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February 5, 2015
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Hey TPE peeps,
So I am in the process of researching Holdem Resources Calculator thoroughly for my blog. Well the pokermonk told me how much work goes in to setting up a blog. Man, he wasn’t kidding. I am a pretty lousy poker player, so my poker content won’t be helping too many people crush any time soon, but I expect I will be asking the kind of questions a lot of other serious amateurs will be asking…and hopefully more. But I don’t want to write a half-ass review of this product… at least, I am determined to research it thoroughly. But unfortunately for me, in trying to research the thing, I have run in to a mental brick wall. I must have watched a 10 minute segment of a webinar HRC tutorial on Pokerstrategy five times before coming to the conclusion that my confusion is not related to the calculator’s graphical output or format, which I thought was the case, but rather that my understanding of the Nash equilibrium is still, after all these years of study, seemingly lacking some crucial component(s).
Between 30:00 to 41:00 the dev is discussing the “best response” feature of the calculator.
I know we have talked elsewhere at TPE about the NE and how it might not even exist outside of two player games. I presume Andrew must have meant post-flop, as HRC certainly has no trouble establishing NE solutions pre-flop for multiple opponents. At 30:42 the Nash equilibrium has the SB pushing 100% and the BB calling 13.4%. However, if the BB moves his calling range away from equilibrium by calling wider, the calculator is able to give us the “best response” for the SB when confronted with the new, wider BB calling range.
I am not expecting anyone to watch the section of video between 30:00 and 42:00, although it actually is a fascinating nugget of Nash theory, but if we look at the graph at 32:00, [and I tell you that the (horizontal) x axis is the BB variable calling range, the (vertical) y axis on the right is the “best response” %, and the solid green line represents the SB’s best response (in response to a variable BB call range)], we can see, for example, that if the BB is calling 30%, the best response of the SB is to tighten up massively, and only be shoving 15% of hands.
So my question is this: initially, we are in equilibrium with our ranges of 100% for the SB push and 13.4% for the BB call. The BB moves away from equilibrium by widening his calling range. So now we have a situation where the SB is still shoving 100% but the BB is now calling 30%…we are no longer in equilibrium. The best response, after noticing that the BB is calling much wider, is for the SB to tighten up considerably by shoving only a 15% range. Are these new 30%(BB call)/15%(SB shove) ranges a new Nash equilibrium? Or is there only one Nash equilibrium in this scenario…the one where SB pushes 100% and BB calls 13.4%? Another way of asking the same question: has the calculator established a new 30%/15% equilibrium, or has it instead given us an exploitative “best response” for the SB in response to a significant deviation from Nash by the BB?
I hope I have made that clear enough…it looks compicated, but I think it really is quite a basic idea.
Many thanks people!
February 5, 2015
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Btw I’m not sure why I wrote the same thing twice in the above post.
The more I think about this the more I am thinking there is only one equilibrium, and the “best response” is an exploitative range.
Thank you Riceman I feel you answered your own question very well!
But any confirmation from any non-Riceman would be appreciated!
TPE Pro
December 6, 2012
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You’re correct that the new range is not an equilibrium. An equilibrium means that neither player can unilaterally improve his EV by changing his strategy. In the 30/15 scenario, the BB is not maximizing his EV. If he knows that SB is ony shoving 15%, then he can do much better than calling 30%. Then once he tightens up his calling range, SB will be able to re-adjust by shoving wider, etc. This process continues until they arrive at the original equilibrium.
February 5, 2015
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Hey Andrew, thanks for your reply.
The scenario the dev uses in this training video is illustrative of a Nash anomaly peculiar, apparently, to tournament play. In chipEV or HU, if hero plays his NE range, any deviation from Nash by villain will mean hero will be able to break even, or more usually make money. In ICM spots, or anywhere where the bubble factor is significantly >0, this isn’t necessarily the case. In the 100% SB push and 13.4% BB call scenario, as the BB expands his calling range, if the SB continues to push the 100% equilibrium range, both the SB and the BB lose: the EV has to go somewhere, so it is shared by the rest of the players at table. If the SB continues to shove 100% in to a widening calling range, his EV get progressively worse, (as does the EV of the BB as his calling range widens). However, by maintaining the 100% equilibrium range, what the SB can guarantee is that the best the BB can do in this entire scenario is to break even, which occurs when both players are in equilibrium.
