Random Game Theory Stuff - Page 4

This is why, a long time ago, I told you that poker is a zero sum game and your "statistical" analysis of your winnings is purely conjecture of playing worse people. Once everyone is equal in knowledge, poker becomes a zero sum game. Being taxed on a zero sum game is ridiculous. Combine rake and taxes makes collecting bottles more profitable.

In the Twilight! Oooh, a UU in the Twilight!

On February 09 2015 22:49 player999 wrote: Shouldn't there be an optimal calling frequency that Player B had to obey in order to breakeven with Player A's optimal bluffing frequency, and then deviations from this calling frequency would make Player B lose money and Player A win?

No, there is no guarantee that a deviation from GTO will yield positive expectation for the other player. A deviation necessarily opens yourself up to exploitation for the opposing player, but that doesn't mean its achieved with the GTO strat. A common example is rock/paper/scissors where one player decides to throw rock 100%. Its a severe deviation from GTO, but still won't lose him money against a GTO opponent throwing 1/3 of each.

How can a GTO strategy win in the long run against a strategy that makes many mistakes if Player B's mistakes won't cost him?

GTO simply doesn't guarantee that you win in the long run. All it means is there's a strat where your wins/losses get capped at a certain amount.

It seems like the unexploitable strategy is making it impossible for others strategies to beat it but at the same time making it impossible for itself to beat strategies that make mistakes.

In some instances this is the case, yes. Usually though, the GTO strat will still be mathematically superior to whatever random strat will be played and it still gains extra EV.

On February 09 2015 22:42 player999 wrote: Show nested quote + On February 09 2015 20:55 traxamillion wrote: A gto strategy ensures you make money versus any other strategy besides another gto strategy in which case you only won't lose money (breakeven). Wrong. It only guarantees that you will breakeven or better against other strategies, doesn't guarantee a win at all. Trivial example is rock-paper-scissors were all strategies break even against GTO.

Yes I understand this is the theoretical definition when talking about GTO and Nash equilibrium in general. I am talking about as it applies to full size NLHE played in practical terms terms.

I.e. Say you have a hunlhe GTO bot. I would postulate it would have a positive winrate versus any strategy besides another GTO strategy. You would disagree with that as well?

unless you know exactly what player B is going to do (call too much or fold too much ) the balanced strategy will bring you the higher EV most of the time

Yep, this ain't rock scissor paper. I mean sure that game follows Nash by it's nature but that's about its only similarity to poker and I think it is useless to compare the 2.

On February 09 2015 20:56 traxamillion wrote: and yea why would you deviate from GTO in order to become unexploitable that doesn't even make sense. GTO by definition is intrinsically unexploitable.

You can't deviate from GTO in order to become unexploitable. That was my point.

On February 10 2015 07:37 drone666 wrote: unless you know exactly what player B is going to do (call too much or fold too much ) the balanced strategy will bring you the higher EV most of the time

But is that EV always 0? This is my question, how can GTO have a positive EV in a given situation?

On February 10 2015 03:11 NMcNasty wrote: Show nested quote + On February 09 2015 22:49 player999 wrote: Shouldn't there be an optimal calling frequency that Player B had to obey in order to breakeven with Player A's optimal bluffing frequency, and then deviations from this calling frequency would make Player B lose money and Player A win? No, there is no guarantee that a deviation from GTO will yield positive expectation for the other player. A deviation necessarily opens yourself up to exploitation for the opposing player, but that doesn't mean its achieved with the GTO strat. A common example is rock/paper/scissors where one player decides to throw rock 100%. Its a severe deviation from GTO, but still won't lose him money against a GTO opponent throwing 1/3 of each.   How can a GTO strategy win in the long run against a strategy that makes many mistakes if Player B's mistakes won't cost him? GTO simply doesn't guarantee that you win in the long run. All it means is there's a strat where your wins/losses get capped at a certain amount.   It seems like the unexploitable strategy is making it impossible for others strategies to beat it but at the same time making it impossible for itself to beat strategies that make mistakes. In some instances this is the case, yes. Usually though, the GTO strat will still be mathematically superior to whatever random strat will be played and it still gains extra EV.

Can you explain a situation where GTO has a positive situation? My whole point was that according to the logic I described GTO could never have a positive EV in any situation, just like it can't on rock-paper-scissors, but in poker it's commonly accepted that GTO has a positive EV against poor strategies, I just don't see how that's possible.

I could see my error being that my toy game is too simple for GTO to have a positive EV on it, but if that's the case can anyone come up with a slightly more complex toy game in which GTO yelds positive expectation?

just think of a nuts or bluff spot vs a bluff catching range

IP player A 10 total combos/5 nuts/5air
Stack size 2

OOP Player B 5 total combos
stack size 2

Pot size is 3

Find Player A GTO river strat

Can you explain a situation where GTO has a positive situation? My whole point was that according to the logic I described GTO could never have a positive EV in any situation, just like it can't on rock-paper-scissors, but in poker it's commonly accepted that GTO has a positive EV against poor strategies, I just don't see how that's possible.

If one player starts going all in every hand. By the 3rd or 4th hand you would probably start widening your calling range in an exploitable manner to start including hands like A8o/55.

GTO ignores this information regarding the player going all in every hand and just calls whatever the correct GTO ranges would be. For the sake of discussion lets say they are AJo/77 ... GTO is still positive EV against your opponent's strategy, just not as positive EV as the exploitable one.

In some instances this is the case, yes. Usually though, the GTO strat will still be mathematically superior to whatever random strat will be played and it still gains extra EV.

Given we have precise knowledge of our opponent's strategy, there's no situation I can think of where GTO is more +EV than an exploitable strategy. I don't understand how anyone can think this unless my understanding of GTO is incorrect but I haven't seen any compelling arguments in opposition to what I've stated.

