indifference
I'm up late thinking about indifference and thought I'd share my ideas. Please excuse me for stating theory as fact:
We can't always force an indifference in games where hands can improve and regress, nor should we want to do so. Before the final round of betting, the probability that our opponent holds a threshold bluff or a threshold bluffcatcher is low. I haven't done the math to figure out just how low this probability is, but I think that building our strategy around making one hand indifferent is inherently wrong.
I think it's entirely possible that before the final round of betting, calling and bluffing frequencies will always be higher than the rate that would make the opponent indifferent with the threshold bluffs and threshold bluffcatchers respectively.
How could this be true?
1) bluffs are +ev before the final round of betting. If they were not +ev, they would be spew.
2) calls are +ev before the final round of betting. If they were not +ev, they would be folds.
3) both players may profit from money going into the pot, assuming that there is already money in the pot.
When does indifference matter?
I think it matters most on the final round of betting, when hands no longer have the chance to improve.
I think it also matters before the final round of betting when one is making an all in bet or call.
The final round of betting
I think threshold bluffs and threshold bluffcatchers deserve special consideration on the final round of betting, as now all bluffs are threshold bluffs and all bluffcatchers are threshold bluffcatchers when considered as a part of an optimal solution. It should follow then that indifference is very important on the final round of betting. Since the threshold hands are so numerous, we must build our strategy around making these threshold hands indifferent.
I apologize if you were hoping that I would tell you how to make your opponent indifferent. That's not the purpose of this post, but rather to put up for debate when to make the opponent indifferent.
We can't always force an indifference in games where hands can improve and regress, nor should we want to do so. Before the final round of betting, the probability that our opponent holds a threshold bluff or a threshold bluffcatcher is low. I haven't done the math to figure out just how low this probability is, but I think that building our strategy around making one hand indifferent is inherently wrong.
I think it's entirely possible that before the final round of betting, calling and bluffing frequencies will always be higher than the rate that would make the opponent indifferent with the threshold bluffs and threshold bluffcatchers respectively.
How could this be true?
1) bluffs are +ev before the final round of betting. If they were not +ev, they would be spew.
2) calls are +ev before the final round of betting. If they were not +ev, they would be folds.
3) both players may profit from money going into the pot, assuming that there is already money in the pot.
When does indifference matter?
I think it matters most on the final round of betting, when hands no longer have the chance to improve.
I think it also matters before the final round of betting when one is making an all in bet or call.
The final round of betting
I think threshold bluffs and threshold bluffcatchers deserve special consideration on the final round of betting, as now all bluffs are threshold bluffs and all bluffcatchers are threshold bluffcatchers when considered as a part of an optimal solution. It should follow then that indifference is very important on the final round of betting. Since the threshold hands are so numerous, we must build our strategy around making these threshold hands indifferent.
I apologize if you were hoping that I would tell you how to make your opponent indifferent. That's not the purpose of this post, but rather to put up for debate when to make the opponent indifferent.
When the bettors range is so strong relative to the caller's range that there just aren't enough bluffs to make the opponent indifferent, the bettor will bet 100%.
When the caller's range is so weak relative to the bettor's range that the caller just doesn't have enough profitable calling hands to make the bettor indifferent.
You are absolutely correct that it is not always correct, or possible, to force indifference on the other players. For one thing, if you do that, you cannot profit from any mistakes. For another, your actions are constrained and there may be no ones for indifference available.
Indifference comes up in game theory in two different ways. First, for many simple problems, assuming the goal is to force indifference leads to shortcut solutions. In this case, indifference is not a goal, just a convenient guess at the solution, which you then verify.
The second way is in some zero-sum, two-person scenarios, any relative profit the other player can make from choosing one option over another is EV you can capture by forcing indifference. This is only a decent approximation to a few situations in poker, like some all-in bets on the river when everyone knows you have only nuts or nothing.
What is generally true in all rounds and all situations is that it's good to force difficult decisions on other players. With bad players, you give them decisions you think they will get wrong, due to their play tendencies. But with top players you sometimes have to content yourself with making their every decision a hard one, to maximize the number of mistakes they're going to make. That's conceptually similar to indifference, but not exactly the theoretical equivalent.
