We are up to problem #6 from Mosteller’s 50 Challenging Problems in Probability. This one asks about the expected loss in a dice game.

The game is played as follows:

(1) You choose 1 number from 1,2,3,4,5,6.
(2) Three six-sided dice get rolled.
(3) If you match 0 numbers you lose the bet,
(4) If you match 1,2, or 3 numbers you get back your original bet plus your bet times the number of matches.

Here’s what the boys thought about the problem:

We actually made some pretty good progress solving the problem in the last video – here we finished solving it:

Finally, we wrote as short program off screen to explore the problem. I thought I’d corrected the lighting problem, but obviously not, unfortunately. Still, hopefully the computer screen shows up well enough to see.

It is fun to see the boys learning to write short programs for these kinds of problems: