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DanielLC comments on Probability, knowledge, and meta-probability - Less Wrong
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There's more than one event. If you assign a single probability to winning the first, third, and seventh times and failing the second, fourth, fifth, and sixth times given that you put in seven coins, etc. that captures everything you need to know and does not involve meta-probabilities.
More succinctly, the probability of winning on the second try given that you win on the first try is different depending on the color of the machine.
Right: a game where you repeatedly put coins in a machine and decide whether or not to put in another based on what occurred is not a single 'event', so you can't sum up your information about it in just one probability.