Introduction to Short Stack Preflop Play
Posted by Daniel Dvoress
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Thanks for the video! I have finished watching it yet, but it seems very interesting. I like your toy 20BB deep game. Unless I'm missing something, I don't agree with your argument showing that we cannot min raise ATC. Right, most of the time we will fold to a shove, but when we can call the shove we are ahead.
I computed in PPT the equity of 57% vs 37% (these are the number I get for Nash push/fold from ICMIZER) and the caller has 54% equity. (Of course, the ranges for 57% vs 37% in PPT do not need to be exactly those in Nash, but I guess they will be close enough.)
Therefore, the equity of minraising ATC is (let's assume blinds are 10/20 and we have 400 chips):
0.43*420+0.57(0.63*360+0.37*0.54*800), which is roughly 401,
so by minraisng ATC we are winning one chip over our starting stack (without counting the SB, that we would lose if we fold some hands).
Am I doing something wrong?
Now I have finished watching the video and I have made the same calculations for your proposed solution. The result is 399,66 chips, which is worse than minraising ATC.
Why do you say that your solution is sort of a Nash solution? I think you're giving way to much importance to the fact that villain doesn't resteal more than 50%. (After all, the Nash push/fold solution at 10BB has negative expectation for the SB despite the fact that he is stealing more than 50% and that more than 50% the BB will fold).
I see that sharfeek has now made some similar comments below.
What you are saying is that raising ATC as the SB is profitable (like you said the SB would win about 1 chip at 10/20, 400 chips deep). This is correct. However, this does not mean that it is the best or the nash play for the SB.
In fact, it's easy to show that raising ATC is going to be profitable as the SB, because if you decide to raise ATC from the SB, the toy game reduces to a 10bb push/fold game, in which the BB has an edge.
Also, recall that hands that a nash solution is not going to contain hands that are individually -EV. You can check that you are losing quite a bit with your bluffs that do not contain blockers if you choose to raise ATC 20bb deep.
I'm not familiar with at all with ICMIZER, but that result can't be right as the strategy of raising 84% from the SB in our toy game is quite +EV for the SB. Are you sure you didn't accidentally miss something or make a wrong input?
Thanks for the answer Daniel. Yes, the easy way to say that raising ATC is +EV is that it reduces the game to the 10 BB push/fold game where you are in the BB. Of course, as you say, this doesn't mean that it is the best possible play. However, I still don't understand why your solution is +EV. We are folding 15.7%. Out of the 84.7% that we are raising, we are picking the BB 51.3% of the times and losing 40 chips 100*0.487*0.62% of the times. Finally, 100*0.487*0.38% of the times we call the shove and then our probability of winning 800 chips is 52.1%. This is the only thing we have to use some software to compute. I used ProPokerTools and I just looked for the equity of 38% vs 48%. The ranges that PPT gives for 38% and 48% will probably not be the same ranges that you give, but I would assume this does not make much difference. Therefore, I get that the expected value of your solution (with the PPT ranges) is:
0.157*390+0.843(0.513*420+0.487(0.62*360+0.38*0.521*800), which is less than 400.
The only figure that is not completely correct here is the 0.521, which comes from the ranges in PPT. In order for your solution to be better than minraising ATC, we need to have a probability of winning when we call the shove >52.9%.
I will try to do the computation with your ranges, but it seems pretty close. How do you know that the strategy of raising 84% is quite +EV?
Edit: OK, now I read your answer to the other comment and I guess that you know it because you saw the expectation that CREV gives.
I think this is the mistake in your calculation:
"losing 40 chips 100*0.487*0.62% of the times"
Could you explain why that is the way it is?
That number comes from the fact that villain is shoving 48.7% of the time and we are folding 62% when this happens. I think there's no problem with that.
