# Casino Bonuses, Variance and expected value

## What effects the profitability of a casino offer?

• ### $6.70 is the expected value of the offer Votes: 0 0.0% • ### The expected value of the offer is actually higher if you stop every time you bust out the$10

• Total voters
0

#### packtim

##### New Member
I am looking to get some views on this from people on here, and would be interested to see what people think. I am an engineer. been a few years since I have studied statistics.

An online slot has a return to player (RTP) of 97%. So for every $100 spent, on average over infinite iterations, you would expect to retain$97 for every $100 staked. There is hypothetical an offer on: Stake$10 and get a $10 bonus. You have to wager the bonus 10 times before you can keep the winnings from it. If you bust out, you stop playing. In theory the total you would have to stake here would be$110, with the RTP of 97% you would expect to lose $3.30, and be left with an overall balance of$16.70. So let's call the 'expected value' of the offer $6.70 (your profit) Now obviously you could run this experiment an infinite number of times, with various results. 1) Would stake size change the expected value of the offer (i.e the number you bet each spin)? It would definitely increase the variance I know. 2) Is$6.70 the true 'expected value' of the offer? Lets say you had an infinite bank balance, and didn't stop when you lost your initial $10, but just played the offer out until you completed the wagering requirement of 10 times the bonus. Would it change the 'expected value' of the offer at all if you didn't play it out (but effectively had a 'stop loss' of$10)? Is the expected value actually higher than $6.70, because you would stop every time you tried the offer and were$10 down, or would it be the same whether you stuck to the stop loss or not?

This is just something I want to find people's opinions on. It has nothing to do with the ethics of gambling/you will always lose in the long term, and it is the maths and statistics side of things that I am interested in.