cEV/game in relation to ROI

Hey guys

I was tinkering with numbers and I have a question about spin and go (3handed, 500 chips each).

We need 1000 chips to win. if we get 70cEV / game, we have 7% of the chips needed to win the average prize;

so for 0.25$ spins the average prize is 0.69$ or 0.44$ profit.
So with 7% / game we would get 0.07*0.44 = 3.08c

3.08 (profit per game) / 25 (buy in per game) = 12.32% ROI in the long term.


Are these calculations correct?

I’ve been thinking some more and my reasoning above is flawed.

If i have 0 cEV per game i will lose all the rake because i dont make profit. In the formula above it doesn’t take rake into consideration correctly. So i thought about it some more and think this is better:

ROI = ((n*b+100*c(e/w)-n*r)/(n*b))-1
N = number of games
B = buy-in per game
C = average amount you cash for whithout rake
E = cEV per game
W = amount of chips needed to win the game
R = rake per game

An example (like the one above):
N = 100 games
B = 0.25 $
C = 0.75 $ (instead of 0,69, which is rake oncluded)
E = 70
W = 1000 (spin and go)
R = 0.02 $

((25 + 5,25 - 2) / 25) - 1 = 13%


If we change C to 20 cEV per game we’ll get -2% ROI. Which seems like a better answer than with the formula in my post above.


Any thoughts?

I think i found it

So I still think something is wrong with my formula and I found a better one I think
If we have 0cEV we have 500/1500 chips won which is 1/3 and we win 1/3 games.
If we have 100 cEV we have 600/1500 chips won and we win 40% of games.
So we integrat this in the following formula
(amount won - buyin - rake) / (buyin) = ROI

(g*p*c/t - g*b - g*r)/(g*b) = ROI
G= games playes
p= average prize money
c= Starting stack + chip EV per game
t = total chips to be won
r = rake

So for 100 games this would be
0cEV/game = (100*0.75*500/1500 - 100*0.25 - 100*0.02)/25 = -2/25 = -0.08 (or -8%) ROI. This should be correct as it is the amount of rake.
70cEV / game = (100*0.75*570/1500 - 100*0.25 - 100*0.02)/25 = 1.5/25 = 0.06 (or 6%) ROI.
100 cEV/game = (100*0.75*600/1500 - 100*0.25 - 100*0.02)/25 = 3/25 = 0.12 (or 12%) ROI.

Well I read somewhere you need 32cEV per game to win at spin and go's but with this formula I need 40 cEV at 8% rake.
35cEV per game for 7% rake.
30cEV per game for 6% rake.

Close enough I'm using this