# Keno Odds

## Introduction

Like any game, the purpose of calculating the odds of a game is to figure out how much of your money will be paid back to you. This will allow you to get the maximum amount of playing time on your money. The percent payout to the player will usually be around 65% for Keno games run by a state lottery and around 90-95% for online Keno. For Keno games played at land-based casinos, they tend to be better than the Keno games run by the state lotteries but still way below the online games. This doesn't seem like a big difference until you look at the inverse of those numbers - the house profit. A game that returns 95% to the player means that the house is keeping 5% of the amount wagered but a game that returns only 65% to the player means that the house is keeping 35% of the amount wagered - 7 times as much!

## Calculating the odds

Here is the equation for calculating the probability (p) of hitting (n) numbers out of the (x) numbers you picked when (y) numbers were drawn out of (z) total numbers (i.e. - "What is the probability of hitting 4 out of the 5 numbers I picked when 20 numbers were drawn out of 80").

p(x,n) = (((combin(x,(x-n)))*combin(z-x,y-n))/combin(z,y))

where:       n = 4
x = 5
y = 20
z = 80

You can download my odds spreadsheet by right-clicking and selecting "Save target as" to calculate the casino's edge of the keno game you play.

## Calculating the edge

In order to calculate the house edge, you simply calculate the probability of winning on each of the number of matches (1 out of 5, 2 out of 5, etc.) and multiply it by its correlating prize, which is shown on the payout schedule. Then you add up the amounts to find out the total expected return of the bet. The difference is the house edge.

## Example payout schedules

In the previous sections I pointed out the large differences in payouts for kenos games and illustrated how to calculate what the house edge is on any keno game. Inside the odds spreadsheet I also provided two payout schedules from real-life to illustrate the point. One is from the Ohio State Lottery and the other is from an online casino - similar to what you would see at Bodog. Both sets of results are based on the standard 80 ball game with 20 balls drawn and \$1 bet.

#### Payout Schedule (Ohio Lottery)

 Numbers picked Matches 1 2 3 4 5 6 7 8 9 10 1 \$2 - - - - - - - - - 2 \$11 \$2 \$1 - - - - - - 3 \$27 \$5 \$2 \$1 \$1 - - - 4 \$72 \$18 \$7 \$5 \$2 \$2 - 5 \$410 \$57 \$11 \$15 \$5 \$2 6 \$1,100 \$100 \$50 \$20 \$10 7 \$2,000 \$300 \$100 \$50 8 \$10,000 \$2,000 \$500 9 \$25,000 \$5,000 10 \$100,000

#### Payout Schedule (online casino)

 Numbers picked Matches 1 2 3 4 5 6 7 8 9 10 1 \$3 \$1 \$1 \$0.50 \$0.50 \$0.50 \$0.50 \$0.50 \$0.50 - 2 \$9 \$2 \$2 \$1 \$1 \$0.50 \$0.50 \$0.50 \$0.50 3 \$16 \$6 \$3 \$2 \$1 \$1 \$1 \$1 4 \$12 \$15 \$3 \$6 \$3 \$2 \$2 5 \$50 \$30 \$12 \$6 \$4 \$3 6 \$75 \$36 \$19 \$8 \$5 7 \$100 \$90 \$20 \$10 8 \$720 \$80 \$30 9 \$1,200 \$600 10 \$1,800

## Comparing profits

I took the two different payout schedules and calculated the casino's edge on each of the possibilities and added them up. The payout schedule for the state lottery shows a house edge of 35-60% while the payout schedule for the online casino shows a house edge of mostly 5-8%. You will lose your money 6 to 7 times as fast playing the state lottery. On the surface, the keno game run by the state lottery looks much more profitable because the payouts much more attractive at the higher end. But this assumption is illusory because the payouts at the higher end have such a low probability of occurring that even large changes in absolute payouts won't have a substantial effect on the bottom line. For example, if you compare the payouts for hitting 10 out of 10 numbers you will notice that the state lottery pays out \$100,000 while the online casino pays out only \$1,800. The problem is that the chance of hitting 10 out of 10 is almost 9 million-to-1. The \$100,000 payout is only about 1% of 9 million so the \$100,000 payout only adds only 1 cent of value to the ticket. Even if you increased that payout to \$5 million, the state would still make money on that ticket in the long-run.

The payouts on the small end occur much more frequently and that's where most of the value of the ticket is. If you look at the payout schedule of any Keno game where the house has a big edge (like the state lottery example) there will often be no payouts for hitting only a couple of the numbers. For example, if you pick 10 numbers the state lottery doesn't pay out anything for hitting less than 5 numbers but the online casino pays out for hitting either 2, 3, or 4 numbers. The payouts are small (\$0.50-\$2.00) but since they occur so often they can add a substantial amount of value to a \$1 ticket.

Another thing to note is that the house edge can change a lot within the same game. The house edge ranges from 5% to 25% in the online game and ranges from 34% to 59% in the state lottery game. On most payout schedules, the house edge will usually be higher when you play either the minimum number of balls (1) of the maximum (usually 10, 15, or 20).

#### Expected Value (Ohio Lottery)

 Numbers picked Matches 1 2 3 4 5 6 7 8 9 10 1 \$0.50 - - - - - - - - - 2 \$0.66 \$0.28 \$0.21 - - - - - - 3 \$0.37 \$0.22 \$0.17 \$0.13 \$0.17 - - - 4 \$0.22 \$0.22 \$0.20 \$0.26 \$0.16 \$0.23 - 5 \$0.26 \$0.18 \$0.10 \$0.27 \$0.16 \$0.10 6 \$0.14 \$0.07 \$0.12 \$0.11 \$0.11 7 \$0.05 \$0.05 \$0.06 \$0.08 8 \$0.04 \$0.07 \$0.07 9 \$0.02 \$0.03 10 \$0.01 Total EV \$0.50 \$0.66 \$0.65 \$0.65 \$0.65 \$0.65 \$0.65 \$0.65 \$0.65 \$0.41 House Edge 50% 34% 35% 35% 35% 35% 35% 35% 35% 59%

#### Expected Value (online casino)

 Numbers picked Matches 1 2 3 4 5 6 7 8 9 10 1 \$0.75 \$0.38 \$0.43 \$0.22 \$0.20 \$0.18 \$0.16 \$0.13 \$0.11 - 2 \$0.54 \$0.28 \$0.43 \$0.27 \$0.31 \$0.16 \$0.16 \$0.16 \$0.15 3 \$0.22 \$0.26 \$0.25 \$0.26 \$0.17 \$0.21 \$0.25 \$0.27 4 \$.04 \$0.18 \$0.09 \$0.31 \$0.24 \$0.23 \$0.29 5 \$0.03 \$0.09 \$0.10 \$0.11 \$0.13 \$0.15 6 \$0.01 \$0.03 \$0.04 \$0.05 \$0.06 7 \$0.00 \$0.01 \$0.01 \$0.02 8 \$0.00 \$0.00 \$0.00 9 \$0.00 \$0.00 10 \$0.00 Total EV \$0.75 \$0.92 \$0.93 \$0.94 \$0.94 \$0.94 \$0.94 \$0.93 \$0.93 \$0.95 House Edge 25% 8% 7% 6% 6% 6% 6% 7% 7% 5%