I've ran two sims over all strategically unique flops for the situation where BTN opens (~41%) and BB calls (~29%). The ranges used are ~GTO and the RFI sizing used is 25 chips (2.5bb). No rake was used.

The two sims have the exact same settings aside from the flop sizing/action allowed for the IP player.

In sim 1. the IP player can either bet 30%, 75%, or check

In sim 2. the IP player is *forced* to bet 30%

The link below shows the EV for IP/OOP player between the two sims for all strategically unique flops.

https://docs.google.com/spreadsheets...it?usp=sharing

This is very cool.
It would be interesting to see how much ev range betting 1/3 is losing vs equilibrium strategy. I'm not sure if you can do that with scripts.
I did for few specific flops.

That's basically what this is.

Solver exploits player who is forced to range bet.

It seems you don't understand these data are from a solver output?

I do, but when you force ip player to bet 1/3 with whole range oop response will be different then in game where ip have options to check or bet bigger vs same sizing bet.

Well that goes without saying. I am really not sure what you dont understand. Oop is not locked at all. Oop response vs the 30% forced sizing is a max exploit ... he ends up x raising >20%

I didn't include all the output values, as I felt that would simply be giving "way" too much information out for free.

Nice job.
I think what Haizem means is what will happen if we node lock oop to play against a forced range bet as it would play against a mixed strategy.

Interesting analysis!

What's the aggregate EV loss of using the forced 30%cbet strat?

What other conclusions did you draw from this data?

I'm not sure why you would want to do that but by definition the ip ev would increase.

This is something confusing to me. Like in this situation if IP is playing his equilibrium (forced range) he will gain EV by definition because OOP deviates.
But from OOP perspective, who is playing his own equilibrium (against a mixed strategy) he will gain EV by definition because IP deviates.

I am missing something and can't figure it up.

Ip ev will go down in the sim where he is forced to range bet

Ip would lose ev when you compare it to strategy where he is allowed to bet and check.

OK so you are saying that we lose 4bb/100 in the worst case scenario which probably will never happen in real life, not to say that we could win ev against some Zenith guys who don't use huds, don't a give a **** about exploits, learn 10 sizes+ on every node and would probably defend very badly against our range bet.
Thank you sir time to range bet some 654 monotone.

I was stating if we node locked the OOP strategy from the (30-75-check) sim for the (range 30%) sim.

Perhaps you didn't look through the spreadsheet? There are 1,755 flops and many of those the full range c-bet strategy would lose > 10bb/100.

You won't lose a significant amount on monotone textures because they are just heavily favored by the ip player.

The node-locked strategy will lose some EV against a fixed (non-adjusting) GTO BB strategy. It will lose more EV against an exploitative BB strategy (which is what we're looking at)

What Brokenstars is measuring is essentially the "regret" of a node-locked rangebet strategy.

I'm still curious what the average loss is? I would measure myself but the spreadsheet is locked.

You should be able to download the spreadsheet or copy paste the data.

Also it wouldn't be accurate because although there are 1755 strategically unique flops out of 22,100, each of the ones listed will have varying weights of 4 12 or 24 depending on the texture. You would have to account for these weights if you wanted an accurate average value.

Can't download or copy paste the data, these options are disabled for this file. Could you perhaps open these options?

I've enabled the ability to copy and download.

Often the GTO straegy for cbetting has every combo being mixed or pure betting, and rarely pure checking.

Therefor the EV of range betting vs Nash Equilibrium will be the same as GTO on a lot of boards, and only be lower on boards where we have pure checks.

Not sure why you'd want to calculate this though

If IP loses EV by range betting, it's either because villain adapts and exploits, or because he is taking wrong lines, like betting a pure check hand.

If OOP doesn't adjust to villains range betting, he won't yield any less EV than in equilibrium, but he will yield the same or more EV (in case IP is betting pure checks). He will, though, yield less EV than he would by exploiting villains deviation

Yes but oop strategy of some hands should change and he will lose ev for taking some zero frequency lines.

There is only one Nash Equilibrium, and everything else is either a leak or an exploitative adjustment.

IP is not playing an equilibrium strategy, and therefor by OOP playing actual equilibrium, IP can't gain any EV over playing NE. If OOP adjusts correctly, he will gain EV by virtue of IP strategy being a leak, and this will be higher EV for OOP and lower EV for IP than equilibrium.

There's no contradiction or paradox

This type of exercise generally won't yield much insight. The main takeaway for most will be that they can simplify their flop strategy to range bet for a small sizing and give up only a small amount of EV compared to a more sophisticated/GTO strategy. The problem with this approach is an understanding of how EV is calculated. It depends on the future actions too. So, if a player decides to range bet the flop, and doesn't have a sound turn and river strategy to support such a play, then the small flop range bet will not be the highest EV option for them. In other words, this small flop can cause more problems than it solves. Today, there is not a shortage of players that range bet the flop and completely botch every action after that--whether it be the turn and river play, or simply facing a flop raise. They've tried to simplify the game so much that they've actually become worse players because of it, and it always seems to begin with an exercise such as this. This isn't to say there aren't things to learn from such an exercise, but just be careful about how you interpret the results.