Yes, I am sure someone will jump in and say "It means every hand in your range has the same EV for bet and check!".

Sure - it does. But I am struggling to know how to use that information/what the practical message is.

I think I've got ok at spotting the hands in a range that are good enough to bet but also not so good we can't check on an early street. Think top pair, weak kicker on a dry, static board. We can often bet or check the flop IP with these because we aren't looking to build a huge pot at all and don't feel great about being raised. In practice if we did bet flop we might check turn anyway, so x flop, bet turn is just as reasonable in EV terms.

But what about situations where solvers tell you every single hand in your range is like this?

Here's an example. SB v BTN, 3B pot, on AT6 two tone.



There's a small amount of overbetting, but big picture, the EV of bet or check is the same for every single hand in the PFR's range.* Does this mean:

- in situations where our range advantage on a certain board is strong enough (our EV here is 57% of the pot despite being OOP), we can do little wrong at least on the flop? Later streets are much more important?
- OOP can safely check great hands because unlike IP, OOP can often check-raise? The urgency of building a pot with our first action just goes down massively?
- something else?

I'd like to get to a point where I can recognise these situations in game a lot without having running them through a solver, and I think the first step is understanding the underlying logic. What do people think?

* Flush draws make a difference to the EV, but not the mixing. E.g. for KJs, we mix all hands even if the nut flush draw one has much higher EV. That EV is just higher whatever we do.

Typically, the betting frequency of X combo is related to the betting frequency of range. Here you don't have pure checks because range is betting ~60%-70% overall. Use this global frequency as a cursor. Mainly look at what bets a lot more/less. That's better ground for analysis. Everything is mixing, but not to the same extent.

Solve to higher accuracy. You didn't let this one converge, so it's mixing more than it should.

For example, KhJh has EVs 5.93/5.72/5.69, but it's mixing all three actions:


If you let it converge, all remaining mixed actions would have the same EV. The solver would stop taking any lower EV actions.

You could try to RNG different hands into different lines at different frequencies
You could simplify the strategy and try to figure out a way to mainly play each hand in 1 way without compromising any line
You could always try to find exploitative reasons to take one line or the other with every hand

You complete me.

I can't tell you how many times I've seen even well-named pros make such a simple error, claiming that the EV of raising is "slightly higher" than the ev of calling because they didn't run their solve to a high enough accuracy. Your posts are almost universally gold, thanks for posting here.