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You're given a unique gamble with two dice - one with 8 sides and the other with 12 sides. Initially, you roll the 8-sided die. After seeing its outcome, you're faced with a choice:
- You can keep the value of the 8-sided die roll, or,
- You can choose to roll a 12-sided die, but then you must accept the result of this roll as your final outcome.
Your payout is based on the value of the last die you roll. What's the strategy to maximize your expected payout, and what is this expected payout?
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