Indifference comes up in game theory in two different ways. First, for many simple problems, assuming the goal is to force indifference leads to shortcut solutions. In this case, indifference is not a goal, just a convenient guess at the solution, which you then verify.
The second way is in some zero-sum, two-person scenarios, any relative profit the other player can make from choosing one option over another is EV you can capture by forcing indifference. This is only a decent approximation to a few situations in poker, like some all-in bets on the river when everyone knows you have only nuts or nothing.
What is generally true in all rounds and all situations is that it's good to force difficult decisions on other players. With bad players, you give them decisions you think they will get wrong, due to their play tendencies. But with top players you sometimes have to content yourself with making their every decision a hard one, to maximize the number of mistakes they're going to make. That's conceptually similar to indifference, but not exactly the theoretical equivalent.
Great topic for discussion IMO. FWIW I read a post that by Spladle in a different forum that I really liked that touched on this concept, pasted below. Matthew Janda talks a lot of about this idea of making bluffcatchers indifferent on streets before the river. I'm sure that has some merit in situations where one player is super polarized and the other holds mostly bluffcatchers, but I feel like since these situations are so rare, and not all bluffcatchers are created equal, it's a pretty questionable way of looking at things.
Originally Posted by Trix
Thanks for sharing Spladle.
If you CBet 3$ with KK on 885, with a preflop potsize of 5, and both players play a balanced strategy that includes making calling down KK breakeven, aren't you losing ~8$ which is the pot at the point where he check-raises and not 100$ as it is as much his responsibility to make you break-even with 'bluff-catchers' as it is yours ? (Ignoring improvement of either players hands)
A few thoughts:
1) It is extraordinarily unlikely that calling down with KK could ever be breakeven. If it were, that would imply that we should be indifferent to how we play KK against a GTO player, and that is almost certainly untrue. Calling the flop c/r should be HUGELY profitable, as should calling a normal-sized turn bet on most cards. In fact, against some smaller bet sizes I would expect calling many rivers with KK to be profitable as well. What I object to is the idea of calling >20x the pot on the flop when we are losing to >10% of our opponent's initial range.
2) Even if we know when facing the flop c/r that we will be indifferent between calling/folding on certain rivers after certain board run-outs, that does not imply indifference to calling the flop c/r.
3) Even if we were indifferent between calling and folding to the flop c/r, that would not imply that we were losing $8. Being indifferent between calling and folding means that your EV is $0, not negative.
4) Villain's goal when check-raising should not be to make us "indifferent" (between what? Calling/folding, raising/calling, raising/folding, raising/folding/calling?) with "bluff-catchers" (all "bluff-catchers" are not created equal and should not be treated/played the same). His goal should be to maximize the EV of every hand he plays. Doing so will almost certainly result in it being profitable for us to continue against a flop c/r with KK but unprofitable to continue with JTo.
5) You can't ignore the possibility of either player improving. If the turn is an offsuit ace, play from that point forward should be very different than if it's a Q putting up a backdoor flush draw, which should likewise be played differently than if the turn were an offsuit 4. Placing hands into static ranges ("value," "bluff," "bluff-catcher") on the flop is inappropriate.
Quote:
Originally Posted by Trix
As you otherwise could just call down when he bluffs too much and fold when he don't. (Play poker :P)
Yes, obviously if you identify an imbalance in your opponent's strategy, you can and should exploit it. However, knowing only that an opponent bluffs too much or too little on the flop doesn't actually help you that much when deciding how you should play various hands. You also need to know other things about his strategy as well before you can put that information to use. For example, even against an opponent who check-raises this flop as a bluff a bit too infrequently, it will still be profitable to continue with KK. The value/bluff imbalance would need to be MONSTROUSLY huge before failing to call a flop c/r with KK could ever be right. Furthermore, even if he bluffs a bit too much, that doesn't necessarily mean that you can continue profitably with A2o or JTo; it simply means that many of the hands you do continue with will be more profitable than they would be if your opponent were playing better/bluffing less (of course, some of the hands you continue with will actually be less profitable against an overly-aggressive strategy than against an optimal one). You are still forced to draw a line somewhere between what you continue with and what you fold.
