Scenario 1
100bb effective stacks. 0% rake.
Folds to BTN who RFI to 3bb.
SB folds
BB calls


Let's say that the poker gods answered me the following question:

What is BB's EV with his calling range, after he calls BTN's RFI, assuming they both play GTO?

I dont know BB's range, I just know his EV.
So let's say the poker gods have told me that BB should expect to win 4bb of the 6.5bb pot on average after he calls BTN's RFI, as per GTO play. Great.

Scenario 2
100bb effective stacks. 5% rake uncapped, no flop no drop.
Folds to BTN who RFI to 3bb.
SB folds
BB calls

Based on what the poker gods told me for the first situation with no rake, what would the answer be to this question now that we have to pay 5% rake upon seeing a flop?

What is BB's EV with his calling range, after he calls BTN's RFI, assuming they both play GTO?


Will he have less EV than in the first scenario? Equal? More?!

Did he flat with queens or something? It's pretty hard for the BB to call pre with the expectation of winning more than half the pot. I'd estimate that the top of his calling range actually has an EV of less than 3bb, with the bulk of it being much closer to breakeven (getting back slightly more than the 2bb he voluntarily invested). The pre-flop raiser is expected to capture more than half the pot, due to his range advantage and position.
/pedant mode

FWIW, there's a GTO solution to a game with no rake, and a different solution in a game with rake. Some hands that are just above breakeven in the zero-rake game become unprofitable in the raked version, so should be folded (or turned into 3-bet bluffs if that is +EV) in that format.

Don't read too much into that 4bb figure ...I obviously don't have the answer and I was just using a random number as an example.

FWIW BB has to call 2bb pre so every hand that is called has to be at least 2bb, so I estimate the true EV is somewhere between 2.5 - 3.3 in a non rake game.


But ignoring the exact figure of whether it's 2.6 or 2.7 (because I'm never going to know, really), should we expect the EV to be less in a raked game than in a 0 rake game? Or is the rake adjusted for preflop in that BB folds more in the first place?

IMO it will be roughly the same because BB shouldn't call any hand that loses money, and this holds true whether there is rake or no rake. But I'm not sure so I wanted to see opinions

I think we have less EV in the raked game.

Without rake, let's say the top of our calling range wins $X and the bottom of our range of course breaks even. With rake, the top of your calling range wins $X minus rake and the new bottom breaks even after rake (we fold everything worse than this). So we end up with some weighted average from 0...(X-r) instead of 0...X.

I agree very much with this. This is particularly noticeable when deciding on preflop ranges in fixed limit small stakes games, and even more so in small stakes fixed limit hi-low split games.

In a word, yes. In effect, the rake 'steals' some of your equity. Consider that you could be playing a coin-flipping game with 100bb stacks. With no rake, your expected value is zero. (You break even in the long run). If the site takes 5% of the pot, you're losing gradually, but it would be noticable fairly quickly, as a whole stack would be missing after 20 flips*. If the site took (a ridiculous) 95% of every pot, you're losing very rapidly, and it would be immediately noticeable since even winning a flip would add next to nothing to your stack.
If you're looking at a GTO solution for a raked game, then the rake has already been taken into account, and would lead to more folding pre than in an unraked aternative. Again, imagine a game where the house took 95% of the pot. It wouldn't be worth playing anything but aces, as every other hand would have a negative expectation. In short, the higher the rake is, the lower the incentive to play the game.

To use a counter-example, a 'bad beat jackpot' operates in the opposite way to rake, and it can turn hands that would normally be folds into slightly +EV calls/raises. Imagine that the BBJ paid a billion dollars if you won with 72o making quads. It would presumably be +EV to try and hit the jackpot. (In the real world, most BBJs aren't valuable enough to make many hands into +EV plays, but a GTO solution would definitely have to figure in the potential EV of a BBJ to calculate the optimal pre-flop play, as the BBJ is literally part of the payoff).

* Or is it 10? I have a headache and can't do maths.

P.S. High rake in the micros (and the raking of chopped pots) is one of the reasons you should sometimes avoid getting AK in pre-flop. The rake effectively "steals" about 5% of your equity, so you're losing money even if villain also has AK.

Thanks for replies all,

in hindsight yes, the BB has less EV from calling in the raked game, and the simplest way to think about it is by seeing the top of our range now loses some equity to rake.


The next question would be to wonder how both players adjust to this, i.e. if BB is folding more because of rake, does BTN open more etc, but that's a question for another day / thread.

With that, you're getting into the concept of "fictitious play" or simulations, where one players imagines using a strategy, the other adjusts his to exploit it, and then first reacts to that adjustment, until they come to a new equilibrium. While they establish an equilibrium, it's akin to a levelling war. Ultimately, higher rake has to lead to both players playing tighter.

To put it another way, the BTN might think "I can open wide, because the BB is folding so often", but the fact the BTN is opening wide means the BB should start defending more, and when he starts doing that it means the BTN should tighten up, which means the BB should stop defending so often... etc etc.
In the real world, players that react or adjust to changes in the game more quickly than others can gain a profitable edge.
If the rake was quietly increased, the player that noticed and adjusted his strategy the soonest would get an edge. You see this in things like tournaments, when some players don't change their strategy when antes first come in, when those antes mean the pre-flop "solution" is actually quite different to a no-ante game.
Another example would be in a specific SNG or tourney that has its rake changed by the room/site. A rake increase in a hyper-turbo (for example) might make the game unbeatable (or at least less beatable), and the good/obsevant regs will immediately stop playing that format, but the bad regs (and fish) won't even notice. Sometimes, so many regs quit the game when the rake goes up that it then becomes profitable for the few that stay (because the reg:fish ratio is better).