In this scenario, it is in the BB’s interest to make a significant move away from equilibrium, and crucially ensuring the SB becomes aware that his calling range has become much wider than Nash, because the best the BB can do overall here is by ensuring the SB tightens up his push range. This is where the BB is able to do the best in this entire scenario.
I thought I must have misunderstood this part, because to my mind this would mean the BB is able exploit a Nash range, which by definition is impossible, until I saw that the calculator even factors in very -EV calls which, apparently, are designed to be so wide that the SB cannot fail to notice the move, and thus tightens up! It is there on the screen, and not only did I see it, the dev even explains it!
I was going to make a joke about how this stuff must have sent John Nash crazy, but then I remembered he did in fact suffer from mental illness, which is no laughing matter. But for my part? Man, this stuff twists my mind!
Andrew or Matt or any other game theory boffin, if you find yourself with a spare 12 minutes, I would really appreciate it if you could take a look at the section in the video and give me your thoughts. I know it is a big ask, so I won’t expect an answer any time soon (if ever!), but I really feel I am on a cusp of a great leap in understanding of this stuff here.
Many thanks…Mark
[Edit: I have just had a thought whilst mulling over your post above Andrew: maybe all this does make sense because we move towards an equilibrium…which is the end point. We don’t move from the equilibrium to the wide ranges, its the other way round…ah whatever if I don’t stop thinking about this I shall give myself a headache! Instead I shall go and kill some demons in Doom!]
[Edit 2: oh crap! I just re-read this and can see there is a glaring contradiction! I must be misunderstanding something badly. If the SB can guarantee the BB can at best break even (by SB playing the 100% equilibrium range), then how can the BB do better by making the SB tighten up??!!! Ahhhhh! I give up mate! I will watch the thing again myself (for the sixth time) and try to make more sense of it…]
[Edit 3: I am sure when you see another Riceman game theory related thread you all collectively moan and think “I give up! KB give him back his sub!”. Sorry if that is true! Matt…you love to get stuck in to all this stuff…please help me! I am sure Andrew is in despair…].
February 5, 2015
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The more I think about this the more I am convinced that your initial post answered the thing Andrew. The equilibrium is the end point here. We reach the point where there is nowhere else to go for either player and the game here is “solved”. Man, by the time I am ready to review this software Trump will have been assassinated, Arnie will have organised a military coup and the European Union will have declared war on Putin and the UK and we will all be dead.
February 5, 2015
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You know? I’m sorry people but I have been off studying this video more, and I am sorry to say…this thread is not yet dead in the water. I shall be back with more thoughts on this, I am sure you cannot wait (joke). I think there is more to think about. Goodness only knows why the dev. chose this particular anomalous spot to talk about. I think even John Nash would be struggling to understand it.
(Do you ever ponder on the bleakness and futility and fragility of the human condition? I dwell on it constantly, in the background, in my subconscious, by default, all the time. I am only half joking (ie: not joking at all) when I say I consider those who are oh so positive! Joyous! and “high on life” and “everything is wonderful!” and “isn’t everything oh so exciting?!” to be the ones who need professional help. Brother, it really isn’t. A human life is a tragedy in waiting from the moment it is conceived. Consider the trajectory of a human life: born, grow, mate, reproduce, age, die, and along the way, watch, as an emotionally sentient being, everything you love also grow old and die.
I guess it comes down to perspective. I have tried to change mine. I now view every day as an opportunity. And if this is not how I feel when I wake up, I tell myself how it is, consciously. But this stuff breaks my heart all the time).
Sorry! I went off on one…I was just thinking about John Nash and his wife dying in that taxi in New Jersey. I suppose at least they were older. I keep wanting to say that it is so sad such a “beautiful mind” was lost but then I remember that was the name of the movie lol! Couldn’t they have come up with something more original? It’s lame. Whoever came up with that name for the movie? If I was the studio head…I’d fire him.
