Reply To: Coin Toss: Not fair?

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Jamairoqui
@jamairoqui

@KerrAvon, @burbman: The chance of getting any particular value is relatively small, but the chance of getting 15 +/- 2 heads is very large, almost 2/3rds of the time you will be within that range. The chance of getting very much less or very much greater than 15 is small. In most statistical analyses, significance is accepted at the 0.05 level. My test found 0.03 (a bit less even). It is highly significant. In fact, I ran 20 more battles, won the toss on five and lost on 15. This gives me a 15 to 35 ratio, and the probability of that occurring by chance is 0.2% (significance level of 0.002).

I don’t doubt that some people believe that have fair coin flips, because for small sample sets you can think the coin flip is fair (turn your example around a little, if the probability of heads is 1/3 and tails is 2/3, it is equally possible you would see 8 heads and 12 tails in that scenario as it is you would see 8 heads and 12 tails in a 50/50 game). But if you were at a casino, and red came up 35 times out of 50 on a roulette wheel, you could almost guarantee that the wheel was rigged.

To be mindlessly pedantic about this, 8 heads out of 12 rolls only happens 12% of the time for a fair coin. If you are betting on something with only a 12% chance of winning, you will go broke in a hurry.