I've seen situations where solvers recommend calling 50% and folding 50% with multiple hands on the river. To me this doesn't make sense. I should pick the best of these hands and call with 100% and fold the worst of the hands.

Since there is no more action we have no need to worry about our range remaining balanced on future streets.

For example: If a solver suggests that I call a river bet 50% of the time with 77 and fold the other 50%. And it also suggests I call the same river bet 50% of the time with 88 and fold 50%, wouldnt it make more sense to call 100% of the time with 88 (since it is marginally better) and fold 100% with 77?

solvers are just really good at optimizing so when playing vs. itself, if it only is allowed to call/fold 100% of a combo on the river then it would lose a tiny amount of EV. Hands have different blockers/etc.

For a really simple example to visualize it, imagine a scenario with very tight ranges (4 bet deep pot with high cards flop, idk) where you arrive at the river with a range of KK/QQ/JJ and your opponent has equal portions of AK/AQ/AJ in their bluffing range. If you are only allowed to call 100% of a combo then you probably call all your KK and fold all your QQ/JJ, but then your opponent can just bluff his AK and check back the others. Instead you can call 33% of each here.

the bluff catch range that is 0 ev is all mixed between those hands if blockers aren't important.


You could run a toy game where its like AA KK QQ 55 66 (3 combo) on 22223 and you have 77 88 99 TT or something the calling frequency will just be mixed with all those at equal frequencies

It's not super important, but basically if you called 88 100% and folded 77 100% I could bluff you always with an 8 and never with a 7 in my hand.

No one will realistically make this adaptation though

Pure strategies can potentially create blocker weaknesses in your range (see aner0's example above).

Solvers have exact knowledge of the opposing range, and can exploit those card removal effects with precision. Humans generally can't approach that level of clairvoyance.

You're both right, but even when blockers have 0 relevance, the bluff catch region is just mixed at the required frequency assuming the other guy has bluffs. See my toy game example. To make sure I wasn't talking out of my ass I ran the toy game and yeah what I said is correct. Also if blockers don't matter for the bluffing region it is also mixed at the required frequency.

so 22223 board with ip range = AA KK QQ 66 77 vs oop range = 88 99 TT in 100 chip pot with 100 chip for each player

ip should jam AA/KK/QQ (18 combos) and then 9 combos of 66/77

oop should call 50% of the time

I think that's just a matter of how the solver's algorithm works. Your toygame has multiple Nash equilibrium solutions (any calling range that has the overall correct frequency) and solver converges to that particular one.

it is, but that answers his question and provides an example. I should have just specifically stated, exactly what you just said. Hopefully that clears it up for him.

I guess the heart of my question is, "Would you be worse off calling TT 100% and folding 88 100% here rather than the mixed strategy?"

No, here it would be the exact same

88 is exactly as strong as TT in that example. They beat and lose to all the same hands. 88-TT might as well be the same hand.

You are perfectly polarized and there are no card removal effects, so any strategy that meets MDF is valid. You could call with all the 88, half the 99, and fold TT, and get exactly the same result.