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I meant expected value of their each player's reward when the next block is found (whenever that is, and regardless of who found it)
The expected rewards over minutes I think is a bit of a harder question and probably requires modeling a poisson distribution, and is additionally complicated by the fact that players can change strategies dynamically. My hope is to build up to a fuller specification of a model iteratively through multiple of these small problems.
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The way 1.c. is posed sounds a bit odd. Are you asking what the expected reward for either party is or do you mean to convey an additional constraint by mentioning the time?