Quote:
Originally Posted by Trix
If you know BB's strategy(CR-Range, c-c ranges), would you still check KK?
That's not enough information to influence my decision. We'd also need to know how he plays after we check back the flop, how he plays after checking twice/three times, how he responds to bets of various sizes on various boards after various actions, etc.
To be clear, btw, betting KK here should be hugely profitable, as should calling a check-raise. The argument for checking is that it will be even more profitable. There are many hands for which I expect this to hold true. I'm pretty sure that betting with any two cards on the flop here should produce an immediate profit against an optimally-playing opponent, so the reason we develop a checking range is not that we can't bet profitably but because doing so is even more profitable than simply c-betting.
Originally Posted by Trix
Thanks for sharing Spladle.
If you CBet 3$ with KK on 885, with a preflop potsize of 5, and both players play a balanced strategy that includes making calling down KK breakeven, aren't you losing ~8$ which is the pot at the point where he check-raises and not 100$ as it is as much his responsibility to make you break-even with 'bluff-catchers' as it is yours ? (Ignoring improvement of either players hands)
A few thoughts:
1) It is extraordinarily unlikely that calling down with KK could ever be breakeven. If it were, that would imply that we should be indifferent to how we play KK against a GTO player, and that is almost certainly untrue. Calling the flop c/r should be HUGELY profitable, as should calling a normal-sized turn bet on most cards. In fact, against some smaller bet sizes I would expect calling many rivers with KK to be profitable as well. What I object to is the idea of calling >20x the pot on the flop when we are losing to >10% of our opponent's initial range.
2) Even if we know when facing the flop c/r that we will be indifferent between calling/folding on certain rivers after certain board run-outs, that does not imply indifference to calling the flop c/r.
3) Even if we were indifferent between calling and folding to the flop c/r, that would not imply that we were losing $8. Being indifferent between calling and folding means that your EV is $0, not negative.
4) Villain's goal when check-raising should not be to make us "indifferent" (between what? Calling/folding, raising/calling, raising/folding, raising/folding/calling?) with "bluff-catchers" (all "bluff-catchers" are not created equal and should not be treated/played the same). His goal should be to maximize the EV of every hand he plays. Doing so will almost certainly result in it being profitable for us to continue against a flop c/r with KK but unprofitable to continue with JTo.
5) You can't ignore the possibility of either player improving. If the turn is an offsuit ace, play from that point forward should be very different than if it's a Q putting up a backdoor flush draw, which should likewise be played differently than if the turn were an offsuit 4. Placing hands into static ranges ("value," "bluff," "bluff-catcher") on the flop is inappropriate.
Quote:
Originally Posted by Trix
As you otherwise could just call down when he bluffs too much and fold when he don't. (Play poker :P)
Yes, obviously if you identify an imbalance in your opponent's strategy, you can and should exploit it. However, knowing only that an opponent bluffs too much or too little on the flop doesn't actually help you that much when deciding how you should play various hands. You also need to know other things about his strategy as well before you can put that information to use. For example, even against an opponent who check-raises this flop as a bluff a bit too infrequently, it will still be profitable to continue with KK. The value/bluff imbalance would need to be MONSTROUSLY huge before failing to call a flop c/r with KK could ever be right. Furthermore, even if he bluffs a bit too much, that doesn't necessarily mean that you can continue profitably with A2o or JTo; it simply means that many of the hands you do continue with will be more profitable than they would be if your opponent were playing better/bluffing less (of course, some of the hands you continue with will actually be less profitable against an overly-aggressive strategy than against an optimal one). You are still forced to draw a line somewhere between what you continue with and what you fold.
Quote:
Originally Posted by Trix
If you know BB's strategy(CR-Range, c-c ranges), would you still check KK?
That's not enough information to influence my decision. We'd also need to know how he plays after we check back the flop, how he plays after checking twice/three times, how he responds to bets of various sizes on various boards after various actions, etc.
To be clear, btw, betting KK here should be hugely profitable, as should calling a check-raise. The argument for checking is that it will be even more profitable. There are many hands for which I expect this to hold true. I'm pretty sure that betting with any two cards on the flop here should produce an immediate profit against an optimally-playing opponent, so the reason we develop a checking range is not that we can't bet profitably but because doing so is even more profitable than simply c-betting.
