Hey friends.

This past few months I've been thinking about two competing concepts in regard to preflop bet sizing.

The first idea is that of decreasing sizing in later positions because fold equity is greater, ranges are wider, and that by using this formula for Required fold equity: R/(R+PG), smaller sizing in later position reduces the amount of money you put into the pot (R). It seems logical and standard.

Then I studied a machine learning program that did just the opposite; Snowie in 6 max actually increases bet sizing in later position.

I think that Snowie's strategy is to quantify the value of late position instead of capitalize on fold equity. I am assuming that the machine is attempting to build larger pots because it assumes that there is more ev to be reaped with larger sizes in later positions, possibly due to its tight range.


Is Snowie's approach +EV for humans, or is it more EV to reduce sizing in late position to increase it through less required fold equity?

This debate has been going on for years.
I used to think that smaller sizes in later position made most sense, because ranges are weaker/wider and you quite like playing in position, whereas EP ranges are strong, but you wanted to dissuade multiple callers when you're OOP.
These days, I think the opposite philosophy might be correct, and that small sizes are more appropriate for early positions, because you're more likely to get 3-bet, and/or be playing OOP post-flop, and you don't want to play big pots OOP, so you'd start with a smaller size.

The thing is, in 100bb deep games, pre-flop sizing isn't going to massively effect your EV, provided your range makes sense in the context of the sizes you use. e.g. If you open tighter than "GTO" in EP, a larger size makes sense (tight range => more value hands), and if you open wider than "GTO" on the button (because the players in the blinds are terrible at poker) a smaller size is better there. Or you could just use 2.5x or 3x (or whatever is common/standard in your game) for every position.

FWIW, when Snowie simulates higher stake games with lower rake, its button raise size comes back to normal/small. It's only up to 100NL (I think) that it likes potting it. It's something to do with leveraging additional fold equity in the high rake microstakes games, but since a lot of micro regs are nits, you can still steal blinds pretty easily IRL with minraises.

It's almost certain that the optimal solution involves some sort of increase in open sizing as you get closer to the button. This was hinted at all the way back in 2006 in MOP. The reasons are multiple:

1. Position itself has value (solvers suggest it's about 5% of the pot), if you are more likely to play in position you want to play larger pots on average.
2. The smaller the threat of getting 3bet the more we can risk with open raising.
3. The bulk of BB ev comes from calling, when you're in late position the main game tree is BU open -> BB call. Bigger opens reduce the ev of calling.

It's also likely that there are multiple optimal solutions to preflop play. It could well be that a minraise with 60% of hands has the same ev as a 2.5x with 50%. In the end it's a balancing act between playing as many hands as you can while not exposing yourself too much to 3bets while reducing BB call ev as much as possible.

Let’s figure this out. We can get an idea of the optimal preflop actions without solving preflop entirely.

We can pick a seat and discuss.

I propose that cutoff should have a range at least as wide as button, and a rfi sizing slightly larger than button. The saying “buy the button” has mathematical merit.

The goal is to win the blinds or to be heads up versus one player. Wider and larger serves both purposes.

If I recall correctly, I remember Chris Ferguson saying that you should raise less in EP and more in LP. This makes sense to me for a variety of reasons already stated.

I think through personal experience I have found it much easier to play against someone who 4xs or 5xs from UTG than someone who 2xs or 3xs. When someone makes a large sizing I can comfortably fold and know I'm not making a mistake. I think the whole smaller-SPR-for-early-position-is-better argument is grossly overrated.

Personally I just 3x from all positions for simplicity.

I believe Harrington said the opposite. I remember him stating that he raises less in late position because he doesn't mind OOP callers (blinds, limpers). He raises more in EP to fold the field and not have to play OOP. Granted, it's been 7+ years since I read his books, but that's how I remember his thinking. I know, poker has evolved a lot since then, but his results in that era speak for themselves in MTTs.