Yeah its interesting because there is an iterative element aswell. Though even if it was in a vacuum that spot has several gto strategies. By definition gto is just the pair of strategies such that neither player can improve their ev by deviating. So take this strategy pair for example:

OOP:
Check 100%, Call 100% when facing IP Bet

IP:
Check 100%, Call 100% when facing OOP Bet

There is no possible adjustment that either player could make that would increase their ev. Choosing to fold when facing a bet will not increase your ev because that part of the game tree is currently reached with 0 probability. Neither player would have any incentive to deviate from this strategy.

OOP shoving 100% and IP folding 100% is another equilibrium. There is nothing that either player could do to increase their ev.

Dominated strategies can actually be part of a nash equilibrium, the definition is just that no party can adjust their strategy to increase their expectation. So if there was no rake, then clearly any strategy set that didn't involve folding would be a nash equilibrium. Betting would be a dominant strategy because it could do no worse than checking, but checking is still part of a different nash equilibrium.

Yeah, seems true that purecheck from both players is another gto strategy pair. Good insight And if we're willing to spite, seems clear that the equilibrium will settle at purecheck in future iterations (which, metastrategically, actually generates more ev for IP over time).

In practice though the spot probably won't come up often enough vs that player to justify spite calling. It is an iterative game, but not played over an infinite sample. I'd recommend the disciplined fold.

ICM formats probably get very similar spots where spite calling might actually be right.

There is so emotional gain in calling though so I'd probably still call in game

We can use the same logic for the other guy too. If you tell him: "I'm going to spite call you every time in pure chop spots", he can then say: "I'm going to spite shove you every time, even if I know you'll call". Now it's back on you.

The solution here is that the first player should always push and the second player should always fold.

You can imagine a HU cash table on which the rake is 100%. The GTO play would be for the BTN to shove 100% of the time and BB to fold 100%.

GTO assumes that the opponent always makes rational decisions and takes the most +EV option.

You're aware of the fact that game theoretic optimal play can change in iterative games, right? I think you have some deep misunderstandings of how game theory works because you're overly attached to this solver concept.

Poker is generally not an iterative game in a relevant sense. If we play 1 chop spot lifetime, then the correct play is for you to jam 100 and me to fold 100. But if we play 100 chop spots lifetime, the correct play may very well be to each pure check. This is actually a spot where a cooperative equilibrium is likely incentivized if we iterate the game enough times. IP has incentive to spitecall a high enough freq that OOP jams become -ev, and at that point OOP gto strat will be to pure check, as will IP gto strat.

This is because in normal poker, if villain deviates from solver line, hero's strategy is *guaranteed to retain its ev,* so there's no risk to hero for following solver line. But in a chop spot (just like in icm spots, actually), hero is not guaranteed to retain their ev in the same way. Hero's bets can start reducing the overall ev of their strategy, which will form a new equilibrium (x 100).

Actually at a hu cash table with 100% rake, it wouldn't matter because regardless of the action the pot would be 0 chips

This strategy set isnt a nash equilibrium as we can then increase our expected value by folding

That doesnt mean that pure call isn't part of a different equilibrium

gto is just the set of strategies such that no party can change only their strategy and increase their expectation

In!

This is similar to the concept called the prisoner's dilemma. It's a similar kind of situation in which two players could theoretically make a higher EV strategy if they communicated and worked together. It has been solved, though, and the solution is for the players to not work together.

You can imagine a HU match between two equal GTO bots. They would both be losing money due to rake. However, if they worked together and decided to play Strategy X - folding any two cards on the button, their EV would actually increase to 0.

The problem with this strategy, however, is that the game has to end at some point. Nothing is infinite. Therefore, once the last hand is being played, it becomes +EV for the player on the button to not play Strategy X and play GTO instead to make some profit. Then, if we look at the second to last hand, the player on the button will now assume that the opponent won't play Strategy X in the last hand and will therefore have no reason to follow Strategy X himself. This goes on and on untill every hand is being played GTO.

This is why GTO doesn't consider future hands. It always picks the option that has the highest EV in the moment.

I also just can't agree with your opinion, that a strategy is in an equilibrium when one player is always making the -EV call, just because that situation happens at a 0% frequency.

There wouldn't be rake preflop in my example.