When the bettors range is so strong relative to the caller's range that there just aren't enough bluffs to make the opponent indifferent, the bettor will bet 100%.
When the caller's range is so weak relative to the bettor's range that the caller just doesn't have enough profitable calling hands to make the bettor indifferent.
When the bettors range is so strong relative to the caller's range that there just aren't enough bluffs to make the opponent indifferent, the bettor will bet 100% unless implied odds make some hands more profitable to check, which will in effect increase the bluffing frequency bringing this frequency closer to the indifference point. In this case, indifference will be a coincidental result of maximizing value with good hands and bluffs, if the indifference point happens to be reached.
Though, I think that in an optimal solution, the bettor will never be bluffing at a frequency <bet/(pot+bet), but will be frequently be bluffing >bet/(pot+bet) before the river because semibluffs are +ev, in some cases even though the caller is folding at a rate <bet/pot; the combined equity of the bluffs and the fold equity realized can add up to a bluffing frequency higher than that which would cause the opponent to be indifferent.
In other words, there is no calling frequency to make the powerful semibluffs indifferent. If a range contains exclusively semibluffs with >bet/(pot+bet) equity, then those semibluffs will always be +ev. Though it's possible that these semibluffs may earn more by checking, which allows the hand to realize equity, escape the check raise, and increase implied odds relative to betting in limit games, but sometimes decrease implied odds in games where the pot grows geometrically instead of linearly, as in limit games.
Except in the cases where the bettor is betting 100% as this implies that the bettor is value heavy, which should allow the caller to call less than the rate that would cause indifference.
I like it. The only minor detail is that I think that it is enough to require that either will bet over leverage point, effectively forcing allin. I mean classically big enough 4-bet will force fold or shove and the indifference matters.
I'm not a betsizing wizard by any means though, but it just seems like in pot limit and no limit games that if the worst price your opponent can offer you is >3:1 then one of you made a mistake with sizing somewhere previously. How can he make you indifferent if your whole range is priced in to call the shove? In this spot, can we even make our opponent indifferent to bluffing with his threshold bluff?
This is interesting because it brings up the question of betsizing affecting bluffs such that they can call a shove because of the good pot odds offered to the one calling the shove. This is in effect the bloat and chase, just with the added possibility of your opponent folding to your raise which leverages the opponent's stack. In pot limit games, I think this argues for a smaller, more manageable raise size that doesn't price in your bluffs. In no limit games, it seems like a reason to either raise smaller or shove.
I'm not a betsizing wizard by any means though, but it just seems like in pot limit and no limit games that if the worst price your opponent can offer you is >3:1 then one of you made a mistake with sizing somewhere previously. How can he make you indifferent if your whole range is priced in to call the shove? In this spot, can we even make our opponent indifferent to bluffing with his threshold bluff?
I'm not a betsizing wizard by any means though, but it just seems like in pot limit and no limit games that if the worst price your opponent can offer you is >3:1 then one of you made a mistake with sizing somewhere previously. How can he make you indifferent if your whole range is priced in to call the shove? In this spot, can we even make our opponent indifferent to bluffing with his threshold bluff?
I think (far from sure) that the right bet size when "close enough" leverage point, is the one that just barely forces opponent's (re)raise to be shove (i.e. minimum bet will take the pot over the leverage point). I think "close enough" might mean that sometimes the bet size is smaller but I think it can be "quite sizable" in right circumstances (being OOP etc.). Not sure if "quite big" can be e.g. bigger than PSB.
I think it's quite possible that the correct betsize could be bigger than a pot sized bet in no limit games. If the pot is 1 and I have 1.1 pot sized bets in my stack, then the only betsize that really makes sense is 1.1 pot unless there's an exploitive betsize which could earn more.