On February 10 2015 12:41 player999 wrote: Show nested quote + On February 10 2015 07:37 drone666 wrote: unless you know exactly what player B is going to do (call too much or fold too much ) the balanced strategy will bring you the higher EV most of the time But is that EV always 0? This is my question, how can GTO have a positive EV in a given situation?

this is incorrect the EV isnt always 0, i used to think this way until I watched Sauce series, Toy Gaming, really mind opening
as I said the balanced range usually have a higher EV compared to unbalanced ranges playing vs random unbalances, unless you know if villain is overcalling or overfolding in a spot ( this is really rare imo )

if you know the basics about CREV I suggest you to setup a simple Toy Gaming and play around with your bluffing/value frequencies and bet sizes and see how your EV changes

but if you talking about GTO vs GTO ( thats what u try to do when solving Toy Gamings ) then yea, obv the EV of the hand is going to be 0 for both

On February 10 2015 06:01 traxamillion wrote: I.e. Say you have a hunlhe GTO bot. I would postulate it would have a positive winrate versus any strategy besides another GTO strategy.

This is incorrect. We already have the ability to calculate a perfect counter-strategy (its nemesis) against any given strategy. The strategy we come up with against a GTO strategy uses pure strategies (there's no mixing). So its heavily exploitable, but has equivalent EV to GTO strategies.

On February 10 2015 12:45 player999 wrote: Can you explain a situation where GTO has a positive situation? My whole point was that according to the logic I described GTO could never have a positive EV in any situation, just like it can't on rock-paper-scissors, but in poker it's commonly accepted that GTO has a positive EV against poor strategies, I just don't see how that's possible.

As Marshall and I have pointed out before, using a GTO strategy against a player shoving allin will yield positive expectation, even if you aren't calling with hands that you should be calling with (say K9o).

For a toy game example, say instead of Rock Paper Scissors, we have Rock Paper Scissor Fish. Fish is exactly the same as paper except it only wins 70% of the time, otherwise it loses. Obviously, using Fish at all instead of paper is completely retarded. Its dominated by paper, so the GTO solution doesn't change at all, its still 1/3 Rock 1/3 Paper 1/3 Scissors. But if we now play against some idiot throwing Fish for whatever reason, we pick up extra value every time we throw rock. Poker is more like RPSF than RPS. Going allin preflop is like the "fish" move though not exactly since its still possible to exploit a player who folds too much vs an open shove).

On February 10 2015 15:36 MARSHALL28 wrote: Show nested quote + In some instances this is the case, yes. Usually though, the GTO strat will still be mathematically superior to whatever random strat will be played and it still gains extra EV. Given we have precise knowledge of our opponent's strategy, there's no situation I can think of where GTO is more +EV than an exploitable strategy. I don't understand how anyone can think this unless my understanding of GTO is incorrect but I haven't seen any compelling arguments in opposition to what I've stated.

I meant GTO strats will generally beat non-GTO strats that is all, not that GTO strats are the best option against non-GTO strats.

On February 10 2015 15:31 MARSHALL28 wrote: Show nested quote + Can you explain a situation where GTO has a positive situation? My whole point was that according to the logic I described GTO could never have a positive EV in any situation, just like it can't on rock-paper-scissors, but in poker it's commonly accepted that GTO has a positive EV against poor strategies, I just don't see how that's possible. If one player starts going all in every hand. By the 3rd or 4th hand you would probably start widening your calling range in an exploitable manner to start including hands like A8o/55. GTO ignores this information regarding the player going all in every hand and just calls whatever the correct GTO ranges would be. For the sake of discussion lets say they are AJo/77 ... GTO is still positive EV against your opponent's strategy, just not as positive EV as the exploitable one.

I'd say this precisely answers your question player999

On February 10 2015 21:40 NMcNasty wrote: Show nested quote + On February 10 2015 06:01 traxamillion wrote: I.e. Say you have a hunlhe GTO bot. I would postulate it would have a positive winrate versus any strategy besides another GTO strategy. This is incorrect. We already have the ability to calculate a perfect counter-strategy (its nemesis) against any given strategy. The strategy we come up with against a GTO strategy uses pure strategies (there's no mixing). So its heavily exploitable, but has equivalent EV to GTO strategies.

You can only create that counter strategy if I give you my bot's and I wasn't really talking about that but even then it doesn't matter. I was talking about any strategy developed independently of my bot. Again I don't think it matters.

it would literally be impossible to beat my bot by definition. If you developed a perfect counter strategy by analyzing my bot it would at best break even vs my bot. Your counter strategy and a co-optimal GTO strategy would have the same winrate vs my bot of 0. The question is does that make your counter-strategy also GTO? That I don't know.

What I meant by this was mostly trying to show Player999 that GTO strategies in poker are quite strong despite what he might have seen in some toy game examples. Look at the limit machines that were releases in Vegas take free. People thought they played weird and bad at first but really they were based on some GTO approximation and crushed virtually anyone. My GTO bot in the example would crush any human by a ton.

Unexploitable and balanced have nothing to do with being breakeven

McNastys example is right, if you open shove 32o for 300BB that against a GTO calling range will have a negative EV even if villian doesnt adjust to your ranges.


I think a lot of the confusion we are having about exploitability is how we define it as someone said earlier, I think the term is used in poker as a one-street perfectly balanced ratio of value/bluff, rather than a multi-street unexploitable line, which would be GTO.

So lets stop using the word exploitability and lets use balance... balanced play =/= GTO, but GTO is always balanced.


Also pragmatically GTO should have in theory small winrates against people making a lot of mistakes so we should deviate as most as we can from GTO but always coming from a GTO starting point