In light of this past weekend’s large lottery jackpot (a tax of sorts, on those that aren’t good at math), I thought it most appropriate to have a puzzle-of-the-week based upon a game of chance — chuck-a-luck.
Chuck-a-luck is a dice game played with three dice that are rolled within a closed container. After wagers on the numbers 1-6 (from each face on a standard die) are placed, the dice are rolled, and payouts are made per the following schedule:
- 1-1 if your number appears on just one die
- 2-1 if your number appears on two of the dice, and
- 3-1 if your number appears on all three dice.
What is the expected loss per roll for a five-die game, with the same payouts as above, and is it better than a three-die game? Would the payoff be better or worse if 4-sided die were used? What about d8? Additionally, propose a set of payoffs that would even the odds, i.e., instead of 5-1 return if your number appears on all five dice, posit a 6-1 or higher return.