Tradermath logoBrainteaser - Dicey Dilemma

Dicey Dilemma
Probability
SIG
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?