Rake vs. expectation
 

Let's assume you know, accurately and precisely, the expectation of every hand from every position preflop, in a rake free game. (Obviously you don't, but humor me.)

Meta-game considerations aside, you should fold hands where EV (BB/hand) < 0.

Now, for whatever reason, you play in a game with a 5% rake.

Because of the rake, you should now fold hands where, according to your rake free knowledge, EV (BB/hand) < x.

What is the value of x, and how do you figure this out?

Re: Rake vs. expectation
 

The additional piece of information you need is the average size of the pot when playing each hand. I don't think it's unreasonable to assume that you know this once we've accepted you know the EV of each hand. Then your x is 5% of the average pot size.

Guy.

Re: Rake vs. expectation
 

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Then your x is 5% of the average pot size x your winning%.



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Re: Rake vs. expectation
 

Sounds good; of course, this also assumes no min rake, no max rake, no rounding of the rake, and no "no flop, no drop".

Let's take this a step further:

Let's say the average pot is 10BB, the min rake is taken at a 5BB pot, and the max rake is taken at a 15BB pot.

How would this change the calculation? Can we approximate the effects due to pot size variance? Any idea what a reasonable approximation of this would be?

Re: Rake vs. expectation
 

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Then your x is 5% of the average pot size x your winning%.



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Good point.