You have a 20-sided die and 100 actions, each either a reroll or collecting the current face in dollars. Which threshold for starting to collect maximises your payout?
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You have a 20-sided die showing 1 and exactly 100 actions. An action is either 'roll' (re-roll the die) or 'take' (collect the current face in dollars; the game continues and you may take repeatedly). You fix a threshold n in advance and start taking once you first roll at least n. What threshold maximises the expected payout, and what is that payout?
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