here's a math question...

suppose a friend offers you to play poker with his money... he eats the losses and the profits are split by percentage, you keep x%.

how do you calculate what percent is break even?

Break even for who? Anything over 0% and you have only upside.

I think OP means "wins" are split by %x and not "profits." Pretty sure the answer to that depends on how good you are (i.e. your expectation). But if OP really means profits, then Rusty is right.

OK, well if he takes all your losses and you split your wins, then I'm guessing you mean "per period of time" or "per session" (like per day, week, whatever?). You can game this to be in your favor

Let's take a hypothetical breakeven player who plays 1000 hands, and the outcomes per 100 hands are
+1 -3 +1 -3 +2 +1 +1 -1 +2 -1
This sums to exactly 0. If you quit after each 100 hand "session" then you'd get
.5 - 0 + .5 - 0 + 1 + .5 + .5 - 0 + 1 - 0 = +4 Not bad!

But let's say instead that you quit the first time you were down at the end of a 100-hand block. So then your blocks would be
-2 -2 +4 and your part is 0 - 0 + 2 = +2, so that's worse.

What if you quit the first time you were ahead after a 100-hand block? That comes out even worse, getting paid +.5

I don't know off hand what the best stopping strategy would be but I think it's going to be the smallest number of hands possible since you'll get to book a lot in wins and write off all the losses.

i forgot to mention i'm a winning player, not sure what my hourly is but let's say it's $30... i understand that i'll never have a losing session if i take my friend's offer but couldn't taking x% on the wins not reach $30/hr? how do we calculate x so that it's the same as not taking my friend's offer?

to exaggerate, say he gave my 100% of wins... and eats all my losses... that's obviously better than my current $30/hr... and on the opposite spectrum, if he gave me 0% of my wins and eats all my losses... then my hourly becomes $0/hr... so there must be an x% that would equal $30/hr, agree? or is this logic flawed?

X would have to equal 100 for you to still meet your 30/hr goal if MY logic is correct..don't invest too much into that tho I'm pretty stoned (^_^)

Yes, and it varies by length of session. Say you're gonna play an 8-hour session. Some percentage of the time you win in 8hr session (a different % of the time than for a 1hr session). In your average winning 8-hour session, you win some amount more than $30/hr because 30/hr is the average of winning and losing sessions combined.

x_8hr = 30 / (win% * avgWin/hr)

That also makes it break-even for the staker.

But if you don't know your hourly profit, you also don't know those other stats, so setting a fair price will be mostly guesswork.

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.

hands	precut	expectation	cutpct
100	42.72	5.00	11.70
200	61.88	10.00	16.16
500	102.43	25.00	24.41
1000	152.19	50.00	32.85
2000	229.87	100.00	43.50
5000	409.39	250.00	61.07

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.

We're in agreement with the basic trend.

The longer the session, the smaller the avg hourly win per winning session will be (the closer it will get to exactly 30). If it's 1 hour then it might be something like 50/hr. So while win% increases with length of session, winrate decreases so the fraction X does get closer to 30/30 = 100%. If hero played a 1 million hand session, it would be basically 100% that he'd win and he'd make very close to 30/hr, so to get anything less than a 100% cut he'd be losing lots of money.

But Rusty, do your results account for the fact that losses are impossible in this situation? I ask because I see you're using expectations (at least as a starting point), and expectation factors in losses.

E(1 hr) = 5bb = (chance of winning)*(amount you'd win) - (chance of losing)*(amount you'd lose)

If we remove the negative term, the bb/hr will increase. (Let's say to R.) So to bring the rate back down to 5bb by imposing a break-even X:

5bb = R * x
x = 5 / R

Your method probably accounts for that somewhere but I'm just making sure.

My "expectation" column is the "traditional" expectation, if you were staking yourself. The rest of the numbers are calculated by taking a standard normal distribution and chopping off everything under 0, which accounts for the fact that we can't have a losing session.

so people sometimes say to me, can i just give you 100 bucks and can you play for me/... how do you respond to that and explain it in a way they can understand that there is no benefit for you since you are a winning player and would rather play with your own money...

You say, "What's in it for me?"