The mistake was that I was computing the equity of 38% vs 48% and this is not what you were doing. You were calling 38% but this was 38% of the 84.7% that you were opening. Therefore, you are calling (38*84.7/100)%, which is like 32$ of all hands. When I compute 32% vs 48% I get 53.53% equity in PPT and this is good enough. (In other word, the 0.521 that I was using in my previous formula, should be replaced by 0.5353.)
I hope this makes sense.
Hi, Daniel! First of all let me thank you for the video!
Here are some thoughts and questions.
While watching a video i opened CREV and created the situation where SB minraises 100% of hands.
As BB response i used 10bb Nash Eq. which says to push about 58% of hands and fold the rest.
And i was surprised to see that despite the fact about 63% of hands SB minraises have -EV the whole strategy has +9bb/100.
You can see the screen below:
I agree with your calculations in 10bb POF game (-0,045 for SB) but in case we play 20bb deep the situation is opposite since SB posts big blind hence the whole strategy of BB becomes minus EV (-0,045*2=-0,09 as you can see on the screen). It means that minraising 100% hands in 20bb is still profitable which contradicts your version.
Following this logic i found the maximum stack depth in which SB can auto profit in POF game:
As you can see if effective stack size is below 15.5bb BB can make an auto profit in POF game and forces SB not to minraise 100% hands.
Actually i'm now sure if i'm right so it would be cool to get your feedback!
I kind of addressed this in the post above, but just to clarify: yes, minraising ATC from the SB 20bb deep in our toy game is going to show a profit from the SB. However it is not the optimal solution. If we play our toy game and you play an open ATC strategy from your SB and I play my open 84% strategy when I am the SB, you will lose because my strategy is better for the SB. You can see this if you put both into CREV - yours shows +0.09 for the SB and mine would show +0.12.
Additionally, keep in mind that the solution after you decide to open ATC 20bb deep and 10bb push/fold are exactly the same game. So it shouldn't be surprising that when you open ATC from the SB you profit +0.09bb. Like you said, in 10bb p/f, the SB is at -0.045, which means the BB is +0.045. But the BB there is just the SB that is opening ATC (with each blind being "worth" half as much). 0.09/0.45 = 2 so everything checks out.
That might have been a roundabout way of explaining things, but I think this is just one of those things that might seem a bit confusing but once it clicks you just get and I'm trying to make that happen. Let me know if my replied helped and answered your question, and if not I'll try again.
Sorry to clutter with a bunch on separate comments, but this is general one although it does apply specifically to answering the two questions above.
When trying to conceptualize what your goal is here, think about whose expectation (in this particular case, the SB's or the BB's) you are trying to maximize. Here, the solution is going to be the one where the SB has the highest expectation. So basically, we lock in an opening range for the SB, and then the BB responds by shoving an optimal range. Now imagine we did this for 1%, 2%, ..., 99%, 100% open ranges for the SB. The SB is going to be showing a profit with a bunch of different open ranges (in fact, any open % above 50% is going to show a profit (!) for the SB given an optimal BB response to that particular open %) [I did this quick and roughly but that should be approximately correct]. However, the nash solution is going to be the one which shows the highest expectation for the SB.
Thanks for detailed answer. I probably understand what you are talking about.
Does the statement that all hands in our Nash range should have +EV applicable to constructing a limping range? I mean if we have 3 ranges from SB (mr, limp and open fold) do all 3 will contain at least 0EV hands or it is possible to have -EV hands in any range?
We have some K6, Q7, 98 and other hands that have miserable +EV playing it minraising. If i understand you correctly we can play them more profitable by limping. My question is if we balance limping range by adding some value so that villain couldn't raise too effectively is our main goal to have +EV strategy with all +EV hands in our ranges despite the fact that we earn more playing for example AA more +EV by minraising it rather than limping? In other words do we consiously strengthen our limping range knowing that value hands will have less +EV but K6 and other marginal hands will compensate it making our whole strategy more +EV than in case we have only MR/F ranges?
It's also interesting what other concepts and rules we are going to use while constructing our limping range?
