| Archive for Tagpoker Forum A friendly place for winning poker players to share their strategy to making money playing poker. |
| Polycarpus |
Understanding Nash - hypothetical exerciseThis is a hypothetical exercise, part of it is to see if people understand Nash.Suppose your poker client introduces a new button, the Nash-button. Whenever you feel like it in-game, you can click it and leave the game, or continu and watch. Whenever you click this button, the software will automatically fold or shove every single hand, according to the Nash-ranges. When one of the two players clicks this button, the other player will be informed that you are in Nash-mode and he will only be allowed to fold or shove as well, but he can choose with what cards he folds or shoves. For those unfamiliar: You can find the Nash calling and shoving ranges here. Question 1: What is your calling and what is your shoving range if your opponent is in Nash-mode? You can for example give an answer for 20BB effective stacks, for 10BB and for 5BB. Comment: This question is fairly easy if you are familiar with Nash. If you know the answer, don't post it as you will spoil it for the beginners. Only post the answer if you're not entirely sure. Now suppose you can also miniraise if you are in position and the other player is in Nash-mode. He will never call you, but consider his BB as the new SB, your MR as the new BB, and will execute Nash from there on. (So in 10/20 level you are on the button and miniraise, your opponent will think we're in the 20/40 level and shove or fold) Question 2: In this new situation, when do you open-fold, MR-fold, MR-call and open-shove? You may distinguish different effective stacks in your answer. |
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| BetMagicMoney |
this thread could get intresting for new players imo good work | ||||||
| nachtwacht |
I think it's even intresting for not so new players 
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| U Cook Socks |
I agree, I would have an attempt at it, and not be sure I was right. I think the lack of responses says a lot actually. Early days , see how it goes. Don't be afraid to be wrong peoples, if you learn something from it, then what does it matter ? No one worth anything is going to laugh at you for trying to get better. |
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| dzikijohnny |
Interesting questions. But, the most important thing a player needs to know about nash is it's unusefullness (not that that's a word). Nash is unexploitive play not optimal. And the most important thing you need to know is to forget it after you have learned it. | ||||||
| nachtwacht |
If you forget it, you don't know how to adjust to it... Because thats the biggest part of the questions Polycarpus is asking. How do you adjust if.....
So forgetting it, does not appear to be the best thing to do.... |
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| JamEaze |
In the second situation surely we are now discussing 3bet shoving. Surely this is very different from playing pure Nash, and our opponent would be playing it differently? | ||||||
| nachtwacht |
No, in the second situation we are the SB and opening and BB uses Nash to shove or fold. |
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| two2go |
This thread has serious potential. I'd like to take a crack at answering #2 when I get home later tonight. | ||||||
| Polycarpus |
You are partially right. Our opponent only folds or shoves. So if we are on the button and we choose to miniraise, villain folds or 3bet-shoves. He still uses Nash but "considers" the size of your MR as being the actual big blind in calculating the stacksizes. Is this different from playing pure Nash? --> Yes it is Is our opponent making a mistake playing like this? --> Probably, but the answer to Q2 should prove we can exploit this Would our opponent play it differently? --> Maybe, but some opponents really do this. And even if they didn't, that does not matter. It's a hypothetical situation and we should be able to find out how to exploit this situation at max. |
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| Wannawin |
Saw a forum once where you post your hand/question and all answers were hidden for 3 days so no one could be influenced by previous posts... makes the answers much more interesting.
I will have a think about this friday - interesting post. |
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| The Angler |
OK I'll take at stab at it seeing as nobody else seems to want to.
In question 1 I would play nash against nash, surely that's the only way not to lose? I thought about shoving every hand as nash calling ranges for low blinds mean you'd have great fold equity, but I don't think that would work. Q2. If the option to min raise is introduced, I'm thinking min raise every hand when effective stack is below 40bb and fold to a shove unless holding 66+,AT+,AKs,AKo,KQs. Open shoving the same range. Then switching to nash when the effective stack reaches 40bb. |
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| kierkegaard1 |
i still don't really get nash. the calling side of it anyway. calling off 18bbs w/A4o just seems horrible to me | ||||||
| Brokerstar |
LOL you just beat me to posting much the same answer. I've never fully learnt Nash, sage or chubokowhatever. I seem to do ok without ever fully understanding these concepts. I think if I 'had' to know them to be a winning player I would of studied them for sure. Not saying that it's not good to learn these concepts though but I just never have. 
