OT: Home Sick for the Holidays, or Probability and Yahtzee

[Krsqk]

I'd start checking your friend's dice, David.

Actually, Geo is absolutely right, with one clarification. The difference in percentage points will likely decrease, eventually dropping near the break even point; the numerical difference will likely increase. There is no guarantee that actual results will even out over time (the usual misapplication of the law of averages).

Put another way, the odds of rolling a six with a single die are 1/6 every time, whether the "score" is 75 to 5 or 40 to 40. Previous results do not affect future results.

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In a separate thought, I found one page (granted, one which wasn't a strictly mathematical approach) which said probabilities which are mutually independent (such as rolling two separate dice) should be added; i.e., the odds of rolling at least one six with two dice is 1/6+1/6, or 1/3. If that's true, though, the odds of rolling at least one six with twelve dice would be 12/6, or 200%. That obviously isn't correct.

As I'm having much trouble finding any helpful information on the web, such as an intro to probability site or the like, I'd appreciate any links y'all can pass along.