When you are asking "do all 3 will contain at least 0EV hands or it is possible to have -EV hands in any range?" - do you mean -EV in the absolute sense, or -EV in the sense that you are making less money with that hand as opposed to doing something else with it (but it is still profitable in the absolute sense)?
The answer is no in for both cases but for different reasons. In the first case, it doesn't make sense to ever do something that is -EV in the absolute sense - if some hand is -EV as part of some range, why would you not take it out of that range? In the second case, the answer is still no because you should take the most +EV line with any individual hand. However there will be mixed Nash solutions where you some hand is only used as part of a range x% of the time.
That last part is going to relate to the answer to your second paragraph. Yes, you would need to include some strong hands in your limp range so that your opponent can't raise/shove on you with impunity whenever you limp. So obviously the first reaction to this would be that now we are taking a hand like AA which is a massively +EV min/call and taking it out of that range to take a less +EV line (which would contradict the answer to case 2). However, this isn't true, because with properly designed ranges limping the AA shouldn't be less +EV than min-raising it. Let's think about how you would try to arrive at a Nash equilibrium if you are just kind of half-blindly poking around. Say you start off by limping only mediocre hands and not balancing at all. Your opponent is going to make the obvious adjustment and start raising/shoving on you a bunch. But when this happens, limping the AA is no longer less +EV than min-raising it was. So the point at which a strong hand would transfer over from one range to another (or split up for a mixed solution) is going to be the point at which going to that other range is going to be the more +EV thing.
Generally, there are two ways to approach this - the first what I just explained above and the second is the one that (I think) you are using where we take some strong hands in order to "protect" weaker parts of our range. The former is correct, I'll try to explain with a more common, general example.
Often players will check back a strong hand on the flop with the logic that they need "protection" against turn probes from their opponents (so this would be what I think is your approach where you kind of go: crap, my flop check back range is quite weak here, better check this strong hand back). However, take a look at what is really happening. Your concern is only valid if there is the condition that the opponent is going to be probing the turn a lot (since if it happened infrequently, why be concerned about it?). But given the condition that the opponent is probing the turn a lot, checking back the strong hand is now valid - not because the weaker parts of your range need protection - but because it actually becomes the more +EV line with the individual hand.
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As for your last question, it's too broad to answer. There are general ideas that we would use but they are all kind of obvious (limp hands with more post-flop playability, raise hands with blockers against shoves, etc.)
Very useful. It seems to me that you're trying to explain explotive strategy and approach to the game. I mean we know some wrong villain frequences an make the most profitable adjustment we can with each particular hand.
What i want to talk about is designing well balanced ranges against qualified regs.
Do i understand you correctly that in this case we are going to find out Nash solution that can also contain mixed strategy for particular hands like in the example with AA? (Using weight option in CREV) Am i right?
Can we say that in this case we have the maximum EV for all hands we can practicaly have against villain's max exploit strategy trying not to be exptloited?
What i want to say is that i understood the concept of playing max exploitive but i don't have a clear vision of how to practically balance our preflop ranges.
Btw sorry for many mistakes, English isn't my native language.
I gave the example that way so that it would be possible to get an intuitive feel for how you get to a Nash solution, even if you know nothing about game theory. And the way that you would arrive at the solution would be to have the players keep making exploitative adjustments until they stop adjusting to each other, and you are at the solution. So in my example it would (this is really simplifying it, but just so you get a feel): Player A limps only weak hands. Player B adjusts by shoving a bunch on his limps. Player A adjust by limping a bunch of strong hands along with his weak hands and his limping range becomes very strong. Player B adjusts by shoving much less. Player A adjusts by taking out some, but not all, of his stronger limps. Player B adjusts by shoving a bit more. Player A limps a few more strong hands.... etc etc until they close in on some range where they are no longer adjusting it. Now this example is really dumbing it down and also has lots of issues (for example, when Player A first adjusts by limping a bunch of strong hands, his minraise range consequently becomes very weak). But the point of the example was to a) show the first step of how we could eventually get to a Nash equilibrium and b) show that there exist conditions such that once a limping range is developed and proper adjustments are made, limping strong hands would not be "less +EV" than minraising them. This was important to address because it's necessary to understand that even when developing balanced GTO ranges you are taking the best line you can with a hand (as in the most profitable line for that hand).