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| nachtwacht |
That depends. If you know 100% sure that your opponent is playing Nash, then thats the only thing you can do. If you are not 100% sure, then you should not use Nash for calling. The Nash calling table only excists for the hypotetical situations where you do know 100% sure your opponent is using Nash. |
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| nachtwacht |
You don't need to know them to be a winning player indeed, but knowing Nash, has some very intresting advantages. For instance it is a great way of getting out of a horrible situation where for instance a $200 regular signed up at your $50 table. Meaning, the situations where you KNOW that your opponent is better. If you get to the 20BB level, you just switch to playing Nash. There is no way that your better opponent can counter that strategy. The only thing he then can do is use the Nash calling table. At that moment you will both be playing break even. (wich knowing you are playing a better opponent can be a big improvement )
Ofcourse, up till the 20BB level you are still lost
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| sausage |
It may feel horrible, but it is the optimal line if you know for sure that your opponent is playing a pure Nash strategy. Do anything else and you are giving up EV to your opponent. As it is extremely unlikely that your opponent is playing a pure Nash strategy then calling A4o 18bb deep usually is horrible. |
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| kierkegaard1 |
how could you ever know that your opp. is playing a pure nash strategy? doesn't this make it a kind of floored concept?
i only really use nash for <12bbs and only for the shoving side |
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| nachtwacht |
I don't know what "floored" means but you are correct, you never know if your opponent is playing pure nash (except in the example from OP). Therefore you in reality you never use Nash for calling
Correct... but for me that raises the question, why start at 12bb and not at 20bb |
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| hjbear |
he ment flawed | ||||||
| Brokerstar |
Because vs most opponents you can still exploit their weaknesses that deep. 
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| kierkegaard1 |
oops yeah. i'm a grammar nazi, too. fml. and yeah, what broker said. i think i have more of an edge to do some more funky stuff rather than just ship or fold for 16bbs or w/e |
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| nachtwacht |
Wich raises the question, why start at all ? Because if you can exploit your opponent at 20BB, then you probably are still able to do the same at 12BB ps: It would save me a lot of asking if you guys would make for some longer more informative answers
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| Brokerstar |
Nacht it really (as always) depends on how the opponent is playing to be honest so it's hard to expand on exact game plans for every possible situation.
I don't end up in shoving games very often and you can see that from most of my videos. |
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| kierkegaard1 |
the dead money in the pot is worth so much more 12bbs deep compared to 20bbs deep. that's why reverting to nash at around this stage is optimal imo. | ||||||
| genher |
I am not going to have the same discussion again, but if you follow nash you are leaving tons of EV on the table!
I said it before (and I am not the only one saying it) but nash is NOT optimal. it's unexploitable but why would you care about being unexploitable?? How is recreational villain going to exploit me if I decide to shove 96o for 7 BB deep and not 5.2 bb deep???? How on earth is he even going to know?? this is just ridiculous. You want to exploit your villain and not being unexploitable yourself. In theory that means having to make yourself exploitable to be able exploit your opponent's leaks. But it doesn't matter because there is no way he is going to know how anyways. This is not 2003 anymore and you need to squeeze any edge you can. Push and fold ranges only? why? what about having a min raising range and limping range? why would I want to open shove KJs 10 BB deep when I can min raise it and watch villain going over the top with worst hands he would have folded otherwise? or flatting me and giving me a great hand easy to play and in position? I am not folding KJs 10 bb deep to a 3 bet shove anyways, so it's all benefit. Don't get me wrong I think this is a great idea for a thread and understanding Nash is still important to understand end game strategy but you should use it at a starting point to your end game strategy and not an end in itself. I play exclusivelly FTP's superturbos where good end game strategy is paramount and I don't just push/fold, I have a limping and min raising range too (even shallow) depending on my opponent and it works much better than JUST using nash. |
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| nachtwacht |
Very intresting that 2 great minds don't think alike
Why I was asking all the questions is because I wanted to hear your reasoning as to when to, or not, switch to Nash and if so, at what blind level. If i would summarize it, Broker thinks he can still outplay his opponents 12BB deep and Kierk thinks that the value of trying to outplay them is very limited or by doing that himself he is opening up for his opponents to exploit him. (I could say here that Kierk does not think he can outplay them but knowing Kierk is one of the better players, we all know that can not be the case )
Please correct me there if I am wrong. I am also curious if you both ever thought about the following: Broker: How much do you think you are gaining by trying to keep outplaying your opponent ? Kierk: How much value do you think you are loosing by reverting to Nash ? (allthough, since you think playing Nash is optimal at that stage, you don't think you are loosing anything I would think... so I might ask you the same questions as Broker )
Honestly, these two questions are very hard, if not impossible to answer. Thats because you just don't have the sample size to check it out. So basicaly for the Nash thread, I think it's very imformative to just hear some of your thoughts. PS: For those that think this might not have anything to do anymore with the original questions by the original poster, These questions relate to question 2 wich the OP posted. |
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| sootedninjas |
will the structure of the game requires consideration ?
