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