Quote:
Originally Posted by YouAreAwesome
Is it possible there are multiple bet sizes yielding the same ev if both players are playing optimally? So rather than trying to figure out the optimal bet sizing on the flop, we pick a bet size and construct our range accordingly? Or is there a theorem that proves otherwise?
I think if you give a solver 3 reasonable bet-sizes to choose from, it will tend to build optimal ranges for all sizes (unless one of them is terrible), and some combos will appear in all three bet-size groups (and some in only two, or just the one, or none), but where a combo appears in all groups (at various frequencies) it will have the same EV in each. Some hands definitely 'prefer' a particular size, however, since that provides the highest EV for that hand.
e.g. In a short-stacked BvB scenario (e.g. in a tourney), it may be equally profitable to limp, minraise or jam with aces, but it's almost certainly better to open jam 22 than take another line, because 22 doesn't flop well. (It makes no sense to minraise with 22 if shoving has a higher EV). Therefore, in that spot you'd utilize a strategy that includes range-splitting, with some hands 'preferring' a particular line/sizing.
For deep-stacked games (i.e. cash), I don't think altering your flop sizing
massively alters the EV of particular combos, but there appears to be some small gain in EV (for individual hands, and also your whole range) by choosing different sizes for different parts of your range. It's very hard for humans to do this accurately, however. (It's hard enough to balance one range, let alone three or four). It's easier to just think "On this kind of board, my range does well by betting big, so that's what I'll do".
(FWIW, Snowie doesn't utilize range-splitting. Although it can estimate the EV of various bet-size choices, in a given spot it just picks the "best" one for its entire range - i.e. the size that produces the highest
average EV for the range - even if some combos could make more profit by picking another size.)
Quote:
Originally Posted by YouAreAwesome
It's an interesting thought that on the same board with the same ranges we can choose from multiple bet sizes and add or reduce bluffs accordingly.
I'm interested in the process.
1. Decide on value range.
2. Decide on showdown range.
3. Find our best bluffs.
4. Choose a bet sizing that caters for the correct ratio of value to bluffs in such a way to make our opponent indifferent to continuing.
I think this is a decent (and very human) approximation of good play, although I don't really like the "indifference" concept. Villain will always have
some combos that are better than breakeven when facing a bet. You just want to make it hard for him to make
much profit by continuing, while giving yourself the chance to maximise your profit as often as possible. Sometimes this means you bet small, because you want to get lots of (thin) value (or deny equity cheaply, or set a cheap price on your draws), and sometimes you bet big, because you want to get fat value with your monsters, but mostly want/expect villain to fold when you're bluffing.
Both of Matt Janda's books have a lot of discussion and examples of post-flop bet-sizing, so I'd recommend reading them.