February 5, 2015
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OK so if anyone is still interested I have been over and over and over and over and over and over and over and even over this one more time, and I am fairly sure I have this nailed:
This is a Nash anomaly peculiar to tournament play. There is in fact no contradiction here… I was just mistaken that the best the BB can do is at equilibrium. It is however true to say that if the SB continues pushing the 100% equilibrium range then the best the BB can do is break even. But if the BB widens his call range even slightly, he harms his own EV, but crucially the SB is harmed more severely by continuing with a 100% range here.
So, it is very much in the BB’s interest to deviate from his Nash call range into exploitative territory, because when the SB responds, as he must…(he is coming off worse here), the EV of the BB goes way up, way beyond what he could achieve at equilibrium.
The best the SB can now do here is to stabilise and minimise his losses, but he must respond or he will end up much worse off.
This is simply a spot where the BB is able to turn things to his advantage. It is crucial, however, that the SB does recognise the BB is calling much wider than Nash for his strategy to work, otherwise both HU players lose EV, which is now shared by the rest of the table. This is why HRC factors in very -EV calls here, so that the SB is forced to respond.
The Nash equilibrium is not being exploited, as I originally thought, it is simply redundant when the BB widens his call range (at least, the most the SB can do by sticking with his equilibrium range is to ensure the BB can only break even).
If anyone thinks I an off with this then I would relish a discussion about this.
Otherwise I feel I should be nominated for this year’s Nobel Prize for Advanced Nob-Jockeys…I meant Mathematics for having de-coded this scenario.
(Oh…and also I won $500 yesterday so instead of re-investing it in my roll brother I am going to purchase an Asus Zenbook with 128GB SSD…mate Asus are the business! If anybody is debating which brand to buy next I totally rate Asus).
Matt, I am kind of disappointed you have not made an appearance here…it’s not the same without you! Andrew or Matt (or Matt Janda or Ed Miller (joke))…does my breakdown of the thing sound plausible to you at least?
And if it does…is it even interesting? It is to me, and I feel a sense of accomplishment for having understood it finally…but maybe pros know all about all this stuff anyhow.
I tell you one thing for sure…the reason I am even reviewing the calculator in the first place is so that I become very familiar with the software myself…and in this way this exercise is already a big success…
February 2, 2013
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I do not know much about this subject but I will call someone lighter if I know that they shove light and tighten up against a nit. The same goes for shoving. Am I at a big disadvantage not studying this subject any deeper than this? I do use shoving charts as a guide when I get below 20bbs. Please let me know if you are making money by having an expert knowledge of Nash Equilibrium.
February 5, 2015
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Hey again Smallcat!
Believe you me…I absolutely do not have an expert knowledge of this stuff. But hey! I appreciate your input! I almost felt like I was some kind of schizophrenic character having a conversation with himself (myself…who? you? me? No way! btw I just became a paranoid schizophrenic there for a second!).
I am just about off to bed, so I can’t talk for long, but let me just say this:
If you had an “expert knowledge” of game theory in the practical rather than theoretical sense in NLHE, which applied to pre and post flop, you would be well on the way to holding the solution to the game of NLHE.
And so I am obliged to say: yes, you are diminished as a poker player if you do not grasp the game theoretically optimal solution to the game. But fear not! Because nobody else grasps it either. Pre flop, we use Nash ICM calculators such as icmizer and HRC which can approximate the solution to the game. But as I understand things, post flop there is evidence which would suggest that such a GTO solution to NLHE doesn’t even exist in multiplayer games, and even HU, the game tree is so complex, that nobody is playing a perfect GTO strategy anytime this millennium.
For sure though, I suggest studying this stuff.
Pre flop we usually talk in terms of Nash equilibrium, post flop…in terms of GTO. But it is all the same thing. In its purest sense it is the solution to the game itself, and it all revolves around balance.
February 5, 2015
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Sorry Smallcat I was off to bed last night so I didn’t answer your precise question regarding making money.
For sure you need to know your default Nash shove ranges. If you really want a free edge I feel not many are studying, do yourself a favour, download SnapShove onto your phone, and study Nash calling ranges also. That’s real money right there being left on the table by even some serious regs…only this year have I devoted much time to it after years of studying Nash shove charts.
