Consider a dice game in which you try to obtain the largest number (e.g. you win a prize based on the final dice roll).
- You roll an 8-sided die, with numbers 1–8 on the sides.
- You may either keep the value you rolled, or choose to roll a 12-sided die, with numbers 1–12 on the sides.
What's the best strategy for choosing what to do in step #2?
I know the 8-sided die has expected payoff of 4.5, and the 12-sided die has expected payoff of 6.5. So I think relying on the 12-sided die is better — but how do I show the probability of this?