So that last statement might make you ask - shouldn't hands almost never be split into two ranges? (since, for a hand to be part of two ranges, that last statement implies that the EV for the two gam tree branches has to be the same for the hand to be split, and it seems like that would be a rare occurrence). But in actuality, it's not that rare an occurrence, because the EV of doing something with a hand can shift quite a bit depending how often you take some line with that hand. To give another simple example the expectation of a minraise (your EV GIVEN that you decide to minraise) is much greater with TT+ if you only minraise 1/6th of your TT+ combos). Hopefully it makes sense why and you can see how it related to the example I gave above and why I used it.
So to answer your question - for sure it's possible for a Nash solution to have mixed ranges.
This is even easier to see for stuff like 4-betting. Let's say the hands available to you to 4bet bluff are: A2s, A3s, A4s, A5s, but based on your value range you are only allowed to bluff 4 combos, so 25% of that range. So when you are 4bet bluffing, should you bluff: A2s 25% A3s 25% A4s 25% A5s 25%? Probably not, since A5s is a has more straight potential and therefore more equity against your opponent's range. So then, should you go: A2s 0%, A3s 0%, A4s 0%, A5s 100%? Probably not, since now you won't get paid much on 5xxxx boards, and don't have 2xxxx, 3xxxx and 4xxxx boards covered. So maybe the solution is something like A2s 15% A3s 20% A4s 25%, A5s 40% where the mix takes into account both the equity of the hand and the consequences/implications of having some particular hand too much/ not enough in your range.
Sorry for the wall of text.
Thank you for posting this, Daniel! Very appreciate it and really have less and less questions left to ask.
the EV of doing something with a hand can shift quite a bit depending how often you take some line with that hand. To give another simple example the expectation of a minraise (your EV GIVEN that you decide to minraise) is much greater with TT+ if you only minraise 1/6th of your TT+ combos
What you mean is that if in first case i have say the EV1,1 with minraising TT (and have strong mr range) against max exploit and in second case use 2 ranges (1/6 mr + 5/6 limp with TT) and have EV1,2 after max exploiting us even given the fact i made the mr range weak? (And the reason for it that while i made mr range weaker my limping range became much stronger what make me feel good about adding some weak hands in it)
So are you saying (just to make it clear) that splitting a hand like TT (and probably many others) into 2 ranges if very often has overall more +EV even if villain play max exploit against both our lines?
In other words - our plan in building ranges is probably something like:
1. We design one line (until it includes only hands having +EV)
2. We make an assumpsion that many hands which are in this range or are open folded can be played with more EV that in current situation so that the EV of our whole strategy is higher than in point 1.
3. We are starting to work with weights of hands (time after time trying to find the most profitable option) designing the whole strategy so that it has good board coverage and villain can't have the EV more than in point 1 (when we had 1 range)
Am i right?
So are you saying (just to make it clear) that splitting a hand like TT (and probably many others) into 2 ranges if very often has overall more +EV even if villain play max exploit against both our lines?
Sam Greenwood has a video "On not splitting your ranges" and can be insightful for this question, also as the "thinking out loud" Galfond series on balance. Every single portion of your range you need to be balanced about it, some parts would be raise/fold, limp/fold, raise/call, limp/call or fold. If you aren't balanced about it, your opponent can max exploit you. Of course there are portions that you would fold pre but balancing properly the hands you are playing would make you the highest EV for each line you may take.
