Chuck A. Luck Wagers a Buck:

PART I  What Are the Odds?Consider the following question posed by Daniel Reisman of Niverville, New York, to Marilyn vos Savant in her column Ask Marilyn (vos Savant 1999): At a monthly "casino night," there is a game called ChuckaLuck: Three dice are rolled in a wire cage. You place a bet on any number from 1 to 6. If any one of the three dice comes up with your number, you win the amount of your bet. (You also get your original stake back.) If more than one die comes up with your number, you win the amount of your bet for each match. For example, if you had a $1 bet on number 5, and each of the three dice came up with 5, you would win $3. It appears that the odds of winning are 1 in 6 for each of the three dice, for a total of 3 out of 6or 50%. Adding the possibility of having more than one die come up with your number, the odds would seem to be slightly in the gambler's favor. What are the odds of winning at this game? I can't believe that a casino game would favor the gambler. Although Marilyn didn't answer the question directly, she provided the following response: ChuckaLuck has a subtle trick that many people don't recognize unless they analyze it. If the three dice always showed different numbers, the game would favor no one. To illustrate, say that each of six people bets $1 on a different number. If the three dice showed different numbers, the operator would take in $3 from the losers and pay out that same $3 to the winners. But often, the three dice will show a doublet or triplet: two or three of the dice will show the same number. That's when the operator makes his money. For example, say the dice show 3, 3 and 5. The operator collects $4 ($1 each from the people who bet on 1, 2, 4, and 6) but pays out only $3 ($2 to the person who bet on 3, and $1 to the person who bet on 5). Or say the dice show 4, 4, and 4. The operator collects $5 ($1 each from the people who bet on 1, 2, 3, 5, and 6) but still pays out only $3 (to the person who bet on 4). The collections and payoffs change according to the bets (sometimes the house wins, sometimes the gamblers win), but with this game, you can still expect to lose about 8 cents with every $1 you bet over the long run. Questions
Go to PART IIDate Posted: mb 02/26/01 