e.g 12bbs on reg speed vs 12bbs on turbo vs 12bbs on super turbo |
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| Polycarpus |
24h after OP, let's give this exercise a little push...
Sorry if my post is rather long to read! About the hypothetical part. Some people said/thought that the situation described here will never happen in reality, but that’s not the point. If in any poker hand, our opponent goes all-in, we make our decision in two steps. Step 1 = our estimation of villains range. This is the hard part! Because our information is limited, we have a small sample size of hands, every villain is different, and villain might not always play his hands the same way. And more: We can never know if our estimation of his range was correct, even if we see his hand in showdown. Step 2 = Make the max. EV decision based on the range we attributed villain. This is the easy part! It’s pure math, it’s objective, you’re either right or wrong, and if you’re not sure, you can ask somebody else to check your math or use software. In this exercise, step 1 is already done for us. We know villain’s range. Only thing that makes it a bit more complicated, is the fact that his range is stack-dependant. So if that scares you off, just pick 1 stacksize, and do the math. If you get it wrong, others will point that out to you and you’ll learn. If you get it right, pick another stacksize and do the math again. Maybe if you do this several times, you will have a complete answer in the line of: For stacks between 0 and 10BB; optimal play = xxxx, for stacks between 10 and 20BB; optimal play = yyyy; for stacks above 20BB; optimal play = zzzz. Or something like that. Using the exercise to improve your game. This exercise assumes our opponent uses purely Nash. In reality this will mostly not be the case. We can see what he does, and think: “he’s a bit looser than Nash, so that means I have to adjust my play a bit and do this: xxxx”. Or, “he’s a bit tighter than Nash, so I have to adjust my play a bit and do that: yyyy”. But don’t fool yourself, if you can’t solve it for an opponent where you exactly know what his range is (like in this exercise), you won’t be able to solve it either for an opponent where you have to estimate his range. About question 1. If a) our opponent uses purely Nash and b) we are only allowed to shove or fold, there is only 1 correct answer to this question: (I’ll spoil it in case some people still want to think it over, which I highly recommend if you’re not sure about the answer.)
About question 2. If we are in the BB, we’re in exact the same situation as in question 1. Our opponent shoves or folds, according to Nash. So nothing else we can do than calling or folding. So for being in the BB, is the answer to question 2 the same as to question 1?
Question 2 in the SB. That’s the hard one. And the most interesting one. Somebody who wants to give it a shot? I got one suggested answer in pm already. You could also post and spoil, but I think some answers – right or wrong – would be good for the discussion, so fire at will! |
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| The Angler |
I did have a go at question 2 from the small blind, was my answer really THAT bad? | ||||||
| Polycarpus |
Sorry, I looked over it
No, it's not that bad, but I'd like to see some arguments. Why do you set the treshold at 40BB and not somewhere else? Why the hand ranges you state, and not others? We can "guess", and find a +EV strategy, but as we know villain's range here, we can solve this question mathematically, and come up with an exact answer that gives us max EV. If you did the math to come up with this stacksize and these ranges, please post it so everybody can discuss. |
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| Polycarpus |
And an answer from a pm:
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| The Angler |
The stacksize being at 40bb was because the OP said villain using NASH treats a min raise as if the blinds were double. NASH will fold more than 50% while the effective stack size is above 40bb so it's +EV to min raise every hand. The calling and open shoving range I used is from here http://www.pokerstove.com/analysis/allin.php that range has at least 10% edge Vs a random pusher/caller while NASH isn't random it's loose enough that the range will have good equity. I'm sure if you plugged all the hands NASH shoves at 20bb into pokerstove you could come up with a range with greater than 50% equity making them +EV to call with, but to be honest I was a little lazy.
