Here are the odds and expected values for any keno games I can get the par sheets of. In most lotteries the odds are listed at the bottom of the par sheet, but they do not list the expected value of the game, which gives a better way of comparing games than odds alone. For keno the odds are easy enough to calculate using a hypergeometric distribution. The expected values are derived from the odds and payout amounts.
website: www.michigan.gov/lottery version: brochure dated 10/02
This keno is played like a lottery ticket: buy your card at the supermarket and see if you win in the next day's paper. It differs from standard keno since the house draws 22 balls instead of the standard 20 and the player must play a 10-spot card. The wager is $1.
| Number Chosen | Number Matched | Probibility | Award ($) | Expected Value ($) | Odds |
|---|---|---|---|---|---|
| 10 | 0 | 0.031691304 | 1 | 0.031691304 | 31.55 |
| 10 | 6 | 0.019226365 | 7 | 0.134584552 | 52.01 |
| 10 | 7 | 0.003196071 | 25 | 0.079901775 | 312.88 |
| 10 | 8 | 0.000321034 | 250 | 0.080258479 | 3,114.94 |
| 10 | 9 | 0.0000175223 | 2500 | 0.043805798 | 57,070.07 |
| 10 | 10 | 0.00000392742 | 250000 | 0.098185408 | 2,546,203.19 |
| Totals | 0.054452689 | 0.468427315 | 18.36 |
Overall, one can expect to win 5 percent of the games, and to earn 47 cents on the dollar. That is, to loose 53 cents of every dollar played.