First find the probability function of X; then determine the expected amount that the player will lose per unit of stake.
A game often played in carnivals and gambling houses is called chuck-a-luck, where a player bets on any number 1 through 6. Then three fair dice are tossed. If one, two, or all three land the same number as the player’s, then he or she receives one, two, or three times the original stake plus his or her original bet, respectively. Otherwise, the player loses his or her stake. Let X be the net gain of the player per unit of stake. First find the probability function of X; then determine the expected amount that the player will lose per unit of stake.
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