Should you play a dice payout game?

Two players each roll a fair six-sided die once.

• If you win (your roll > opponent’s roll), the opponent pays you $n .
• If the opponent wins or it’s a tie (your roll ≤ opponent’s roll), you pay the opponent $m .

Assume both dice are fair and independent.

Questions

1. What is the expected value of playing one round as a function of n and m ?
2. For what values of n and m should you choose to play ?
3. (Optional) Show a short Python snippet that computes the expected value analytically.