Kalith said
Hey Ginger,

 

What is it that George Danzer is doing with dice then?  I feel like he’s trying to use GTO numbers in certain situations where he doesn’t want to be able to be exploited by making standard plays, similar in situations with PokerSnowie when it says you should be calling 20% of the time and raising 80%.  So is Danzer just trying to imitate poker snowie’s GTO betting situation and somehow knows the GTO numbers of his situations?  He never says what number he needs to hit on the dice in order to make a raise or call viable, but it would seem there is some validity to the idea of using dice to improve your GTO in certain situations if you have a decent idea of the percentage options you should be playing.  

Not familiar with Danzer’s methods, but while choosing bet sizing using dice will avoid giving away any bet sizing tells on his part over a large sample of hands, it will end up with him making lots of theoretically incorrect decisions. If he rolls the dice in a spot where his range is super polarized and it tells him to bet 25% of pot, that’s not GTO, that’s just a mistake.

Which brings me to my next point – GTO bet sizing, as Riceman asks. Bet sizing should usually depend on how polarized the range of the bettor is, and how strong it is. Fewer bluffs (i.e. less polarized) means smaller because your opponent gets better odds to call, and more bluffs (i.e. more polarized) means bigger because it forces your opponent to give you more value with your strong hands.

Finally, Riceman, you’re exactly right – all GTO strategies are unexploitable, but not all unexploitable strategies are GTO. The GTO strategy is the best of all possible unexploitable strategies.

The Riceman said
Hey again! 

I have been away…I thought the Rice Dice was finished with me, but not yet!

So now I can’t get the Dice out of my head again…now I am totally confused…

Ginger said:

“Finally, Riceman, you’re exactly right – all GTO strategies are unexploitable, but not all unexploitable strategies are GTO. The GTO strategy is the best of all possible unexploitable strategies.”

Matt, I am sorry, but the more I think about this the more this seems impossible.

A strategy which is 1%, 5% or whatever % exploitable is still exploitable by definition. If a strategy is truly un-exploitable it must be an equilibrium strategy surely? And if it is an equilibrium strategy, the strategy must be GTO.

I know Andrew had some misgivings about terminology, but I didn’t understand his post 100%

Is this what you were saying in your reply Andrew?

(BTW I really enjoyed the latest Thinking Poker podcast…GTORB sounds great! Have you tested its output against Pokersnowie Andrew?).

The first part of the bolded is correct, but the second part isn’t. In any given scenario there are multiple ways to achieve a Nash equilibrium solution to a situation.

You can use HRC to prove this by changing the parameters of the calculation. If you run a push-fold calculation, and then run the same spot again but with push-fold disabled and minraising enabled, you’ve created two different Nash equilibrium solutions to the same mathematical scenario. Whichever of these two options has the higher EV for the player in question is going to be closer to the GTO strategy for that spot, but they’re both unexploitable because they were both achieved through a Nash equilibrium calculation – the two calculations just used different parameters, restricting the strategic options of the players in each case.

The reason I say ‘closer to GTO’ and not ‘exactly GTO’ is because you’ve only run two of the possible strategies for that spot – you haven’t analysed the equilibrium for the 2.1x open-raise, or 2.2x, or 2.3x, or 3x, or 4x…etc, etc. You also haven’t run a calculation that gives the player the option of having both a range for 2x opening and a range for open-shoving, which is another equilibrium entirely, and a far more complex calculation. Until you’ve run every possible strategic scenario for a spot you can’t say for certain what the exact GTO play is – all you can do is estimate, and collect a variety of Nash equilibrium calculations based on different strategic parameters that each give different EVs.

With this in mind, establishing GTO strategies is usually a matter of boiling our options down to two or three potential strategies for which we can actually calculate a Nash equilibrium (i.e. deciding that in a particular spot we want to have an open-shove range and a 2x range, but not a 2.5x or 3x, etc), and then taking the time to run a calculation that allows for each of those options.

In everything but the simplest cases, complicating our strategic options beyond two or three different choices results in incredibly complex strategies that are completely impossible to execute (e.g. minraise with T7s 42% of the time, 2.2x 9%, 2.5x 14%, shove the rest of the time, repeat for every combination of hole cards…you get the picture). The theoretical GTO solution to No-Limit Hold’em is so complex no human could ever execute even a fraction of it, so when we talk about an actual ‘GTO’ strategy, we’re talking about a strategy being GTO within the simplified parameters of ‘traditional’ NLHE betsizings and approaches.