Once the effective stacks reach 40bb or less than NASH is no longer folding more than 50% of the time so the only way not to lose EV is to switch to using NASH yourself. |
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| Polycarpus |
The Angler,
You make some good points, but let me point you towards a weak spot in your reasoning. What is wider, the Nash calling range for a 20BB shove, or the Nash shoving range for 10BB? Taking that into account, suppose you're in the SB with 20BB effective stacks and you get dealt AA. Do you shove? Taking the answer to above into account, you may want to modify part of your answer? |
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| The Angler |
I see what you mean the shoving range at 10 is much wider. So a min raise would get more shoves than an open shove would get calls, so min raising and calling the shove works a lot better. | ||||||
| genher |
that was the point of my KJs example. if you min R KJo at 20BB deep and villain consider it to be 10 BB because u always min R and therefore villain plays Nash (as polycarpus said), he shoves his K2o that we have crushed. But if instead u play stricktly Nash push/fold and open shove KJo he is folding his K7o. it works much better and this is true at pretty much any stack size. |
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| two2go |
So if I'm understanding it right we minraise the top of our range when we're way ahead of his shoving range (bc he can shove lighter than he can call esp. bc of the 2x blind increase), and shove the marginal nash hands so we have more fold equity at the lower blinds? Basically we change the blind level so he is forced to shove a worse range against our stronger hands than he will be calling against our weaker hands. Pretty cool. | ||||||
| genher |
Well, probably not that simple otherwise: 1. it becomes a bit obvious you probably need to balance your range a bit with some stealing hands 2. sometimes villain's flats so you need a hand that is easy to play too (for instance A3o is top of your range but is awful to play if he flats 10BB deep)
But I am probably sidetracking from polycarpus's original questions and we probably should stick to ansering that. I have no idea if it's the way he intented his thread to go.
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| Polycarpus |
To genher: let's make this thread about the math only and percieve villain as a bot. So don't think about balancing your range etc, but only about max EV decisions.
Balancing in HUSNG is overrated anyway 
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| Polycarpus |
I'll be posting part of my "solution" to this topic later today. Still have to see when I have time. Also: I can't download pokerstove here because I'm at work. Could somebody verify something for me?
==> At what blind level does the Nash shoving range correspond with (about) 50% of all starting hands? Could somebody check that and reply here or pm me? Thanks already! |
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| nachtwacht |
Nash and Stove have different understandings about hand value. For instance, 22 is not in the top 58.5% of hands according to stove but for Nash it is a push at the 20+ BB level.