Now you need to decide to limp or raise inside a context. The highest EV would be the same strategy that achieves the Nash equilibrium, because, by definition, it is the best response to your opponent strategy. Considering that you create a limp/fold range that is very wide, your opponent can profitably shove a wider range than yours and also make profit from it, because the portion of your limping range that you call a shove is so infimum that he's making a high % of the 0.5 extra bb you posted voluntarily. And again, you can't create a wide limp/fold range to later create a strong limping range and expect your opponent, if he is balanced, to shove a portion of his shoving range. That is -EV.
I don't think splitting in to 2 ranges is the correct definition of what you are saying and merging a hand on the top 5% into two different strategies is better than splitting TT into raising and 85s into limping. If yes, I totally agree. I don't know if I focused on what you need, but anything you can ask me.
Oxota, excellent video.
Daniel Dvoress, ScienceBitch1 and others who are interested
I've just made it in CREV to begin with something:
Please check the file
Click to download
Some questions:
1. Do 2 opportunities to raise me after limp (3bb or shove) look good or should i add other raising sizes such as 2bb 4 bb etc?
2. Is it ok for BB ro realize 110% of its equity after raising a limp and being called by SB or there should be another number?
3. The same question about realizing 80% of equity when checked back to our limp
Sorry, I skimmed over this the first time around and then it didn't show up in notifications so I forgot about it.
I can't open that file in CREV - am I just being a fish or is it because I haven't downloaded the new beta?
To answer your questions generally (will revise once I get the file open):
1. Are you asking in terms of what the GTO raise size would be for the BB vs. a SB limp, or what you should do? I don't know know what the proper GTO sizing would be - I'm 99% sure it would not be a minraise but beyond that it's hard to say. However you should probably make the raise size what you see most commonly in practice, so 3bb/shove seems fine.
2. Can't see what the range is so it's again hard to say, but you should break the hands into groups and assign different equity realization percentages to different groups. For example AA is not only going to have way more equity than say 97s, but it is also going to realize way more of its equity. So ideally you don't want to just have some single checkdown % for your whole range. If you do, the stronger your range the higher the checkdown % should be, but again I'd have to see the range. I'd be careful assigning more than 100% realized equity for when you are OOP, though, unless your range in insanely strong.
3. For this you have the same considerations as above, and again I have to see the actual range, but I would be more comfortable assigning a higher checkdown % there. Yes your range is weaker, but you are still fairly balanced, your opponent also has a range that is weaker because of preflop action, and most importantly you are in position.
Daniel, Rapha, it is very cool that you continue our dialog! Really appreciate it!
Daniel, great post, and yes, the problem is probably that you need to update your current version of CREV.
That's interesting that you offer to break hands into groups.
In what groups i should break them into and what % of realization you think is reasonable for each one?
And another important question is do we need to set equity realization for both players in HU or it is ok to do it for one player (if yes, should it be SB or BB)?
I realise that questions are complicated but there are so little qualified people who can answer that every your message is super valuable for me!
If we are playing balanced poker, BB can't realise his equity at all. Even considering a standard game with complete information, the probability distribution of our strategies should look very flat for every single situation we play. Considering that, also our range will be.
Changing the size on limp/3b will only make a part of his range -EV to call. He may adjust taking a part of this range that is unprofitable to call now to his 4b range, considering the value of its blockers and how properly balanced the strategy will be.
What do you mean by this?
If our strategy set is balanced in our range, the R (how much equity we need to realise OTF to make a preflop call) from the villain would never be 100% or close to that.
Hey, very very intresting video for players like me that have always played 100bb+ ! Thanks !!
I didnt understand how you could know at what stack you could no longer min 4b/5b since this 6bb toy game.
juan,
Do you mean how we can know an what stack we can no longer minraise and should only push or fold?
It's not that we can't, it's just that at a certain stack it becomes nonsensical to. To take an extreme case: say stacks are 4bb. If SB minraises and gets shoved on he is calling 100% of the time since any hand will have 25% equity or more against a resteal. So he might as well shove. In our toy game there is no difference between the two strategies at 4bb deep because the BB can't flat.
