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.