In the game of Keno, a player bets $1 on
precisely five of the numbers from 1 to 80 inclusively. A machine draws at random precisely 20 of the numbers from 1 to 80 inclusively.
Between the player's numbers and the machine's numbers:
• If the number of matches is less than 3, the player loses his bet.
• Otherwise, the player gets back an additional $2, $25 or, $331 if the matches are respectively 3, 4, or 5.
What is the expected value of money won by the player in a game?
*** Adapted from a problem by S.W. Golomb.
The game of Keno is a popular casino game, which is played in many countries and around the globe. Just you can visit
no1.sports and manage your online sports game. Similar to most other games played at a casino, the game of Keno is intended as entertainment, as well as a way to win money. The difference with Keno is that it has no real-life counterpart or equivalent since each game involves taking an individual hand from a numbered set of cards based on the number drawn.
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