Spot on Ernie.

That's how I model the mechanics of bet sizing. I'm open to critisizm about that model.

@tombos This is very helpful. I think I'm guilty of following solver output at times without fully understanding why. I hope you will do more of these vids as they really do help explain why solvers do what they do and that allows us to create better heuristics.

Another big takeaway from these vids is how you create experiments to isolate the main causes. I think I can use my solver in a better fashion now.

Most obvious example i can come up with is BvB cbets on 842r versus 842tt
Same thing with rainbow turns versus single flushdraw versus double flush draw.

Thanks, I'm glad you found it helpful!

Experimenting with variables to try and understand cause/effect has been really valuable to me.

Because there is some indifference threshold between calling and folding when facing a bet of a given size we can also interpret the value of a bet sizing from the calling side as value extraction rather than from the folding side as fold equity.

So on a dynamic board 66% pot might get us more valuable fold equity with our strong hands than 33% pot. It also might extract more value (because a substantial class of medium strength hands now exist and will have to call the bigger size but would not have existed on a more static board).

Something like that?


Of course there are trade-offs at either size which is why usually solvers use multiple sizes in a given spot.

You're trying to choose a sizing that gets folds from relatively high equity hands while getting calls from relatively low equity hands.
Getting calls from high equity (and more importantly, high implied odds) hands, is not a great incentive when tehre are a lot of nodes left to play for reasons you probably intuitively know from playing the game.
You're trying to find a compromise sizing that keeps you from reverse implied odds situations both by making those hands fold and/or by not narrowing villains range to too many of those hands.

An easy example to understand this concept is, when you have say top pair, overcards probably have more equity than second pair versus your top pair. You can choose a sizing that makes overcards fold while making second pair call. This is partly why we size up with vulnerable top pairs.

When a low SPR spot, weighting your opponents range towards higher implied odds hands becomes less of a concern because the magnitude of those implieds is going to be relatively smaller, specially when we can get all in before the river.

Really interesting discussion and something I was just thinking about myself. Like aner0 said, we definitely bet bigger on 842rb compared to 842tt, presumably because our value hands have better equity when called. On twotone boards, we also have a region of flush draws as the aggressor, which devalues every bluffcatcher in the caller’s range. Vs the same size he ends up folding more bluffcatchers, and this has the effect of weighting his calling range towards high equity hands (including flush draws).

At the same time, I suspect part of the reason we size down on twotone boards is the presence of nut hands in the caller’s range. An interesting experiment to do would be to remove 2p+ from the caller’s range, and see if our overpairs still bet bigger on the corresponding rainbow board. If I had to make a guess, I’d say we actually go bigger on the twotone one now (and I think this is also what tombos is saying, correct me if I’m wrong).

If this is true, it would mean that it’s the combined presence of both nut hands and flush draws that make us want to size down. One without the other would make us size up instead, which I think is fascinating.

Could you elaborate on some of these reasons?