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Why people think bots cheat

Posted By: Timothy Chow
Date: Tuesday, 24 August 2010, at 3:40 a.m.

In Response To: Why people think bots cheat (Daniel Murphy)

Daniel Murphy wrote:

How come nobody says "cheat!" when a bot rolls, say, 2-2 twice in a row -- which is much more unusual than rolling less than 44 pips in 9 rolls?

That's not quite correct. The probability of rolling 2-2 twice in a row is 1/1296, or about 0.00077. The probability of rolling less than 44 pips in 9 rolls is 23999899/49589822592, or about 0.00048. Close, though.

The simplest way to get the latter probability is to let

f(x) = x24 + x20 + x16 + x12 + 2x11 + 2x10 + 4x9 + 5x8 + 6x7 + 4x6 + 4x5 + 3x4 + 2x3

(where the coefficient of xn is the number of ways of getting n pips in one roll) and then add up the coefficients of x27 through x43 in (f(x)/36)9. This is easy to do with a symbolic algebra package like Mathematica or Maple.

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