Expected turnover on slots

Is there a way of calculating the expected total turnover on a machine given how much is put in, how much is net per spin, and what the return to player % is?

Eg if I put $100 in a machine and bet $2.50 per spin on a machine with a return to player % of 90% what would the total value of credits played expected to be assuming I played until I lost all of the credits?

I believe on average it would be $1,000 in action. But also depends on what you do when you end up with fewer than $2.50 remaining, do you keep playing for lower amount or does that count as “losing it all”? But that’s kinda closer to splitting hairs.

Thanks for your reply. Yes I guess the last part of your answer is splitting hairs!

What is the formula that allowed you to get your answe?

Essentially, if your expected loss is 10%, and your expected loss is also $100, then you need to figure out “$100 is 10% of what number?” The answer is going to be $100/10% = $100/0.1 = $1,000.

Remember, of course there’s variance. Some sessions you might only do $150 or $200 coin in. Other times you might hit something big early and end up doing several thousand coin in. But on average, it should be $1,000 coin in.

Quote: RS

Essentially, if your expected loss is 10%, and your expected loss is also $100, then you need to figure out “$100 is 10% of what number?” The answer is going to be $100/10% = $100/0.1 = $1,000.

Another way: At $2.50, that means each time you press the button your expected return is a loss of 25-cents. With zero variance you could push the button 400 times before dropping to zero, 400 x $2.50 = $1000

But that's the mean. We've all put in $100 and lost it all after only earning 200 points. And sometimes we can put it $100, cash out with $100 after earning 1000 points. With a bit more information, are there any good ways to estimate median amount of action?

Starting with $100 and wagering $2.50 on a machine that averages 10% hold, I get an average loss of $0.25 per spin. That gives you an average of (100-2.25)/0.25=391 spins. (You are left with $2.25 which won’t cover the next wager.) Your average coin in would be 391*2.50=977.50. Average results are just that: average. If the variance of the machine is known you can get more useful information, such as a probability your results will be within a given range.

Edited: changed 1000 bankroll to 100.

No expert on this, but with high variance, as an example 10% of EV is a $10,000,000 jackpot that is rarely hit, you will rarely make it to $1000 in with your $100 start.