Calculator Use

• Keno Odds Calculator
• Keno Odds Chart

Convert stated odds to a decimal value of probability and a percentage value of winning and losing. This calculator will convert 'odds for winning' an event or 'odds against winning' an event into percentage chances of both winning and losing.

The keno cards and layouts of the games can change from one version to another, so get a good handle on any of the differences by playing for free before betting real money on a cash game. Most of the world’s best online casinos will ensure registered players have the option to try games for free.There, you can ensure you actually enjoy the aesthetic of the keno variant before kicking off.

Calculating keno odds? Ask Question Asked 3 years ago. Active 2 years, 2 months ago. Viewed 2k times 3. 1 $begingroup$ In keno, the casino picks 20 balls from a set of 80 numbered 1 to 80. Before the draw is over, you are allowed to choose 10 balls. What is the probability that 5 of the balls you choose will be in the 20 balls selected by the. There are specific odds for matching up to 10 numbers in keno. For example, when players select 1 number on their keno card, the odds of a match occurring during a drawing are 1 in 3. The odds of being able to match up to 10 numbers are as follows: Matching 1 Number – 1 in 3. Probabilities in Keno. To understand keno probabilities you must first fully understand the combinatorial function. For example, in the Maryland lotto the player picks 6 numbers out of 49. Then the lottery will draw 6 numbers out of 49, without replacement. The player wins the jackpot if all six numbers match (order does not matter). To use this calculator, enter the point spread and over/under line, then click the 'calculate' button. For example, you might enter -7 for the spread and 43 for the total. The calculator will calculate the fair line on some common props based on this information and historical NFL games from the 2000 to 2014 seasons.

Be careful if you are using sports teams odds or betting odds. If you see that the Patriots super bowl odds are 9/2, that is most likely 'odds against' and should be entered in the calculator with 'Odds are: against winning.'

When playing a lottery or other games of chance be sure you understand the odds or probability that is reported by the game organizer. A 1 in 500 chance of winning, or probability of winning, is entered into this calculator as '1 to 500 Odds are for winning'. You may also see odds reported simply as chance of winning as 500:1. This most likely means '500 to 1 Odds are against winning' which is exactly the same as '1 to 500 Odds are for winning.'

Probability Formulas:

This calculator will convert 'odds of winning' for an event into a probability percentage chance of success.

Odds, are given as (chances for success) : (chances against success) or vice versa.

If odds are stated as an A to B chance of winning then the probability of winning is given as P_W = A / (A + B) while the probability of losing is given as P_L = B / (A + B).

For example, you win a game if you pull an ace out of a full deck of 52 cards. Pulling any other card you lose. The chance of winning is 4 out of 52, while the chance against winning is 48 out of 52 (52-4=48). Entering A=4 and B=48 into the calculator as 4:48 odds are for winning you get

For 4 to 48 odds for winning;
Probability of:
Winning = (0.0769) or 7.6923%
Losing = (0.9231) or 92.3077%
'Odds for' winning: 1:12 (reduced from 4:48)
'Odds against' winning: 12:1 (reduced from 48:4)

Further Reading

To understand keno probabilities you must first fully understand the combinatorial function. For example, in the Maryland lotto the player picks 6 numbers out of 49. Then the lottery will draw 6 numbers out of 49, without replacement. The player wins the jackpot if all six numbers match (order does not matter). If you don’t know the probability of winning per game is 1 in 13,983,816 then you need to review the combinatorial function before going further.

In keno the casino, or game machine, will draw 20 numbers out of 80, without replacement. Before this happens the player may pick 1 to 15 (or more) numbers. A 'catch' is a number the player picked and was drawn by the casino. A 'miss' is a number of the player picked but was not drawn by the casino. The player is paid according to the number of picks made and catches.

Keno Odds Calculator

Although the player picks first the combinations get very huge when calculation the number of ways the casino can match the player’s picks. To start with there are combin(80,20) = 3,535,316,142,212,180,000 ways the casino can draw 20 numbers out of 80. Many calculators don’t support numbers this big. So to keep the combinations smaller we will assume the casino draws first, but keeps the numbers secret, and player tries to match the numbers already drawn. I assure you the math is the same either way.

All the following images were taken from the Luxor keno rulebook. All pays are on a 'for one' basis. In other words the player never gets his original bet back, even if he wins.