This is actually not true. Iterated prisoner's dilemmas actually encourage cooperative play, with relatively cooperative (but not completely naive "always cooperate") strategies outperforming selfish ones in simulations with a wide variety of strategy pairs. It's kind of interesting stuff.

This is flawed thinking. Whichever bot on the button could profitably deviate by opening some hands, because from the button plenty of hands are higher ev to open than folding. In our "always spiting" example, the OOP player would maximize ev by pure checking, and there is no profitable deviation the OOP player could make from that strategy.

Sorry but no, this is all an irrelevant side track. GTO doesn't consider future hands because GTO is a guaranteed strategy that basically has untouchable ev. It has X ev or better regardless of what counterstrategy the opponent uses, so it doesn't really have to care about whether you deviate or if the game is iterated or whatever. But it breaks down in cases like this where deviations actually can decrease the ev of the strategy. This is similar to why "GTO" isn't guaranteed to be +ev in a multiway game -- collusive strategies on the part of other players can undermine the ev of the gto strategy.

It is, technically speaking, absolutely a gto equilibrium. In a game where each player was checking 100% and calling 100% vs bet, how could either player change their strategy to increase their own ev? If there's no way, then it's a game theoretic equilibrium.

SB could increase his EV by starting to shove, which would force BB to fold instead of call.

In the Nash equilibrium every player knows the strategies of the other players. Therefore SB knows that if he shoves, the other player will be forced to fold, right?

I guess it all depends on what the exact deffinition of "Nash equilibrium" is. But at the end of the day, I think that you can probably agree with me, that the "SB 100% shoving equilibrium" is in some way superior to the "SB 100% checking equilibrium".

I agree with you that GTO can change in some iterative games (such as the prisoner's dilemma), but I don't think that this applies to poker. Spite calling/shoving can go both ways, so it shouldn't give one player an advantage over another. I've thought about this a lot in the past and am quite certain that there's no situation in poker in which GTO would make a -EV play vs another GTO, just to increase his EV in the future. For example, in GTO there's never any logic in making a -EV play in order to "protect your range" or similar.

The bb is not forced to fold. The definition of a Nash equilibrium is that no party can unilaterally change their strategy to increase their expectation. This means that it can not increase expectation by just changing the strategy of one player. For sb to increase his EV you need to change the strategies of both players. Increasing sb betting range and increasing bb folding range.

May update?

Damn, I hoped no one would notice ><

I'll be straight forward about this - I was the laziest f*ck ever last month. I did pretty much everything but play poker. I played some new online games, worked out, watched a lot of new anime, made my first AMV, made a MTG "card case" out of cardboard:

Everything but play poker is my point. I mean... I played some HU SNGs for fun, but that's pretty much it.

Anyways, here you guys have it...

May:



Bankroll is at 30.3k

I won't be posting any hands for obvious reasons.

This month I'll definitely start playing again, though. I'll play at least 50k hands and start taking poker seriously once more. Last few months were just embarrassing when it comes to volume.

June 2020:



Bankroll is at 30.3k

The downswing at the beginning of the month completely demotivated me from playing and made me start questioning if I can even still beat the games. It's one of the worst downswings I've ever had. I had a 3 week break after that.

I'm quite upset by my volume in the last few months. It's really embarrassing to even post these graphs... But I guess that's my punishment.

If I don't reach 50k hands next month, I've decided to send one of the last 10 posters here 100€. This should motivate me to play, as I'm honestly more greedy than I'm lazy.

worse downswing you ever had? thats 5 buy ins bro

He is joking because someone said in here that never had a 5 bi downswing before lol

Gl nyu, vamo!

Just ignore that first paragraph

Thanks

To be honest, this downswing was just an excuse for me to slack off the rest of the month. I don't actually give a f*ck about the $100.

I really don't understand how you're able to play 7+ hours/day. It's very impressive to me.

Congrats on a great month!

Gl next month!

I know the "move up in stakes" has be said alot in this thread but why not mix in a few 50nl/100nl tables as that should give you more motivation to play?

It may just be me but playing higher with more money in play, different players taking different lines and even bigger whales always motives me to play more and makes it feel like less of a grind.

INB4 no I want to complete this dumb 100k profit challenge at 20nl

In for the free $100

^ I see that you have a lot of faith in me and my motivation to reach the 50k hands

50k hands is like a day and a half for you

^ Yeah, if I played 24/7.


What do you guys think about this?

What are you targeting?

AK/K9