So having Stove do it automaticaly will not work. So lets select the hands manualy then
Below range is 50.5% of hands Taking out K4o will get you 49.6% This is everything Nash, 13BB and up. 22+,A2s+,K2s+,Q3s+,J4s+,T6s+,95s+,85s+,75s+,64s+,54s,A2o+,K4o+,Q9o+,J8o+,T8o+,98o,87o |
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| Polycarpus |
So how about this for a first part of the answer to question 2 - from the SB:
Suppose miniraise our hand, we risk 1,5BB (our raise), to win 1,5BB (the blinds, the dead money in the pot). That means that, suppose we fold all our hands to a shove, it is +EV to miniraise every single hand if villain shoves less than 50% of his hands. (When he folds, we win 1,5BB, when he shoves, we lose 1,5BB) 50% of the hands correspond with more or less the Nash shoving range for 13BB (thank you nachtwacht). But as villain is perceiving our MR as the BB, that means actual stacks are 26BB deep. Conclusion: Above 26BB stacks, we MR every single hand. If villain shoves, we call only those hands that are ahead of his range (which we know). Under 26BB stacks, villain will shove >50% of his hands, we only MR the hands we want to call a shove with and open-fold the rest. I think this is the baseline for our answer. Two more questions rise here imo. 1) Is there any argument for open-shoving any hand above 26BB? (Personally, I don't think so) 2) The lower the blinds, the more we want to have fold-equity. From what point and with what hands do we want to openshove? And two more remarks: 1) I got inspired a bit by this post about 3-betting behaviour. Definitely worth reading. 2) I'm here to learn just as all of you. If you think my reasoning is flawed here, please don't hesitate to point that out to me. |
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| nachtwacht |
And I was thinking you allready had the answers
You are forgetting a small thing in the answer.... You mention that we are only calling the shoves that we know we are ahead off. Thats a mistake. There is also a considerable amount of dead money in the pot. This means we should be calling a lot wider. (how wide you would need to calculate and will change when the blinds go up)
It would make it a lot easier.... the problem is in the assumption as to what villains calling range will be. He will fold a lot more hands than the Nash range.... So if we assume he will only be calling the top 10% of hands, we pick up 1.5BB every 9 hands and the 10th time, when we are called, we still have roughly 30% equity. (that is our random hand against his 10% range) So if stacks would be 30BB, every 10 hands the following happens: we win 13.5 by villain folding. We are called 1 time and in that 60BB pot we win 18BB In the end... that still looks like +EV to me... and the lower the stack size gets, the more +EV it will become. (but this all depends on villains calling range !! That will become wider also when stacks get shallower) So assuming we have a lot of fold equity, yes, shoving can be a good play... and one would need to calculate if it would be more or less profitable than minraising and then calling or folding.
Since open shoving totaly changes your "question 2" because villain does not get to play Nash, just call our shove, it realy depends on his calling range. I would suggest to, at a minimum, just follow Nash. This means, at 20BB we shove whatever Nash says. Also, keep in mind, Nash does not say "20BB" it say's +20BB. So you might even start at 30BB my example, with that given fold equity suggests its allready profitable there so why wait..... Ofcourse, if villain sticks with only calling 10% of his range, we can shove wider than Nash. (and start at higher blinds !) ps: since you know the exact play of villain, your question 2 can be answered to the exact holding. You could put it into CardRunners EV to check it out exactly. |
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| The Angler |
Correct me if I'm wrong here, surely it's 36bb not 26bb that you have to stop min raising? At 18bb Nash is shoving just over half of all hands (85 hands) So at 36bb over half your min raises will be shoved over making it -EV to min raise every hand. | ||||||
| nachtwacht |
At 13BB Nash pushes about half the hands. Therefore Poly uses 26BB ps: even if you get shoved over more than 50%, that does not mean it becomes -EV. There is also EV to be won by calling since there is money in the middle. |
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| The Angler |
At 13bb Nash is pushing 99 out of 169 hands - 58.5%
Do the times we're min raising and calling a shove make up for what we lose in fold equity? I'm not sure on the maths involved here..... how can we know if calling a shove with less than 50% equity is +EV or not without knowing exactly how much money is in the middle? We know both stack sizes but without knowing the blinds I can't see how to workout a solution. I ran a quick calculation in Poker Stove, vs 22+,A2s+,K2s+,Q3s+,J4s+,T6s+,95s+,85s+,75s+,64s+,54s,A2o+,K4o+,Q9o+,J8o+,T8o+,98o,87o (Nash 13bb+) we can min raise and call a shove (if my maths is right) with a massive range of hands; for example with a range of 33+,A2s+,K2s+,Q2s+,J4s+,T6s+,96s+,86s+,76s,65s,A2o+,K5o+,Q7o+,J7o+,T7o+,98o (50% according to poker stove) we have 50.186% equity It just seems absurd to min raise and call a shove with T6s though. The more I think about this the more it's giving me a headache. |
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| nachtwacht |
Angler, I don't know why but at some point in your post you are using the range I am giving but you start off with saying that at 13bb Nash is pushing 58.5%
It's one or the other... and your 58.5% of hands is wrong because in that calculation, you are putting suited and unsuited as the same number of hands. In reality there are 1326 different starting hands, not 169 As to it being absurd to be calling a shove with T6o, it is. T6o is only 40.086% so that is -EV for that specific hand against the range of Nash 13bb+ You have to check how every specific hand does against the total range. You can not check a complete range. and yes, if it is +0.01 EV, then it is not just profitable in theory, it is also in practice. Ofcourse, it is very marginal, but it is profitable. |
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| The Angler |
OK that makes sense, thanks nacht.