In pot limit games, I still think awkward stack to pot ratios will be the result of a poor bet sizing somewhere in the hand. If you happen to be calling down with a bluffcatcher and your opponent leaves you with an awkward stack to pot ratio then I think you should be thankful for that. Even though there's not much else to do but call down or fold, I think the opponent made a mistake which we should be able to benefit from by either calling down or folding, whereas if he had planned the sizings better early in the hand, he could make us indifferent with a proper sized final bet. Without the proper sizing early in the hand, the price on the final bet could be too good to make us indifferent with our threshold bluffcatchers.
On the other hand, if we're the one who made the sizing mistake early in the hand, then with the small final bet, we're either missing value or not bluffing as much as we could if we used a better sizing. We have misused our stack and as punishment we will not be able to make the opponent indifferent on the final bet.
In pot limit games, I still think awkward stack to pot ratios will be the result of a poor bet sizing somewhere in the hand. If you happen to be calling down with a bluffcatcher and your opponent leaves you with an awkward stack to pot ratio then I think you should be thankful for that. Even though there's not much else to do but call down or fold, I think the opponent made a mistake which we should be able to benefit from by either calling down or folding, whereas if he had planned the sizings better early in the hand, he could make us indifferent with a proper sized final bet. Without the proper sizing early in the hand, the price on the final bet could be too good to make us indifferent with our threshold bluffcatchers.
On the other hand, if we're the one who made the sizing mistake early in the hand, then with the small final bet, we're either missing value or not bluffing as much as we could if we used a better sizing. We have misused our stack and as punishment we will not be able to make the opponent indifferent on the final bet.
button raises pot, big blind calls.
After we take out the small blind for rake, we have a 7 big blind pot. Each player has 91 big blinds left for a stack to pot ratio of 13:1.
flop XXX
big blind checks and the button , whose range happens to be uncapped on this board, needs a sizing plan to get all in by the river with his good hands.
If the button bets pot pot pot, then the price on the river for the big blind will be 2:1.
Had the stacks been just 10 big blinds deeper, the sizing should change because the button now is in a position where betting pot pot pot would leave him with an awkward stack to pot ratio that the big blind could likely exploit.
Had the game been no limit then a slightly larger sizing on each street would help the button get all in by the river with a healthy optimal bluffing frequency.
With the extra 10 big blinds in a pot limit game at the start of the hand, the button should be looking to make his sizing smaller perhaps going back all the way to preflop because not doing so would lead to an awkward stack to pot ratio of <1:1 on the river should he face a raise.
Thought I'd bump this and put an idea out there, which isn't something that I came up with, but I wanna try to put it in my own words:
Strategical indifferences
Let's say we're playing limit holdem. The classic ways that these hands play out is that if the button raised preflop and you called in the big blind, that you should check to the raiser at or near 100%. The exception to this has always been that you should donk bet into the preflop raiser if he likes to check back a lot. Then after you check the flop, you have the option of closing the action with a fold or a call, while retaining the option to raise with your stronger hands or bluff raise.
Standard.
What if we found that when we're the one on the button, that we could make the big blind indifferent to check raising or donking by checking back just the right amount to make him unsure of whether he should donk or not with his threshold value hand/bluffcatcher? Should we do it?
I use the term strategical indifference here because it's not just about making your opponent indifferent to playing this one hand one way or the other, but instead it's a choice between two entirely different strategies. If he hasn't studied donking situations much, then that's incentive to check back more. This would induce him to donk more, which should benefit the in position player. The exception should be that if the big blind has a solid donking strategy, then we should be more inclined to bet as the button. This should induce the opponent into check raising more.
I think it would be analogous to choosing one chess opening over another because you know your opponent sucks at one opening but is good at the others. If he studied that opening more, then maybe he could make you indifferent to sitting down and playing a game with him.
Strategical indifferences
Let's say we're playing limit holdem. The classic ways that these hands play out is that if the button raised preflop and you called in the big blind, that you should check to the raiser at or near 100%. The exception to this has always been that you should donk bet into the preflop raiser if he likes to check back a lot. Then after you check the flop, you have the option of closing the action with a fold or a call, while retaining the option to raise with your stronger hands or bluff raise.
Standard.
What if we found that when we're the one on the button, that we could make the big blind indifferent to check raising or donking by checking back just the right amount to make him unsure of whether he should donk or not with his threshold value hand/bluffcatcher? Should we do it?
