chillolini

Hey, I am new to this forum so please tell me if there is somewhere else this post should go.

I am planning on playing tournaments with a reentry option and was trying to figure out how to calculate my EV of playing such a tournament. It is easy to calculate for a no-reentry

NewBankroll(no-reentries) = (BankrollBeforeEntering - Buyin) + Buyin * (1 + ROI).

An example. If I was to calculate the EV of me playing a 100$ no-reentry on sunday with a ROI of 25% it would be (with a bankroll of 200$)

NewBankroll(no-reentries) = (200$ - 100$) + 100$ * (1 + 0.25)= 100$ + 100$ * 1.25 = 225$.

So how does one try to calculate this for a tournament with a reentry option (assuming we allways take the reentry option)? Surely my new expected bankroll after playing this kind of tournament should be higher than 225$? I feel like it is going to look something like

NewBankroll(reentry option) = P(reentry = 0) * (100$ + someEV) + P(reentry = 1) * (0$ + someOtherEV)

But not sure.

Also I have another question. Is it allways a +EV decision to reenter, assuming one have a positive ROI in the tournament from the start? I feel like there might exist stack distributions later in tournaments such that ones edge is not enough to compensate for the chip disadvantage.