Don’t think about equilibrium strategies as a poker concept. They’re applicable to any game or competitive environment. You can come up with an approximate Nash equilibrium strategy for literally anything if you know the rules of the game – politics, economics, sports, or whatever else. In order to find GTO poker strategies, we need to define the rules of the game more specifically (usually with bet sizings) in order to make the results intelligible, but if we change the rules a little bit, we get different results. After that, our job is to figure out which set of rules we want to impose on ourselves in order to make these strategies easier to execute.

Hope that all makes sense.

Foucault said
Matt,

The “equilibria” in your example are not true equilbiria. They are equilibria for some sub-game that you are using as an approximation for NLHE. Once you expand the parameters of the game, these strategies are no longer necessarily equlibria or unexploitable. The Riceman is correct: by definition, an equilibrium strategy, at least in a two-player game, is necessarily unexploitable.

What you are saying, I think, is that we can find equilibrium strategies for a bunch of different sub-games (always shove or fold, allow min-raises, etc) and then see which has the highest EV and use that as an approximation of an equilibrium strategy in a more complex game. However, it is not a true equilibrium strategy in the full game.

I probably waffled too much and wasn’t clear enough. I used the word ‘situation’ in the first paragraph where I should have used your word, sub-game, since that’s more appropriate. We’re in agreement that Riceman’s first statement is correct, as I pointed out – I was trying to elucidate the difference between ‘unexploitable’ and ‘GTO’, rather than the difference between ‘equilibrium’ and ‘unexploitable’.

WRT Riceman’s point, I do actually believe that to some extent the proliferation of GTO strategies, if it hypothetically went far enough, would kill a lot of the edges currently available in poker. Much in the same way that players playing GTO strategies at a full-ring table are essentially just splitting up the blinds every hand, 8 pros playing pretty close to GTO would be splitting up the money belonging to the one fish.

What I do believe, however, is that we’re ridiculously far away from that point, and the only people who would actually lose out in that scenario would be a) people who steadfastly refused to branch out into games beyond NLHE, and b) people whose egos would not allow them to drop down in stakes and hunt for better value in games where they had a bigger than 5-10% ROI.

If you’re not letting your ego get in the way and making good decisions about where to find value, you have no cause to ever worry about the death of poker. Outside the 2p2/online pro bubble there are a lot of good things happening that keep poker profitable.

The Riceman said
I wrote something here then deleted it…it was unnecessary. 

I figured the software would cancel the whole post, but it just left a blank post…so I came back to write something.

But I don’t know what to say…except that I have been running so bad for 6 months now that I am not just tilting after a session…I’m already on tilt before I even start. 

Expecting to lose before one begins a competitive event is never going to be a winning mind set.

I am running at a similar -ROI to when I first started playing 5 or more years ago. 6 months. I have gone beyond that down-swing stage when you wonder whether you ever knew anything at all about poker and that it is all just luck. That was 2 months ago I felt that. I have never been in this stage…I am numb to it. When I get aces I expect to lose more often than not, instinctively.

Sorry, but I had a space to fill, so I filled it!

If you really expected to lose, you wouldn’t play. Convincing yourself you expect to lose is actually just a way for you to protect yourself from the pain and discomfort you experience when you lose. To assume that losing is inevitable is less painful than hoping to win (or, preferably, not hoping or wishing for anything) but ending up disappointed, so you stop getting your hopes up.

In reality though, these emotional judgments about how likely it is you’ll win or lose, and this focus on how bad you’re running, is only doing one thing – preventing you from thinking clearly about the hands you’re playing, and thus from making the best decisions. I guarantee you you’re making more mistakes at the table than you were before you started expecting to lose.

Detach yourself from results. You’ve heard that before, but this time think about what that means – it means you literally don’t care whether you win or lose. It’s a hard place to get to, but the route to getting there involves giving up thinking you have any control over whether you win or lose each time you sit down to play. You don’t even really have any control over whether you win or lose over longer periods, unless you’re playing enough volume that you actually reach the long run (which many people don’t – some people play less than 100k hands lifetime and think it’s a huge injustice that they ran bad for 75% of that time).

You need to go into every session expecting nothing (and I don’t mean expecting to lose, I mean literally trying your hardest not to have any picture in your head at all of how you want your session to go), and recognising that there is a pretty good chance you’re going to lose that day. If you can’t go into a poker session recognising that you have no control over whether you win or lose that day, if you’re going to keep fighting the nature of the game day in and day out, the game will break you. You have to give up that fight. You have to let the game win, and agree to play by its rules. You’ll never be good enough to just sit down and win every day, none of us will. You’ll never have control. Accepting that is the first step to never being tilted again.