I was using the same range as the one you gave anyway. From looking at the nash chart I can see what hands are pushed, I just thought it was 58.5% because I'm retarded and totally over looked the combinatoric aspect as you said.
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| genher |
yes my apologies polycarpus, I realized I was side tracking the thread. I stop.
Yes, I very much agree with that. (it was meant as: include stealing hands too) |
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| Polycarpus |
If you get shoved over more than 50%, it becomes -EV to MR with a hand you won't call a shove with. So you only MR with hands you want to call a shove with. |
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| Polycarpus |
I don't see your problem. Stacksize is expressed in blinds. So we do know the blinds and we do know how much money is in the middle. Also: We don't care how much money is in the middle, because that's irrelevant here! Let's say our stack - before posting the blinds - is 30BB. We get some random hand in the SB and we miniraise. For the point of view of our opponent, we're now in a situation where he considers himself in the SB with stacks of 15BB. He checks his Nash shoving range for 15BB and sees it's a shove (when that's the case), so he shoves. We know he is doing just that, so we check our Nash calling range for 15BB, and call if we're supposed to. Nash takes the blinds into account, and seen the perspective of the case, there's nothing more than the blinds in the middle. |
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| nachtwacht |
So what you are saying is, our MR is -EV because we know we want to call a shove... My point is, with looking at it that way, you are isolating the MR and only looking at that particular action. However, since we know what is going to happen in the rest of the hand, it might very well be a +EV strategy to take an action that in isolation, might be -EV. Lets try to give an example. Suppose we are holding 72o on the SB We are playing a very straight forward villain. He will only go all in on the flop if he is holding AA. So we minraise from the SB, villain calls. If we isolate that particular action, it is definetly -EV. Against his range we are like 35% to win. However, knowing he will only continue after the flop if he is holding AA, we can simply take a stab on the flop and we know he will fold. So is the action of minraising the 72o -EV ? Same applies here. If we know villain will shove on us with 60% of his hands, we get the following results in stove: equity win tie pots won pots tied Hand 0: 56.078% 54.45% 01.63% 915967800244 27398180256.00 { 22+, A2s+, K2s+, Q2s+, J2s+, T3s+, 95s+, 85s+, 75s+, 64s+, 54s, A2o+, K2o+, Q5o+, J7o+, T7o+, 97o+, 87o } Hand 1: 43.922% 42.29% 01.63% 711488904044 27398180256.00 { random } We are roughly 44% with our random hand (that is 100% of hands) So lets imagine that blinds are 10-20 and we only have 200 chips. (so we have a 10BB stack) We minraise 100% of hands, to 40. Villain shoves on us. This will lead to a 140 chip pot and we only have 60 chips behind. Easy call since we are 44% against his range. With the fold equity etc. I would think this is still a +EV strategy. So villain is calling us wider than 50% and we minraise wider than 50%. The thing is that we just have to call with all the hands we are minraising with... wich is 100% of hands. |
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| BetMagicMoney |
^^this
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| Polycarpus |
If you plan on MR + calling his shoves with ATC, isn't it more +EV to MR the hands that are ahead of his shoving range (to maximize equity), and to open-shove the hands that are behind (to maximize fold-equity)? |
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| nachtwacht |
You don't hear me say anywhere it is the most +EV line to do X or Y
For instance, just for tilt control, I would probably still open fold 72o knowing that I have to call a shove and look stupid if I do (wich by the way is definatly -EV in the example above... so I should rethink that )
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). The great thing about this problem is we know our opponent’s exact shove /fold range and there’s a small number of options so… Pokerstove. My idea is to break up the problem into each possible action, calculate the corresponding EV for that action against NASH, and choose the action with the highest EV. So here it goes (starting with the easiest cases first).