Saving the average strat on the turn and river will not change the flop strategy at all. I'm not sure how much it would slow the process down (I don't expect very much as I know where in the algorithm that happens, the bottleneck tends to be elsewhere). The memory increase does not translate to slower time or increased nodes in this case, it's just saving a bit of extra information at each node.
People using PIO don't rerun turn and river nodes (or do they?) so it might give you good turn and river results without needing to rerun them. Or might give you good enough one street ahead. And I presume rerunning turns is annoying as you have to run flop, get the flop range, put that into the turn sims etc. Similarly if you wanted to do turn sims you might be able to get away with increasing avg strat to 2 and get good river info. There is the algo issue which might mean the look aheads are less accurate. But a question of checking.
Turns and rivers without avg strat fixed are garbage at worst and very volatile at best. It's a bit of a nasty gotcha with monker. Average strat is not an improvement on them, it's a totally different thing.
Lmk if you do try it, I may give it a shot at some point, will post if i do.
June 10, 2021 | 11:58 a.m.
Obvious question but do you change the keep avg strategy on streets setting? Otherwise you are just getting the current strat of the CFR algorithm not the avg strat. and it's the avg strat that converges to Nash.
Or are you changing that setting and think it's a function of the fact it's doing Monte Carlo CFR rather than full CFR and so it's sampling the flop nodes much more frequently.
June 10, 2021 | 6:31 a.m.
Hey man, think you hinted on a previous video that you run turn and river spots separately ie not from a flop sim? Is this correct? I just wondered what the reason for this was.
Also how long do your monker sims take to run - I guess I am asking about the level of complexity of the game tree - what RAM you use
June 9, 2021 | 6:26 a.m.
EV is a denoised version of your win rate (as it removes the AI noise - assuming by EV you mean AIEV). It will have it's own (lower) standard deviation so that allows you to refine your analysis slightly.
June 5, 2021 | 8:11 a.m.
Your bigger problem here (as I pointed out on a previous video) is that the normal distribution is a terrible model for a 245 hand sample (2.45 100 hand samples). So the Pokerdope model doesn't even work on this level.
June 5, 2021 | 8:10 a.m.
Do you think that's a general theme in mixed games - people play much too passively?
May 22, 2021 | 4:47 p.m.
Yeah that was my Q. The HU BB defence range seemed strong and so the cbet frequency was lower. More GTO defend ranges produce much higher cbet frequencies.
But in some sense this lower cbet frequency is an exploit as well of the fact their range is too strong).
May 22, 2021 | 3:47 p.m.
Hey, like the idea for the video. One thing the BB call range (in the HU example at the start)is pretty strong compared with GTO - this might be driving the cbet freq down. Out of interest why did you choose this range?
May 20, 2021 | 7:02 a.m.
Yeah I think overcoming that starting inertia indicates the difference between those two things pretty well. I used to find I would just leave it around 10% of the time but 90% of the time I would then feel ok. Maybe I'm lazier than you though :)
May 10, 2021 | 7:51 p.m.
Not sure if any use but an old trick I used to use for the gym when wondering whether I needed the day off was go, do the warm up and if you still want the day off you can have it. Can be adjusted for poker in a fairly obvious way. Gl.
May 10, 2021 | 6:03 p.m.
Interesting. maybe I should run some with the rake changed. I guess one thing is if opponent's are calling "too much" vs GTO in a high rake sim their call could actually be hurting both of us (as we both lose more to the rake). So although the call for them is -EV vs folding they could also be decreasing the EV of our 3 betting range by calling more as it's a non zero sum situation.
May 1, 2021 | 4:29 p.m.
What are your rake settings on that Monkersolve? The BTN range vs CO open seems way tighter than the one I have for 500PLO.
As an additional Q my solves show that the amount of folding that should be done by CO vs 3bet here is around 20%. Again maybe it is the higher rake thing - or are you saying that the population calls even more than that?
Also again looking at my solve that AQ97 hand is not an open in LJ
May 1, 2021 | 8:26 a.m.
My claim actually works even in the case where Y holds 100% medium hands. Just did a PIO solve on the board AAA33 gave IP 99% KK 1% 22 and gave OOP (Y) 100% 99. Note the 22 is very small on the PIO but is there. Also solve to very high degree of accuracy 0.002% - will still be very fast though
You get the same result even if you move 22 to 33%. You could go to KK 100% and 22 49% and I believe you would get the same answer
April 25, 2021 | 12:47 p.m.
