re: Mike and Mike posed an interesting question

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Eta: although now I'm questioning how I'd find the expected value myself. So frick if i know

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I could be wrong, but this is how I found the expected value based on a 5% chance of a making a single shot.

Probability of making at least 1 shot is easier to calculate as 1 - (the probability of not making one shot): 1 - (.95^20) = 0.64151.

Then the expected value should be the probability of making a shot multiplied by the reward: 0.64151*$20,000,000 = $12,830,282.

Now this would be incomplete because you would have to figure the costs of not making a shot 36% of the time (e.g., lost income, loss of future income, debt increasing etc.).

I also think that the probability of making a single shot will change with each successive miss because the psychological pressures will change, but I think this is roughly a good way to figure it out.