I use the term strategical indifference here because it's not just about making your opponent indifferent to playing this one hand one way or the other, but instead it's a choice between two entirely different strategies. If he hasn't studied donking situations much, then that's incentive to check back more. This would induce him to donk more, which should benefit the in position player. The exception should be that if the big blind has a solid donking strategy, then we should be more inclined to bet as the button. This should induce the opponent into check raising more.
I think it would be analogous to choosing one chess opening over another because you know your opponent sucks at one opening but is good at the others. If he studied that opening more, then maybe he could make you indifferent to sitting down and playing a game with him.
Thought I'd bump this and put an idea out there, which isn't something that I came up with, but I wanna try to put it in my own words:
Strategical indifferences
Let's say we're playing limit holdem. The classic ways that these hands play out is that if the button raised preflop and you called in the big blind, that you should check to the raiser at or near 100%. The exception to this has always been that you should donk bet into the preflop raiser if he likes to check back a lot. Then after you check the flop, you have the option of closing the action with a fold or a call, while retaining the option to raise with your stronger hands or bluff raise.
Standard.
What if we found that when we're the one on the button, that we could make the big blind indifferent to check raising or donking by checking back just the right amount to make him unsure of whether he should donk or not with his threshold value hand/bluffcatcher? Should we do it?
I use the term strategical indifference here because it's not just about making your opponent indifferent to playing this one hand one way or the other, but instead it's a choice between two entirely different strategies. If he hasn't studied donking situations much, then that's incentive to check back more. This would induce him to donk more, which should benefit the in position player. The exception should be that if the big blind has a solid donking strategy, then we should be more inclined to bet as the button. This should induce the opponent into check raising more.
I think it would be analogous to choosing one chess opening over another because you know your opponent sucks at one opening but is good at the others. If he studied that opening more, then maybe he could make you indifferent to sitting down and playing a game with him.
Strategical indifferences
Let's say we're playing limit holdem. The classic ways that these hands play out is that if the button raised preflop and you called in the big blind, that you should check to the raiser at or near 100%. The exception to this has always been that you should donk bet into the preflop raiser if he likes to check back a lot. Then after you check the flop, you have the option of closing the action with a fold or a call, while retaining the option to raise with your stronger hands or bluff raise.
Standard.
What if we found that when we're the one on the button, that we could make the big blind indifferent to check raising or donking by checking back just the right amount to make him unsure of whether he should donk or not with his threshold value hand/bluffcatcher? Should we do it?
I use the term strategical indifference here because it's not just about making your opponent indifferent to playing this one hand one way or the other, but instead it's a choice between two entirely different strategies. If he hasn't studied donking situations much, then that's incentive to check back more. This would induce him to donk more, which should benefit the in position player. The exception should be that if the big blind has a solid donking strategy, then we should be more inclined to bet as the button. This should induce the opponent into check raising more.
I think it would be analogous to choosing one chess opening over another because you know your opponent sucks at one opening but is good at the others. If he studied that opening more, then maybe he could make you indifferent to sitting down and playing a game with him.
I'm no expert in limit but it seems like finding optimal indifference points on the flop may create bigger issues on turn and river.
For example, ending up getting thinly priced in for bd stuff that may be overall -EV when including the flop?
Edit to add: I guess what I'm trying to say is that delta EV for optimal or near optimal will be minute but for those hands your doing it with may be much more -EV down stream.
I'm assuming your talking about HU? FR, there are going to be too many scenarios where indifference points will be too specific to achieve, or matter.
I'm no expert in limit but it seems like finding optimal indifference points on the flop may create bigger issues on turn and river.
For example, ending up getting thinly priced in for bd stuff that may be overall -EV when including the flop?
Edit to add: I guess what I'm trying to say is that delta EV for optimal or near optimal will be minute but for those hands your doing it with may be much more -EV down stream.
I'm no expert in limit but it seems like finding optimal indifference points on the flop may create bigger issues on turn and river.
For example, ending up getting thinly priced in for bd stuff that may be overall -EV when including the flop?
Edit to add: I guess what I'm trying to say is that delta EV for optimal or near optimal will be minute but for those hands your doing it with may be much more -EV down stream.