If you don’t know your basic Nash ranges, then how are you going to tell if someone is deviating from Nash in order to exploit them? In tournaments and SNGs learning Nash ranges is an absolute must.
Regarding the specific scenario outlined in this thread which I have been talking to myself about (joke…actually that isn’t a joke), even here there is a practical application which can translate into real money in your game, which can be inferred from the conclusion I drew (if it is indeed correct):
If you are playing at a table of competent regs in a high ICM spot who are all playing approximate Nash ranges, then you can demonstrate to your SB when you are in the BB that you are deviating hard from a Nash call range (by calling ultra wide), and you can exploit this very specific situation for the reasons I go into detail about above in this thread.
Again, money to be made by becoming very familiar with the Nash equilibrium (and in this case, its anomalies).
So yes, you are certainly missing out on significant $ if you are not studying the Nash equilibrium or GTO at all.
And it is extremely complex and profound maths theory, at least to my maths pea brain. Not many players will be putting significant effort into really studying this material, so there is a real edge to gain here also if you are very willing to work hard.
This may or may not be a chore to you. For myself? For some reason…I really don’t know why…but GTO in NLHE has become of serious and specific interest to me. So I actively enjoy learning about all this…sad as it might be to admit, but I study this concept as a hobby! If you are not naturally interested in it, then for sure I can see how it might be way too much like being back in college! The truth be told? Through poker, i have discovered my “inner geek”!
So my advice to you my man, is to look deep inside your own soul and try to discover the Geek within you. Once you have found him, embrace him! Nurture him! encourage him! Feed him! And keep him warm, and he will teach you how to love all this stuff…
February 5, 2015
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You see I just knew I was on the verge of a huge leap in my understanding of Nash here.
All that thought…from the “Starting Point” thread here in the GTO forum through P-Aire’s thread in the Strategy section on the Q 10 hand…the thread which I “muddied”…
All this has now become clear to me.
There is only one equilibrium in every situation. This is the thing which was causing me so much confusion. And after watching this webinar tutorial…Actually, after studying this webinar tutorial, it has all become clear.
No wonder Andrew thought I was being obscure. In fact I simply hadn’t grasped this basic idea.
Well TPE thank you so much for giving me the space to think this all through. I am sorry if I have come across as a lunatic talking to myself. Hopefully some other people have benefitted some from this Riceman Ramble.
I am sure not too many people care if I do some lame review of a product which has been around a while and for which there are many tutorials and webinars. But people would be missing the point entirely if they thought this…
The review is for me. I undertook the research in order to force myself to study the calculator in full. (Of course, I hope others also benefit from my research). An almost purely selfish motivation. And a total success!
TPE Pro
August 25, 2012
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smallcat66 said
I do not know much about this subject but I will call someone lighter if I know that they shove light and tighten up against a nit. The same goes for shoving. Am I at a big disadvantage not studying this subject any deeper than this? I do use shoving charts as a guide when I get below 20bbs. Please let me know if you are making money by having an expert knowledge of Nash Equilibrium.
The short answer to your question is a resounding yes. It is overwhelmingly likely that if you’re not studying Nash ranges, you’re leaving a ton of money on the table in push-fold spots.
Until you know what you should theoretically be calling against a perfect opponent, you can’t possibly know how far from that you should be deviating against an imperfect one. You might say “I think this opponent is too tight, I’m only going to call top 10% here”, and then run the calculation and find out that not only should you be calling top 30% according to Nash, but you should still be calling top 20% against that specific opponent based on your read – so your calling range is still not as good as it could be.
Not to mention, when you’re in early position playing push-fold against an entire table of opponents, you can’t possibly exploit all eight players at once, so you need to know your optimal shoving ranges. Otherwise you’re just guessing and throwing your chips in.
I recommend getting hold of a copy of HoldemResources Calculator and running some calculations. 95% of players I’ve ever coached have been shoving and calling much too tight in most spots, and roughly the same percentage are much too intent on constantly ‘waiting for a better spot’. If you’ve never done any Nash range calculations it’s pretty likely that your EVbb/100 winrate at
February 5, 2015
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And the latest Riceman GTO thread is complete! After a post by ginger!
Ginger perhaps this is not the correct place to ask…I don’t know. But I’d like to do some work with you in the new year.
