttons range will be QJs and the like, which should bluff on such rivers.

Seems like you're not giving the button a wide enough turn and river betting range by assuming that the button never, or only rarely, will have bluffs. I think that any decent strategy should have bluffs on every imaginable runout or else there will be no reason for the out of position player to call.

I think you're mixing up (what most players would do) and (what they should do).

I think they should have bluffs on every runout. Thus if they don't then it goes back to a loss of bluffing ev that I was talking about here:

This is why bluffcatchers may be -ev river calls vs value heavy opponents, yet gto will not lose value. It's all part of what I refer to as the Law of Conservation of Expected Value. If someone is missing value in some way, then that is ev that is realized by gto in other forms, as compensation is awarded for the opponent's mistakes.

Of course, you can fold the river exploitively and make even more money vs a value heavy opponent, but that is not the purpose of this thread.

Then in that case (river check through ev) will be quite high and will more than compensate any loss of value.

ps I love these talks. Not trying to be argumentative, I'm actually having a blast. <3

I don't think any hands you mention (Ajs, QJs, 67s, 86s, or 87s) should check the river once you call the turn. If you meant check turn and river with AJs and QJs then I could see that.

After betting the turn I don't think pairing the straight draw hands should check back the river to showdown vs your turn calling range either. I think they gain too much by bluffing out other hands even ones they would win against at showdown.

I think AJs and QJs should mix lines with betting the turn/checking the river unimproved, and checking the turn and river unimproved, with the exception being those really bad runouts that make QJs the bottom of the button's range, where QJs should bluff the river.

seems like a lot of bluffs to me unless you're gonna bet really big as the button on the river, which I wouldn't.