Lottery Sums

Introduction

This page shows the probability of any given sum of in a 6-49 lottery. For those not familiar with a 6-49 keno, it is a game in which the player bets on the draw of six balls, without replacement, numbered 1 to 49. It is a classic form of the lottery and one found in most states with a lottery. I created this page when I noticed bets on the sum of the draw in the game 49 Gold Rush.

There are combin(49,6)= 13,983,816 ways to choose 6 items out of 49. The following table shows the number of combinations for any given possible total from 21 to 279, the probability of that total, and the probability of that total or less.

The average ball is 25, so the average sum is 25×6=150. As the table shows, the probability of getting exactly 150, which the mean, median, and mode, is 1.19%, or 1 in 84.4.

Internal Links

Keno Sums — The exact same topic, but based on a draw of 20 balls out of 80. Contains a section on programming tips.

External Links

Here are some links on the math behind find the number of combinations of each sum in keno (20 balls drawn out of 80).

• WHAT IS KENO EXACT SCORE'S HOUSE EDGE? — First time this topic was raised on my forum.
• SUM OF ALL 20 KENO BALLS — Second time this topic was raised on my forum.
• Subset Sum Problem — How to solve this problem with a generating function (I don't recommend this method)
• Ways of getting a sum of S with M unique numbers in the range 1..N — More on the generating function method. The page seems to assume an understanding of Mathematica functions, so I wouldn't recommend trying to understand it if you're not familiar with that software.