For the past 20 years, I’ve been going to Las Vegas for a weekend here and there and, just like everyone else, I couldn’t even stop gambling to eat; and why should I? The casino owners so graciously offer to take even more of my money as I munch on the buffet of the day with the lottery alternative, Keno.
In case you’re unfamiliar with the game, its basic version goes like this. On a grid with 80 spaces labeled with numbers 1 through 80, the player may choose between 1 and 20 spaces and mark them. The computer then randomly chooses 20 spaces (regardless of how many the player chose). A win is determined by how many spaces marked by the user were chosen by the computer (these are called matches).
| Matches | Payout |
| 1-2 | $0 |
| 3 | $2 |
| 4 | $5 |
| 5 | $150 |
| 6 | $3000 |
People from all over the casino turn in $2 and a card containing their marks for the next game and the computer’s same 20 chosen spaces are played against all of them. Note that the more spaces the player marks, the more spaces must match in order for the player to win. In this example, the player chose 6 numbers, then hoped for 3 or more of those number to match. Please note the marked increase in the payout as the number of matches increases, this is what first got me interested in the game. I also wondered how the computer could control the total payout (in some cases a player can win over $100,000) when so many people are playing, and the computer must pick the same 20 numbers. I knew there was no way a casino would run a game where the odds weren’t in their favor, so I set out to determine the actual probabilites involved.
Continue reading Keno: an odd game