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Why people think bots cheat

Posted By: W Womack
Date: Tuesday, 24 August 2010, at 6:34 a.m.

In Response To: Why people think bots cheat (Timothy Chow)

I made the mistake but it was not in dealing with the overlaps it was in counting the possible sequences. Each starting point in the summation represents a new possible sequence of 9 rolls so there is no need to divide by 17. Likewise there is no need to skip every other roll as the stream of random numbers could just as easily represent the rolls by one player. If you just add each series of 9 rolls there are 11 sequences that are 43 or less (eliminating overlap) but there are actually 25740-8 possible sequences of 9 in the data. The -8 is because you cannot sum the last 8 rolls as you can't make a sequence of 9. Taking 11/25732 gives 0.00043! This is in very close agreement with your calculated value of 0.00048.

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