Let's say you win 5bb/100 hands with a standard deviation of 100bb/100 hands. Let's consider identical session lengths of N hands. Your win rate/hand is .05bb/hand and your stdev is 10bb/hand. So your expected winning are going to be .05N and your stdev over the N-hand sessions would be sqrt(N)*10 bb per session.
Your expected outcome is the integral from to inf of x*f(x) where f(x) is the standard normal curve with these parameters, because f(x) is the chance of having an outcome of x, and x is how much it's worth. You can just write a little program to calculate these, so that's what I did.
If I didn't screw it up, here are the results. "hands" is how many hands in each accounted session. precut is how much you're expected to make before your cut. That is, if this number is $1000 and your cut is 30% then your profit would be $300. cutpct is the percentage of cut you'd need to take of precut to make your cut equal to your expectation.
As you can see, the shorter the sessions are, the less of a cut you need to take, because almost all your losses get eaten by your staker. For longer sessions, you will eat some of your own losses, because you will have winning sessions that include mini-downswings that your backer would have absorbed under shorter sessions.