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In an enchanted math realm, a mystical mathematician offers you a game with a standard 6-sided die. You're given a chance to bet on the outcome being even or odd. Here's the catch:
For every $4 you bet on the outcome being even, if you're correct, you'll receive $6 back. On the other hand, for every $6 you bet on the outcome being odd, a win gives you $9 back.
If you play this game optimally, how much should you bet?
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