I am doing some testing on a game to try and establish whether the outcomes from various mini-game mechanics match their advertised odds.
Here are a few examples
- Rolling two dice (presumed 'fair' dice)
36 total outcomes with equal distribution, 11 equivalent outcomes - Spinning a 10-segment wheel (presumed fair, i.e. odds of each segment being 1/10)
10 outcomes with equal distribution - Drawing a card with 1 of 3 outcomes (odds of each being: 3/6, 2/6 and 1/6 respectively)
3 outcomes with un-even distribution, lowest common denominator of 1/6th
How many samples are 'enough'
I am trying to understand how many samples I need to gather for each mechanic (and some others not mentioned) in order to say the results are within "X% margin for error"
Please can someone advise if there is a formula something along the lines of...
O [number of outcomes] ÷ N [sample size] * X [some value of equation] = margin for error
Any help would be greatly appreciated!
Research attempted / knowledge used
- I did stats in school but that was admittedly many years ago now. I know there are terms like 'margin for error' and 'confidence interval' - I think the former is what I'm after(?)
- As part of my googling I read about
p-andz-scores but don't really understand these or how to calculate them - I looked through: Calculating Margin Of Error but this was way above my level of understanding
- I looked through: Correlation between margin of error and sample size, but this (and other pages I read) talked about a mean value - however that doesn't apply to my data/intended calculation (AFAIK).