Optimal RFI size relative to rake?

I’m not aware of a way to calculate it directly or a heuristic to approximate it. It doesn’t vary a ton AFAICT. It seems to bottom out at about 2.25x (0.5p) and I haven’t seen it any higher than 3x IP (80%p).

It will fluctuate some based on other factors (additional blinds or antes, position, exploitation, limpers, some stack sizes), but rake alone isn’t forcing you out of that range, except for some extreme river boat gambling rake trap situation.

Surely it can be measured in terms of EV? From a theoretical point of view I guess there is a reason 2.5-2.25 bbs is considered optimal? RFIs of this size stand the best chance at winning the blinds outright, but also keep the calling ranges of the blinds wide enough to maximize EV against them postflop perhaps?

In live poker there are of course practical considerations to take into account - if you open to $7 in a $1/$3 game the whole table is liable to call.

So the next question is - how does increased rake affect the above? It clearly has a direct impact on the hands that the BB can defend profitably, and also on the hands that players can defend with when facing 3bets/4bets etc - that much is obvious. But how does it impact the optimal RFI size? Ultimately I believe the higher rake will just make the EV of opening hands smaller (as the pot will be smaller) - but does it have an impact on the optimal RFI size itself? I'm actually starting to think that it might not have an effect on that specifically; rather - the lowered EV simply means that many of the threshold zero EV hands that one could open in a lower rake structure simply become unprofitable opens?

I don't think rake has much to do with raise size. Rake affects how often you cold call vs 3bet (if you cold call at all). It also affects how tight our opening ranges are. It also affects our range composition. At lower rake or no rake structures, lower pocket pairs and suited connectors become more profitable to either RFI, 3bet, cold call, or even 4bet. At higher rake structures we prefer high card hands that decrease the likelihood of us being reraised when we enter the pot. So hands like AJo UTG might be better at high rake while hands like 65s might be better UTG at low rake.

Optimal raise size is generally between 2 and 2.5 from UTG to the button and 3-3.5x from small blind (or bb when there is an UTG straddle. But that assumes everyone else is playing optimal - IE they are correctly folding a lot of hands, 3betting a polar range in position, and 3betting linear/merged range from out of position. IE, if you raise UTG 9 handed, MP is folding KQo, but they are 3betting a range that includes KTs. The optimal open range might include a hand like K9s UTG. But if droolers are cold calling hands like KQo and KJo, maybe we don't open K9s. But marginal hands like AJo and KQo might become stronger opens from UTG.

Generally the more tight passive fish who aren't 3betting you, especially if they are in the blinds, the stronger it is to open a larger raise size with a range that is more high card heavy, which is more likely to hit top pair good kicker and be good. The more that you face aggressive, polar 3bets, and less frequently the hand goes myltiway, the more you want to open hands that are speculative, suited/connected, and the more you want to open those to a smaller size, so you lose the minimum when you have to fold to a 3bet, or for hands like 65s because you opened so small, if the 3bet is not too big and you are deep enough, you can profitably continue at the high SPR.

Another thing I've been considering lately if you've seen Marc Goone's 2/5 vlogs (hungry horse poker on youtube) is that if your pool had a lot of weak passive fish and you ha e a very aggressive recline driven approach, then larger raise sizes can really benefit you. Marc Goone is opening 5x a lot in 5/5, so straight 25, but he had a very strong postflop edge where opponents are putting in more money when Marc had value, snd they wre putting in more money on earlier streets to fold later to bluffs, so his style of using a very big raise size works very well for him.

However, one of the things that seems to give him trouble is when regs 3bet him. There was one hand where he opened to 25 from UTG with 99 and he got 3bet from the small blinds by a reg who was over 300bb deep. The reg was able to go bet, bet, jam and get Marc to fold on the river where Marc was left with a pure bluff catcher thst had to fold. Villain didn't have to overbet any street postflop to get in 300bb, and that is not the position you want to be in with a hand like 99. It really turned Marc's strategy of getting his opponents to call flop, call turn, and fold river and used if against him.

That's not to say his strategy is not good for the table he was playing at. This was the only other reg at the table. His strategy is probably printing against the rest of the table. But I think it is important to understand why large raise size can be good and why small raise size can be good, and what the weaknesses of both strategies are. Large raise sizes are an offensive adjustment that attacks weaker passive players. Smaller raise sizes are a defensive adjustments thst protects us against aggressive or more theoretically sound players.

Sure, but I don’t know how a human could calculate it. Situations with 9 players in the pot and five cards left to come are very difficult for determining EV. It takes solvers weeks using 100gigs of RAM to solve this stuff.

