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So just for shits and giggles, how many trials should be included (assume perpetual isn't an option) to truly gauge the 'fairness' of a die?
Toying with a /tg/-related experiment, but wanted to get /sci/'s opinion. Assuming all other variables are excluded, just a simple drop and result scenario.
100 is my guess, also an easy percentile conversion.
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Well mate you have to make a dice throwing machine to minimized randomness,then do & record about 500 results,and calculate ratio.I don't know what the diversion ratio is,depending on your definition of fair I guess.
Or use a computer program
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لا إله إلا الله محمد رسول الله
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>>8814063
Move your Islamic propaganda somewhere else.
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I guess for 'truth', you would need an infinite number of rolls.
But for a standard significance level and a regularly powerful test, 100 rolls is probably fine. Probably you could do with less.
http://math.stackexchange.com/questions/57624/how-many-rolls-do-i-need-to-determine-if-my-dice-are-fair
>6-sided: 52 rolls
>10-sided: 63 rolls
>20-sided: 83 rolls
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>>8814053
The rule of thumb I was taught for the specific statistical test you need here is that you should roll until you've seen every face of the die at least 5 times.
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>>8814053
Zero. Fairness of the die is a product of its construction. Gauging through trials is basically gambling and will not always produce accurate results.
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>>8814077
Never seen loaded dice before, champ?
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>>8814072
interesting read, thank you.
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>>8814073
interesting trick. any reasoning behind that or is 5 the arbitrary, defacto -numeral?
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>>8814077
I think that OP is looking for a way to determine the fairness of his die, not to prove that it is necessarily fair.
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SImply roll the die infinite times. By the large of law numbers the ratio
(Number of times you rolled i within the first N rolls)/N converges almost surely to the probability to roll an i. So you can check if the probabilites are right.
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>>8814172
what is the probability that the rolls converge inaccurately
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>>8814053
In addition to the power of the test (whether you want to be able to detect a biased die 95%, of the time, 99% of the time, of whatever else) it's also going to depend on how small of a bias you wish to be able to detect. An unfair die that rolls a one 80% of the time is obviously going to require far fewer rolls than an unfair die that rolls a one 18% of the time.
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>>8814980
>converges almost surely
this means the probability that it converges to 1/6 is 100%
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>>8814053
try to roll yahtzee
https://www.youtube.com/watch?v=fiTwar7mFws
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