1 Spot

Let’s examine the 1 Spot card first. Here the player just picks one number, from 1 to 80. Then the casino will draw 20 numbers. If one of these 20 match the player’s number then the player is paid $3 for a $1 bet.

There are 80 numbers the player can pick. 20 of these will result in a winning ticket. So the probability of winning is 20/80 = ¼. The expected return is thus ¼ * 3 = 75%.

2 Spot

We need to start using the combinatorial function for the 2 Spot card. The player picks 2 numbers and casino must draw both of them for the player to win. There is no consolation prize for only catching one. There are a total of combin(80,2) = 3160 ways the player can draw 2 numbers out of 80. However the player must draw 2 out of the casino’s 20 drawn numbers to win. So there are only combin(20,2) = 190 ways to draw 2 winning numbers. So the probability of winning is 190/3160 = 6.01%. A winning $1 ticket pays $12, so the expected return is (190/3160) * $12 = 72.15%.

Alternatively, the probability the player’s first pick will match one of the casino’s numbers is 20/80. If it does match the probability the second pick will match one of the casino’s other 19 numbers out of 79 is 19/79. So the probability of winning is (20/80)*(19/79) = 6.01%.

3 Spot

With the 3 Spot card we start having consolation prizes for not matching every pick. First let’s determine the probability of catching all 3 marks. There are combin(80,3) = 82,160 ways to draw 3 numbers out of 80. To catch all three the player must pick all 3 numbers from the casino’s 20 drawn numbers. There are combin(20,3) = 1140 ways to do this. So the probability of catching all 3 is 1140/82160 = 1.39%.

There is a consolation prize for catching 2 out of 3. Imagine the casino puts the 20 drawn numbers in a winning urn and the other 60 numbers in a losing urn. The number of ways to catch 2 out of 3 is the number of ways to draw 2 balls from the 20 in the winning urn, which is combin(20,2) = 190. The number of ways to draw one losing ball out of 60 is obviously 60. So the number of ways to catch 2 out of 3 is the product of the number of ways to pick 2 winning balls from the winning urn and 1 ball from the losing urn, or 190*60 = 11,400. We already know there are combin(80,3) = 82,160 total ways to draw 3 balls out of 80. So the probability of catching 2 out of 3 is 11,400/82,160 = 13.88%.

For any bet the expected return is the dot product over every possible event of the probability and what it pays. The following table shows every possible outcome, with the total in the bottom row.

The bottom right cell shows that over all 82,160 combinations the player will get back $59,280. So the expected return is 59280/82160 = 72.15%.

4 Spot

For the 4 Spot ticket the number of ways to catch all four is combin(20,4) = 4845. The number of ways to catch 3 and miss one is the product of the number of ways to choose 3 out of 20 and the number of ways to choose 1 out of 60, or combin(20,3) * 60 = 1140*60 = 68,400. The number of ways to catch 2 and miss 2 is the product of the number of watch to choose 2 out of 20 winners and 2 out of 60 losers, or combin(20,2)*combin(60,2) = 190 * 1770 = 336,300. The following table shows all the possible outcomes.

The return of the 4 Spot ticket is 1,122,900/1,581,580 = 71.00%.

4 Spot Special

Keno Odds Chart

Next, let’s look at the 4 Spot Special. We just worked out all the combinations, so we only need to apply them to a different pay table as follows, based on a $7 ticket.

The expected return of the ticket is 7,957,200/1,581,580 = $5.0312. However we must divide this by $7, the cost of the ticket, to get the expected return, which is $5.0312/$7 = 71.87%. So, if you don’t mind extra volatility, and were going to bet $7 anyway, the 4 Spot Special is a better bet than the regular 4 Spot.

5 Spot

For the rest of the tickets I will present just the return tables. Following is the return table for the 5 Spot.

5-Spot return = $17,037,300/24,040,016 = 70.87%

6 Spot

6-Spot return = 70.99%

7 Spot

The 7-spot has a return of $2237033400/3176716400 = 70.42%

8 Spot

8-Spot return = $20445589920/28987537150 = 70.53%.

9 Spot

9 Spot Return = 70.23%

10 Spot

For some reason there is a $2 minimum beginning with the 10-spot. Here is the return table for a $2 ticket.

The $2 10-spot returns on average $1.4092. So the expected return is $1.4092/2 = 70.46%.

The Luxor keno rule book goes through a pick 15, plus a pick 20. However hopefully you understand how to do the math yourself by now.