Early tree bet sizing is either the most complicated sh*t ever, or I’m the dumbest MFers in the world when it comes to it.

I think there are two things in tension here:

• We’re inclined to bet large because our opponents can realize a huge chunk of equity from seeing three cards with just one call.
  
  
• We’re inclined to bet small because it’s a multiway spot (where it’s easy to cheaply deny equity from everyone but the OOP BB) and we’re playing a perfectly linear strategy.
  

So the two…kinda just even out I guess? And you get yourself a standard 1/2p-3/4 PSR?

The “perfectly linear” part is an important caveat. Things quickly change if you’re incorporating a ISO/overlimp/fold strategy over limpers (say OTB), it is viable to ISO for a large size. It’s just good old fashioned getting more value with your value and getting more FE with your bluffs, while your middle strength hands cheaply realize equity with a limp. When it limps to the BB, they might raise 2xp with a very polarized range (with middle-strength hands very content to take the free cards, but bluffs wanting to squeeze all the dead money).

I’m skeptical that thinning the field is a huge motive for raising. I’ve been playing a lot of 9-handed bomb pot poker, and I can assure you if you were somehow to devise a way that you always had the top 10-20% of hands against 8 opponents with ATC, you would absolutely print money. (It would just be high variance.)

I think the intuition that you need to thin the field comes from two fallacies:

1) The natural inclination to want to win more pots, whereas raising an amount that entices -EV calls from multiple opponents will win fewer pots in route to winning more money.

2) Survivor bias - The times that you DO get called by 8 opponents, it’s often because you’re in an unlucky scenario where all of your opponents have a hand that’s great for busting Queens. If you had to choose between having 8 opponents dealt PPs and SCs and suited Aces or your opponents being dealt junk and having it fold around, you might prefer your opponents are dealt junk, so getting folds is a good result for your raise. But since you have no control over what cards your opponents get dealt, your choice is really between having the players with J2s and 87o fold or tag along with a bunch of terrible calls, and I’m confident you want them to make the bad call.

The real downward pressure on EV for raising and what puts a ceiling on how often you can do it is 3bets. When there’s a whole table of people who are going to 3bet you 5-15%, you have to show up with the goods often enough to not be donating whatever amount you raised (the larger the raise, the more pressure to have a sustainable frequency).

The reason you can raise more often and/or larger sizes live is because no one 3bets as much as they should.

With rake, you want to disincentivize the BB from defending, so you raise a bit larger to make their range a bit narrower, and the rake makes your 0EV raises slightly -EV, so your own range becomes a bit narrower, which makes it easier for you to sustain a larger raise size because when players 3! you, you’re showing up with a hand that can defend against it more often.

Thanks for the post, those were great points and I agree. I recently started watching Marc Goone too and really love his content; he's an excellent player and I love the psychology behind how he plays. For sure he may run into difficulty against regs, but that's just the nature of the beast, and the majority of the player pool are simply not going to know what hit them when playing against a player like that. That kind of style is massively profitable in low stakes poker and it's a style and psychology I aspire to myself.

I'm thinking of pushing up my RFI size from $15 to $20 at my local $2/$5 game. $15 has served me pretty well but I get the feeling $20 is gonna accomplish better what I'm trying to achieve. The drawback (at least in theory) is it means I should open fewer hands - and I am already a tighter than average player. So we'll see.

A human wouldn't need to calculate the EV; they could have a solver do it and then simply memorize the ranges. But yes I agree solving preflop EV is an enormous task because of the number of possible permutations before getting to showdown.

I agree with your arguments about betting large/small preflop too. But I think ultimately the purpose of the bet is to win the blinds without a fight, and whichever size does that the most efficiently is the size we should use.

Sure I see what you're saying with iso-raising and limping etc, but that's a different kettle of fish altogether.

I think the logic behind thinning the field makes sense, because even when a pot is 3-way instead of heads up we are forced to play a lot more passively and effectively face-up, especially if there's 5+ players or whatever.

I'd much rather have the top 10-20% of hands against one opponent with ATC, as opposed to 8 opponents with ATC - as I suspect the former is a much higher EV situation. I definitely prefer one player making a bad call for a large amount than 8 players making a bad call for a small amount.

For sure the risk of getting 3bet is a major issue with raising too wide and of course it's essential to keep in mind the players yet to act before you RFI.

So I guess what you're saying is higher rake = tighter RFI ranges and bigger RFI sizes? Makes sense.