Nothing too grand, I shall be a little hard up after Xmas, but how can I contact you?
February 5, 2015
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You know, I have been thinking about this thread recently, and I have realized why I became confused around such an obvious and fundamental concept: of course there is only one equilibrium in any given situation; that is the point of the equilibrium in fact.
What threw me off and has caused me so much confusion, is that ICM/Nash calculators also give out exploitative solutions. My confusion stemmed from the presumption on my part that every output of an ICM/Nash calculator is an equilibrium solution.
Evidently, this is not the case.
Hell, now I am confused again.
Oh, by the way, I am glad neither you (Matt) nor Andrew saw my requests for coaching. I am about as skint as I can ever remember being right now.
TPE Pro
August 25, 2012
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The Riceman said
You know, I have been thinking about this thread recently, and I have realized why I became confused around such an obvious and fundamental concept: of course there is only one equilibrium in any given situation; that is the point of the equilibrium in fact.What threw me off and has caused me so much confusion, is that ICM/Nash calculators also give out exploitative solutions. My confusion stemmed from the presumption on my part that every output of an ICM/Nash calculator is an equilibrium solution.
Evidently, this is not the case.
Hell, now I am confused again.
Oh, by the way, I am glad neither you (Matt) nor Andrew saw my requests for coaching. I am about as skint as I can ever remember being right now.
Apologies on that last part, I tend to miss a lot that’s posted here. If you still want to discuss coaching, just drop me a PM.
WRT your point, you’re both right and wrong at the same time. Let me explain.
A Nash calculator like HRC attempts to establish the highest-EV strategy for each player according to the parameters you set. If you run a simple Nash calculation with all ranges left unlocked, it’ll run many iterations (usually 300) of the same situation with each player adapting to the others and eventually settling at an equilibrium. Each player is playing the Best Response to the others, and cannot increase their EV.
If you lock in a range for one player (which is what we do when we want to do an exploitative calculation) and the Best Response changes, it’s actually still doing the same thing – it’s just factoring in the range we’ve given. It’s running the same calculation where each player plays the best strategy according to the parameters we’ve set. The calculator doesn’t necessarily ‘know’ we’re running an exploitative calculation, if that makes sense.
The reason it’s important to understand this is because we can do something that’s in between a Nash and a Max Exploit calculation – a Min Exploit calculation, where we change one variable but keep the rest the same. An example might be if we know what range a villain would be raise-calling, but not exactly how wide they’d be raising in the first place. We change the one variable and lock it in, and then we allow the program to tell us what the best adaptation is, in the event that we have no info about the rest of villain’s strategy.
These calculations can be very useful, and if we keep ourselves stuck in the binary paradigm of GTO vs Max Exploit then we miss out on the chance to use them. So basically, Nash calculators just figure out optimal strategies given specific parameters – if we set no parameters, they give us GTO, but the process by which they establish our exploits is actually the same.
February 5, 2015
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My goodness…
admittedly I have just supp’d upon my before bed whiskey, but man alive! I actually managed to comprehend that through to the end just then, and although I have now forgotten the finer points…Matt! That is genius writing/ thinking/ explanation.
So I wasn’t being stupid then…this really is some in depth cr@p!
Optimal solution(s) to a fixed parameter.
I am interested here now though…you call it a “Min Exploit”. Although I guess that is a…hmmm…I really don’t want to crawl inside my own behind here…colloquialism? Is that the correct term? You are a writer Matt! Am I using the correct term? ie it isn’t literally a minimum exploit, but I understand what you mean… it lies between GTO and a max exploit.
Hell…I have lost it here! I am going to bed before I confuse myself further.
(Does any of what I wrote make sense?).
February 5, 2015
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OK Matt, so colloquialism was a total literary misfire! I asked my daughter’s English teacher. I haven’t had a whiskey and I still love your answer. It is a bloody stroke of genius man. In fact, it answers the question I didn’t even know I was asking in this thread. I’m still not sure I could articulate exactly what the question is, but you answered it.
Although my game theory threads always manifest around a mistaken idea or confused understanding, they always seem to end up utterly fascinating. At least to me. This is always thanks to yourself Matt, and Andrew of course.
Great stuff!
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