I like the chess opening selection example particularly because it's so intuitive. If my opponent sucks at defending the Ruy Lopez, then I'm always going to play that opening. If I'm indifferent between the Ruy Lopez and the Queen's Gambit, then that's incentive to improve my openings or even select a different opening, such as the King's Gambit, in order to exploit my opponent by selecting a strategy that he hasn't studied.
Another poker example might again come from limit holdem, where it can be correct to just call preflop in the big blind with 100% of your continuation range as long as the preflop raiser cbets the flop above a certain exploitable frequency, which is extremely common. The idea is that you exploit a future street mistake of overaggression by delaying value raises on the previous street. However, if the preflop raiser does not cbet at an exploitable frequency, then that's incentive for the big blind to 3 bet preflop with his stronger hands. If the preflop raiser could make the big blind indifferent between these two strategies, that could be of great benefit because the big blind will be spending time thinking about preflop strategy when he could be spending his time thinking about more pressing concerns.
What is a "threshold bluff"?
I agree with everything you said, but the point was that by forcing a strategic indifference, we might be able to increase our pot share by inducing the opponent to change his strategy. On a long enough timeline I think this could be of great benefit. On a short enough timeline, this could be very bad because of missed immediate value, which cannot be recovered if the opponent quits.
I like the chess opening selection example particularly because it's so intuitive. If my opponent sucks at defending the Ruy Lopez, then I'm always going to play that opening. If I'm indifferent between the Ruy Lopez and the Queen's Gambit, then that's incentive to improve my openings or even select a different opening, such as the King's Gambit, in order to exploit my opponent by selecting a strategy that he hasn't studied.
Another poker example might again come from limit holdem, where it can be correct to just call preflop in the big blind with 100% of your continuation range as long as the preflop raiser cbets the flop above a certain exploitable frequency, which is extremely common. The idea is that you exploit a future street mistake of overaggression by delaying value raises on the previous street. However, if the preflop raiser does not cbet at an exploitable frequency, then that's incentive for the big blind to 3 bet preflop with his stronger hands. If the preflop raiser could make the big blind indifferent between these two strategies, that could be of great benefit because the big blind will be spending time thinking about preflop strategy when he could be spending his time thinking about more pressing concerns.
I like the chess opening selection example particularly because it's so intuitive. If my opponent sucks at defending the Ruy Lopez, then I'm always going to play that opening. If I'm indifferent between the Ruy Lopez and the Queen's Gambit, then that's incentive to improve my openings or even select a different opening, such as the King's Gambit, in order to exploit my opponent by selecting a strategy that he hasn't studied.
Another poker example might again come from limit holdem, where it can be correct to just call preflop in the big blind with 100% of your continuation range as long as the preflop raiser cbets the flop above a certain exploitable frequency, which is extremely common. The idea is that you exploit a future street mistake of overaggression by delaying value raises on the previous street. However, if the preflop raiser does not cbet at an exploitable frequency, then that's incentive for the big blind to 3 bet preflop with his stronger hands. If the preflop raiser could make the big blind indifferent between these two strategies, that could be of great benefit because the big blind will be spending time thinking about preflop strategy when he could be spending his time thinking about more pressing concerns.
I've intentionally invested in -EV play to create an image bias which isn't the same thing but I get that poker isn't always about optimizing every single hand as some would believe.
I'm just not sure how effective this can be though since they can opt to not attempt to counter with an exploitative style that they're less familiar with and chose a more neutral style instead. At this point your initial -EV play to induce the change will be a wasted investment.
I'm mostly speculating here because I only have a moderate amount of experience at HU and almost no experience at limit but it seems like the opponent will always have at least a couple ways to respond so pushing them into a style which you can better exploit seems like it would need to include some amount of overconfidence by your opponent in their ability to play the style where you hold an edge.
Also I wonder how long it would take for a good player to realize they don't have an edge and adjust to something they're more familiar with?
I know that when I used to play tournaments where I thought a player had more experience when we got to HU play, I'd tend to neutralize rather than exploit.
check 100% > donk a lot > donk sometimes and check raise sometimes
If he checks 100% as is pretty much standard, then he's gonna miss a ton of value when I check back a lot.