In terms of how you would figure out the stacks at which you can no longer minraise: you would basically lower and lower stack depth until you get to a point where the worst hand SB raises is still calling a jam, and that is your cusp.
Your last comment you said it wouldnt be prudent to 3bet small in the BB when 13-15 bbs effective, and that this video should show us why. I am not seeing how this video has shown us why. can you expand?
Sure. Does it make sense why you shouldn't minraise from the SB when we are 6-7bb deep? If it doesn't, let me know and I'll backtrack.
Working on the assumption that it does, while it doesn't directly follow that no minraising 6.5bb deep --> no small 3betting 13bb deep, one does hint the other. This is because once the SB minraises 13bb deep we are basically playing a slight variation of a game half as deep (where the would-be BB is getting dealt the top 75% of hands or whatever). The major differences are that in the 13bb game we a) are OOP and b) get to choose the action by calling, both of which would be reasons against considering a small 3bet.
[19:00] How is it 'easy to come up with a solution for the big blind [3bet]' when given the small blind open? We still need to adjust the BB's shoving range to the SB's calling range which they just change back and forth. The only method I can think of is using a loop which loops through all the ranges and comparing for the best performing tree at the end.
[20:00] You tried to explain how the SB open and SB call relate, by reducing it to a 10bb game. How does not getting dealt the bottom 12% affect our calling range in the 20bb game?
Excellent video btw, watched it more than 10 times, as an HU CAP player this really helped me understand the game and its invaluable for me. I'd love to see your approach to constructing a range for c-betting (very looked over topic on RIO), delayed c-betting, and 'probing and barreling' for CAP games.
Hey Daniel when you were talking about 10bb unexplo push/fold equilibrium and referring to 43s q7o and how we don't shove these 100% because of how many future hands we may play vs villain: can you elaborate on this please? For instance 888 poker has a pof game where 5bb is the min/max buyin but there is no cap on your stack so can get very deep obviously.So if we were to increase our stack to 40bb while villain has 10bb, should we be folding these hands because it is very thin and we risk doubling our opponent up when we have an edge with the bigger stack if we are sure villain is going to play on for 500 hands more?Ofc we would be employing a limping strategy in this scenario but i wouls still like to hear your thoughts on this and pof on 888 if you are aware of these games.
Hi Jimmer,
This video is from a while back, could you give a timestamp for the part where I said this? The way the question is asked makes me think I either misspoke or misscommunicated.
Hey Daniel It's from 13:30 to 14 minute mark where you say we should play a mixed strat here (i'm assuming you mean shoving these hands x% and limp y%) with hands like q7o 74s @ 10bb stack depth. You mentioned that if we play future hands with a villain we should take this into account. Can you elaborate on that please?
Hi,
No I am not talking about a strategy that involves limping: those hands should be shoves with a non 100% frequency in a push/fold only solution. This sort of mixed strategy (folding some hands sometimes and shoving them sometimes) comes up occasionally in push/fold equilibrium with borderline hands which are close to a 0EV shove. The reason we shove those hands sometimes is because if we always shoved them our range would get wide to the point where the opponent response would be to call a range that would make those hands -EV shoves. However, if we never shoved them, the opponent response would be to call a range that is tight enough such that shoving those hands would once again be profitable. So the solution is somewhere in between, and therefore those hands are shoved sometimes.
The future games is a mostly unrelated topic but I mentioned it here because accounting for the EV of future hands will have an impact on your close to 0EV decisions. The way that it applies here is that a hand like Q7o is shoved with 100% frequency in nash solutions that do not account for future hands. However, when you start accounting for future hands, particularly for the fact that if you fold the SB you are necessarily going to be in the BB the next hand, Q7o is now sometimes getting folded. This is because in a 10bb push/fold game the BB actually has the edge. So you are essentially passing up a close to 0EV spot knowing that your next hand will be on average more than 0EV.
TY Daniel ^^
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