What confuses me, DanielB, is that at somepoint, you're going to have two prisoners with tokens, or points, or whatever. To dump them off, the one, the counter, will have to directly follow the other one. Each has a 1 in 100 chance in any day, so the chance of a consecutive sequence is 100 x 100 = 10,000. That means that once you get to that point, even if you are able to check every day, the minimum is 10,000 days (I understand it will often happen significantly sooner than that). To execute in 3,000 days, on average, you have to get around this last step somehow, because 3,000 average doesn't come from a 10,000 probability, which doesn't even start on day 1.

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Should Ric, Daniel, and I discuss this in a separate thread since it killed the riddles-proper?