There were a few things that I immediately noticed about your analysis (that may or may not be entirely accurate since I need to run it myself later tonight). Firstly, why is HJ never calling any KQo combos but calling hands like KJo? Also, having watched some of the LATB streams, I would have to say Andy is definitely calling some hands like QJo and 89o some percentage of the time.

I believe your oop cbet strategy that you provided is completely wrong. Boards like these require a very highly mixed strategy, especially with hands like 4x, and other middling pairs. You have the IP player cbetting 100% of 4x, and 66/77 type hands and also betting every pair at a super high frequency. Many of IP player's hands gain massive EV from raising because we end up having to fold pairs.

A result of your cbetting strategy is that our checking range becomes way too imbalanced. You have us checking AA/KK 50%, which I assume is our range "protection", but this is clearly not enough. We are also checking basically all our non pairs, so IP's clear strategy is to just bet everything when checked to. To succinctly sum up your cbetting strategy, you are betting all pairs for protection/value as well as some bluffs, and checking AA/KK everything else. I don't think we need pio to find an exploit for this strategy.

KQo is being called but KJo folded. Where did you see otherwise?
Also accurately ranging Andy is irrelevant to the video and I also disagree. He flats very wide IP, but this is vs utg and he is HJ.

I believe your oop cbet strategy that you provided is completely wrong. Boards like these require a very highly mixed strategy, especially with hands like 4x, and other middling pairs. You have the IP player cbetting 100% of 4x, and 66/77 type hands and also betting every pair at a super high frequency. Many of IP player's hands gain massive EV from raising because we end up having to fold pairs.

The purpose of the video is not to learn how to exploit cbet strategies. Nor is it to construct an optimal strat for this hand. The purpose is to discover what characteristics and to what degree each factor affects implementable optimal strategy in the pursuit of learning how to in-game customize our strategy to various situations.

As for the cbet strat used in the video, it isn't wrong. It's an arbitrary cbet strat. Our opponent is nemesis so any non gto strat will be suboptimal ie wrong in that sense. The locked cbet strat is a rough approx of what we might encounter, not one we are looking to use unless we deem IP to be playing passive and over folding. If you mean to say that it is flawed and/or exploitable, then yes it certainly is.

We know exactly what the perfect mixed cbet strategy looks like. It is the GTO solution we are using as the baseline. However, that is not realistically implementable. Attempting 10% freq (infrequent) cbet with mixed composition on one particular flop among the myriad of flops we will encounter each optimally requiring a unique cbet strategy is not going to be a wise pursuit.

Despite the fact I in practice chose to impliment a more checking heavy strategy as played, and despite the fact that the example cbet strat is very exploitable, it might do very well vs a typical IP locked strategy. This is investigated in Part 2.

The video aims at showing 2 things:
A) In this specific hand on a dry low flop of 842 even with our strong range pf we should be checking 100%.
B) More importantly, to teach a methodology for deciding when to have a 100% check, a 100% bet, and an implementable mixed strategy of bets and checks.

Good to see some PIO examples of live play vs different opponents. Keep it going! :)
GL

Zach,

Thank you for a thoughtful video.

One point that seems critical is that we can simplify GTO strategy in many cases by rounding off small percentages of mixed strategies to one or zero. But it seems critical to include a carefully considered amount of nutty combos in all the ranges (according to the strat) and perhaps even nut-making combos for future streets. It seems one needs to be careful what and where one simplifies. Preserving nuttiness throughout the game tree at thoughtful frequencies is critical in limiting the ability of opponents to exploit us as demonstrated in the video. This prevents unhindered overbets and such.

Sincerely
Brian

Nice vid. Regarding part 2... I think looking at how the EVs of each strategy change when faced with poor counter strategies for IP will be really relevant to live poker, so thanks for that. Also, please include something where you add stack depth in as an extra variable. maybe including some larger turn or river barrells (if you have enough RAM to do so) . I assume X 100% will be MES for OOP if we increase stack size to lets say 500bb (something I'm often dealing with).

Depolarizing,

You have him calling 6 combos of KJo and 0 combos of KQo. Also while we're on this topic, I'm very confused on how you decided Andy's range. Why is he calling 60% of 64s and 54s, but never any combos of 86s? However, I don't know what you mean by "ranging Andy accurately is irrelevant to this video." I might have a fundamental flaw in understanding how pio works, so please bear with me.

You are correct. Sorry for missing that. It was unintentional to leave out KQo and 86s at some frequency. That said given its just a few combos of additional air and 4 combos of TP the strategy won't be affected.

When i say accurately ranging Andy isn't important i mean that my goal is not to learn how to play vs Andy. Sure in the context of this hand it would be nice if I inputted his exact range, but any arbitrary range is sufficient given we are trying to learn about how characteristics of range vs range affects strategy. That said I think the inputted range even with the missing combos does an adequate job of modeling his range.

As to your last paragraph, I gave exactly symmetric ranges in one pio sim and it still produced oop high check freq so we can directly attribute that to position and nothing to do with his range.

Hi Zach,
Do you think restricting your cbet size to 60% pot instead of a smaller size made Pio want to check more hands?

Wouldn't it be better to cbet 100% with a much smaller sizing (i.e. 25%)?

Thanks.

My guess is that if we constricted our bet size to 25% we would be betting more often but I'd be surprised if it made us bet a lot more.
If we gave option of 2 different sizes, 25% and 60% I think we would see some smaller bets with hands like AK, and bottom pair, for protection with a dab of strong hands for balance.
The reason sizing won't just switch our strategy from checking a lot to betting a lot is because all the reasons we check are still there: OOP, nominal to 0 equity advantage, inferior nut frequency. Making a smaller bet will be less of a mistake than a large bet yet still a mistake compared to checking.

That said the above is only my guess. I will run it if I find the time.

Looks like very little changes when we offer the option of betting small.

thanks for your quick and informative reply

Zach,

I think one issue with your analysis of the 76s hand when you don't bet is that you show rightfully so that we lose $30 of EV with 76s since the best response is to liberally raise vs your c-bet strategy denying you equity. After spending some time with PIO and node locking you quickly realize that c-bet strategies can often be as high or higher EV against opponents that don't correctly exploit you for having a wide c-betting range here and not raising at a large frequency. I think it's important to node lock what you think his response will be (even if we think he will raise quite a bit but not anywhere near 40%) vs your c-bet as I think even times you find that the most aggro of players in spots don't even employ as heavily as a raise strat as PIO suggests. The cool thing about this analysis is that you now know if the tables were flipped you can just liberally raise vs someone that c-bets this spot wide (falls in line with a lot of live cash game players and MTT players).

I ran pretty much the exact simulation as you did where I got 143 for OOP Equity and then changed his raising strat to raising this board 15% of the time and you see that it goes back up into the 170s.

https://gyazo.com/d3b9d4536466376f02041d196ac6eb36

Here is the raise strat I was using which for some players which is actually quite a liberal raising range in their mind.

https://gyazo.com/98548d10036dd1f37342cefdd0fcce62

Probably should of waited to comment, but i'll leave it anyway. Looks like this is part 2 :)