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Notes -
Are you taking Alice's money or Bob's money? From what I can see, they've got a nice system set up that's not letting you take their money, but it's not the case that the only number involved in their system is 1/3.
I think there's a sort of Monty Hall-style switcharoo going on with regards to what Alice puts into the computer. Only what she puts in the computer on Monday matters, so she should put the probability conditional on it being Monday into the computer, but bet her true probability (since she doesn't know whether or not it is Monday) herself.
You're being shifty with your language, though. First, you have an underspecified "probability conditional on it being Monday". I'm being a bit picky with this one, but please fully state "probability of ______" even if you think it's "...conditional on it being Monday". Second, you have that she is supposed to bet her "true probability", but what do you mean by "true" probability? This phrase is not defined. "True probability" of what?
Notice further that there are three variants. She doesn't always put the same number in the computer in each variant. How does that work? What name would you call the number that Alice puts into the computer in Variant 2, for example?
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