That is incorrect. There will be no calls at equilibrium. think about the EV.
X bets 100% 1 unit into 1 unit pot. What is the EV of any call by Y with a medium hand?
EV[call] = 0.99 * -1 + 0.01 * 2 = -0.97
EV[fold] = 0.0
If you postulate any call frequency for Y then Y can unilaterally improve his EV by reducing the call frequency (so this cannot be a nash equilibrium) so Y must fold 100%.
A similar analysis shows that X cannot improve their EV by reducing their bet frequency.
You might think X should bet value less in order to "tempt" Y into calling but this is also doesn't work as as soon as Y starts to call more X can unilaterally improve their strategy by value betting more so again cannot be Nash.
Also the value of the game to X in this example betting 100% of the time is 1 (the pot). it should be pretty clear that X cannot unilaterally do something to further improve their equity (and neither can Y by the analysis above). hence this is a nash equilibrium.
A common misconception is that Nash equilibrium is that it is about indifference. It isn't. It's about whether we are at a point in strategy space where neither player can change their strategy in such a way that would improve their EV. There may only be one point in strategy space that realises Y's max EV vs X nash (and vice versa).
April 25, 2021 | 12:30 p.m.
My comment directly below this one has it. A contrived situation obviously but with stuff like this a single counterexample is enough.
April 25, 2021 | 11:01 a.m.
Except there is an example below of a zero sum two player game where GTO is the highest EV against an opponent not playing GTO. It's not a contradiction though. Nash just showed the existence of Nash equilibria - the only thing he said about the EV of Nash strat against non nash strat is that it would be greater than or equal to its EV vs another Nash strat
April 25, 2021 | 9:33 a.m.
Also in addition this was intended as a counterexample to a claim (maybe not intended that way) that you always defend <= MDF. This does not mean that it is exhaustive. Proving that you do defend exactly MDF except when a range of only draws implies that you can define what a "draw" really is (which I suspect is difficult) and then use that to prove a range would only defend MDF in their absence. It's quite a big ask.
April 24, 2021 | 11:17 p.m.
The distinguishing between value, bluff catchers and draws is not really clear on earlier streets. And it gets even more complicated when you look across ranges. all you can really say is that you need to defend >= to MDF if you bet. You can't be sure that == MDF is Nash. Can write more later
April 24, 2021 | 5:37 p.m.
Well there are circumstances where it is correct to defend more than MDF because enough of your hands have enough clean equity vs range. But the situation is not that common. You see it in limit games more frequently. I think it's a bit of a smell about your sizing choice if your opponent can do this.
Imagine known AcAd on turn facing 6h7h on Qs Td 5h 2h with 100 in pot. AA bets 10 6h7h should call 100%
April 24, 2021 | 11:41 a.m.
Your first claim is correct if the game is symmetric. ie in 2 player Hold'em gets to play both positions.
April 24, 2021 | 11:23 a.m.
Your claim "who can stick to his perfect gto strategy and print EV against Y who's exploitable" is not correct. It is possible for Y to have "exploitable" strategies that have the same EV against X's nash equilibrium strategy as Y's nash strategy would. As pointed out above if your opponent continues to play nash it actually doesn't matter what you do with your mixed hands - the EV of each action is the same.
So initially i thought your final claim ("It is impossible for perfect GTO to be the highest EV strategy against an opponent who does not play perfect GTO") was true but I actually don't think it is proveable and is certainly not true in general for zero sum 2 player games (counterexample below).
Consider a situation where at the Nash equilibrium it is correct for X to bet 100% frequency pot size all in on a particular river as you only have 99% nuts 1% air. Your opponent has 1% medium and 99% air. Nash for Y is to fold 100% here as you can't have enough bluffs.
Imagine Y calls his 1% medium hands. the nash strategy makes some EV (from when he calls medium). However X cannot exploit this call as he should still bet his 1% air (to fold out the 99% air which he would chop with) and so in this case the maximum exploitative strategy is the same as the Nash strategy (bet everything).
You might try to argue that both players would never reach a state like this at nash in NLHE but that is a very strong claim which would be extremely difficult to prove. In addition there may be other more complicated scenarios that you do get into which can have similar results.