If he donks a lot, then that's better than checking 100%, but it's still not good because his checking range becomes very transparent.
If he donks sometimes and check raises sometimes, then this is pretty hard to play against and I'd probably abandon my gambit.
I think that in terms of strategy ev that the opponent's worst response would be:
check 100% > donk a lot > donk sometimes and check raise sometimes
If he checks 100% as is pretty much standard, then he's gonna miss a ton of value when I check back a lot.
If he donks a lot, then that's better than checking 100%, but it's still not good because his checking range becomes very transparent.
If he donks sometimes and check raises sometimes, then this is pretty hard to play against and I'd probably abandon my gambit.
check 100% > donk a lot > donk sometimes and check raise sometimes
If he checks 100% as is pretty much standard, then he's gonna miss a ton of value when I check back a lot.
If he donks a lot, then that's better than checking 100%, but it's still not good because his checking range becomes very transparent.
If he donks sometimes and check raises sometimes, then this is pretty hard to play against and I'd probably abandon my gambit.
Again, I'm no expert in HULH but I'm surprised you didn't include just abandoning the chk/raise on the flop and make it a balance of donk/call, donk/fold, chk/call, chk/fold. It seems this would better support the turn where chk/raise then becomes much easier to balance.
Sure, that's what a lot of players do, but I don't necessarily like it unless the guy is known to barrel the turn at a high frequency. I think the reason check raising the flop is so important is specifically because the turn gets checked through a lot relative to the flop, which misses lots of value with your good hands. You also forfeit the ability to check raise and barrel with good equity bluffs, thus forfeiting the ability to win the hand unimproved unless you're gonna bluff the river.
I agree that some value is lost with good hands but those are going to be relatively few and some of the value is made up with an extra small bet that gets chk/called or donk/called and a lot of free turn cards for draws. Also, when the turn gets checked through then, as you said, some amount of bluffs are are going to be viable.
Also when this happens, because unexposed strong hands are still in the range blocking river bluff raises, then some amount of thin bet/folds will also pick up some extra equity.
I think the net value lost is mostly just a byproduct of being out of position. I could be wrong, I'm just modifying some short handed NL strategy so clearly I could be overlooking a lot here.
I no limit, because of the betsize, it's much easier to recoup lost value later in the hand. This is not as easy in a limit game. This is why pot control is important in no limit, but in limit you're just missing value when you slowplay.
Makes sense, thanks for taking the time to explain.
If the game is no limit, then such transparent ranges become much more exploitable by the opponent specifically because of the large bets. You're still only being exploited for a fraction of the bet, but since the bet is typically much bigger, then it's a big enough problem to warrant check calling the flop and turn with strong hands.
Getting back to the specifics of having donk fold, donk call, donk 3 bet, check fold, check call, and check raising ranges in a limit game:
Yeah it seems like a lot to construct, but I think we can simplify the model a bit by considering that certain hands want a certain number of bets going in.
Once we decide that the board is dynamic enough to warrant a donking range, then it's easy to pick the top of our range to donk 3 bet because that's how we get the most bets in the pot. Then the hands too weak to donk 3 bet, but too strong to donk call, become or check raising range. Then we go down the line of our range and a pattern is revealed from the top of our range to the bottom:
bet 3 bet/check raise/bet call/bet fold/check call/check fold
The selection of bluffs will follow a similar trend, with the strongest semibluffs being selected for bet 3 bet. Then there will be a range of semibluffs that aren't quite as strong which get check raised. The bet call region will be value hands turned bluffcatchers and perhaps some semibluffs that will check raise the turn selected for their ability to turn very strong draws. Then a region of pure bluffs that will bet fold the flop. I'm not sure about this final region of bluffs though. Perhaps they should be selected by a process of elimination. I think I'll select this region by choosing my worst hands to check fold, and I'll donk fold bluff with the leftover junk.
It should be noted that on a static board, the preflop raiser will have such a strong range that betting near 100% on the flop will be correct. Therefore there is no need to have a donking range on a static board and checking 100% to the raiser will remain standard.
Yeah that sounds wicked complicated, which is the reason why I want to induce my opponent to donk when I've raised preflop.
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