Volatility

Hi Everyone,

I wonder if you can help me. I've designed a slot game that has an average win 70.835 with a Standard deviation of 205.54. I'm trying to calculate how often the average win across 1000 games would exceed 100.

I've tried using this formula:

z = X - Avg Win
--------------
SD/ SQRT(n)

The result i'm getting is 1 in 276684 but when i run the 1000 games multiple times i'm getting more like 1 in 20,000.

Can anyone shed any light on this? Am i using the correct formula?

Trevor

Quote: Trevor

Hi Everyone,

I wonder if you can help me. I've designed a slot game that has an average win 70.835 with a Standard deviation of 205.54. I'm trying to calculate how often the average win across 1000 games would exceed 100.

I've tried using this formula:

z = X - Avg Win
--------------
SD/ SQRT(n)

The result i'm getting is 1 in 276684 but when i run the 1000 games multiple times i'm getting more like 1 in 20,000.

Can anyone shed any light on this? Am i using the correct formula?

Trevor

The math looks okay. When you say ‘multiple’ of times about how many times are you referring to?

The central limit theorem that you are using only tells you that your average will converge to a normal distribution for a sufficiently large number of plays. It doesn't say anything about how many plays you need to get a a desired accuracy out in the tails of the distribution where it is most inaccurate. You are out at 4.5 standard deviations. Your underlying distribution of scores is not at all normal if negative scores are not allowed since your standard deviation is larger than your mean. Large jackpots will also slow convergence. We need to know the probability distribution of the scores (payout schedule), and how many 1000 game trials you ran. Then we could bound the accuracy with the Berry-Eseen theorem.

Hi BruceZ and PeeMcGee,

Thanks so much for your replies.

I ran 1000 games 200,000 times twice and got around 10 hits both times.

BruceZ,

I have the probability for all possible win values.

Also, there's a lot of jargon and different formulae in your link. Is it possible to provide a single formula and a distilled explanation.

Cheers,

Trevor