Small Experiment Demonstrating Randomness of Online Cardroom Shuffles

[zaphod]

if one wanted to make a quick and easy demonstration that online poker cardrooms' shuffles are indeed random, i guess it would be pretty easy, right? just use a little probability to state how many times a given even should happen, then compare data to the theoretical outcome, right?

 

the only part i'm iffy on, because its been so long since i've slept through a stats class is this: how much deviation from the theoretical outcome is considered acceptable error?

 

for example, here's the little experiment that i did:

 

while observing a texas hold'em game, i chose to observe how many times a flop (3 cards on the board) would contain no ace.

 

in theory, the probability of this happening is:

 

P(No Ace On Flop) = (48/52)(47/51)(46/50) = (4324/5525) = approx. 78.26%

 

now, observing 100 flops i ended up with this data:

 

after 15 flops: 12/15 = 80.00% no ace: +1.74% deviation

after 30 flops: 21/30 = 70.00% no ace: -8.26% deviation

after 45 flops: 32/45 = 71.11% no ace: -7.14% deviation

after 60 flops: 43/60 = 71.66% no ace: -6.59% deviation

after 75 flops: 55/75 = 73.33% no ace: -4.93% deviation

after 100 flops: 75/100 = 75.00% no ace: -3.26% deviation

 

would this be sufficient, statistically speaking?

 

whats the calculation to determine how close to the expected outcome i should be in order for it to be acceptable given the amount of data available?

[matt grime]

Just google for hypothesis testing, I"m sure there must be many many sites explaining this (high school in th UK) level of statistics.