GTfO

Actually there’s a very good video on this topic here on RIO. I will put a link to it, and I really recommend it regardless…

My main question remains; What is a good estimate of 6-max bb/100 lose rate for a good pro vs solver strategy (non clairvoyant)?

https://www.runitonce.com/poker-training/videos/clairvoyance/

The equilibrium strategy can never lose EV with it’s strategy. A specific combo can “loose EV”, but other combos will then gain EV and make up for it to a minimum of what it lost. 

I think you would be right if poker was a game starting at the river with simple ranges and SPR 1. To see that we can obviously loose EV let’s look at extreme’s. It’s usually a good way: 

Extreme ex 1:

Solver open BTN 2,5BB, Human calls with 3c3s in BB. 
Flop: 3h3d8s
Human check, Solver bets 25%, human fold. 

This is clearly an EV loss. Calling and raising has obviously many BBs in EV for the human and we chose an option with 0 EV. The solver gain EV from winning a pot it clearly should lose at a minimum what was in the pot after it’s bet. 

Extreme ex 2) 
Solver Opens 2,5BB OTB, Human calls BB with 7h2d.
Flop AsKd8s
Human checks, Solver bets 150% pot, human calls. 

Also clearly an EV loss for human and an EV gain for the solver. Even if the solver doesn’t take advantage of the humans bad preflop ranges or terrible flop strategy, it’s winning a bunch just by playing normal. 

Obviously this won’t happen in reality vs any human that knows the rules of poker. It’s just to illustrate a point. A realistic example could be something like this:

In this action line, if we bet small or checked the Qs9s combo we loose about 0.1BB in EV because it's a pure 2/3 bet

A clarification: A human player WILL lose EV vs a equilibrium output. It’s just a matter of how little/how much.

Strong players will not be making “EV loss” decisions that often, whereas weaker regs will make more.

”Other example is RPS: if one plays the optimal strategy of 1/3rd each, you can play 100% paper, 50/50 paper/stone, dance around the table, sing your name or whatever else comes to your mind, the result will always stay the same. Add a "rake" for each draw any the solver will lose (as well as his opponent).”

I’m a little surprised you said this after reading your previous posts (that were very good). The quote is a common miss understanding.

It’s true for RPS but in poker the equilibrium strategy can gain EV by the opponent taking an option that is lower EV then the optimal option(s).

What would actually be the outcome if a strong player battled the solver over a large sample? I always assumed anyone would be destroyed for a huge lose rate. Not so sure it’s the case though...

The solver creates the GTO strategy by max exploiting back and forth until there there are no exploits left - equilibrium. This is possible because the solver is clairvoyant to it's opponent (itself). Actually, when the solver creates a solution, it is always clairvoyant to the opposing strategy. If we have a spot and plug it in to a solver, we either assume our opponent plays perfect equilibrium, or we put in a node lock how we think they deviate. Regardless, when we solve it, the solver is clairvoyant both ways.

However, if we play vs a solver output (like you can in various different software today), for example BTN RFI vs a BB defend. The solver is just playing the output it got from reaching equilibrium against itself and is obviously NOT clairvoyant to OUR actual strategy. IF it was somehow clairvoyant to our strategy (all mixing errors etc etc.) it would absolutely destroy us by taking advantage of our deviations from equilibrium. However, it won't be. It will only assume we play perfect and respond with a "static equilibrium strategy".

If we just play vs the static solver output (like you typically would in such software), the solver only gain EV when we make blunders that are 0% frequency . Mixing errors are at most making small EV losses from one option with slightly higher EV in a vacuum being played too infrequent. Perhaps by losing value/bluff potential etc. in certain nodes on certain run outs(?). However the solver wouldn't adjust to those imbalances because it just assume equilibrium ranges in all nodes.

A good reg probably can "survive" by making roughly 2bb/100 worth of mistakes from EV-losses in 6-max. Remember in 6-max we only vpip around 25% of hands, and many of them never reach post flop. So in 100 6-max hands, there's only really 10-15 hands where we risk an EV-loss. If you want, you can try to import a hand sample in a GTO software and you can see the avg EV-loss/hand.

Questions that come to my mind:

1) Would a solver be loosing after rake if it reg battled nl500z vs the top 5 regs in the 500z pool?

1b) Would it even beat lower stakes with higher rake (let’s not consider all non existent GTO spots)?

2) Lets imagine someone proposed a prop bet where we got a 7BB/100 head start over a big sample vs the solver, would it be an easy win? Could we just play a "safe strategy" where we never worry about mixes but just select an option that we are almost sure is at least some percent frequency? What I mean is if we suspect a play is 85% A and mixing a small frequency of option B & C, but we are not sure - we just 100% play option A to avoid potential EV blunder. We now get away with a very very small EVBB/100 loose rate and the head start would make it a profitable side bet?

2 b) The solver gains EV by playing a more advanced strategy? For example multiple sizes in spots most people would play 1 size.