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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.
KENO PAYOUT CALCULATOR. After entering the payouts, click 'Calculate.' The defaults values are used with Microgaming, Odds On, and Rival. Numbers on Ticket: Number of Picks: 0 hit payout: 1 hit payout: 2 hits payout: 3 hits payout: 4 hits payout: 5 hits payout: 6 hits payout. Keno Odds Calculator Keno is fast and fun. It is a lottery style card game that players can enjoy as a break from the strategy and skill needed to play poker online. If you are short on time, but want a game that offers huge potential rewards then Keno is the game to play. Prize value based on $1 wager. For wagers over $1, multiply the prize amount by the amount wagered. Check your ticket's validation with our 180 Day Calculator. For more information, call 1-800-686-4208. KENO Booster® Keno Booster may increase your winnings up to 10 times! At the top of every KENO bet card is a Booster option.
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.
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%.
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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.
| Catch | Formula | Combinations | Pays | Return |
| 3 | combin(20,3)*combin(60,0) | 1140 | $42 | $47880 |
| 2 | combin(20,2)*combin(60,1) | 11400 | $1 | $11400 |
| 1 | combin(20,1)*combin(60,2) | 35400 | $0 | $0 |
| 0 | combin(20,0)*combin(60,3) | 34220 | $0 | $0 |
| Total | 82160 | $ | $59280 |
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.
| Catch | Formula | Combinations | Pays | Return |
| 4 | combin(20,4)*combin(60,0) | 4845 | $120 | $581400 |
| 3 | combin(20,3)*combin(60,1) | 68400 | $3 | $205200 |
| 2 | combin(20,2)*combin(60,2) | 336300 | $1 | $336300 |
| 1 | combin(20,1)*combin(60,3) | 684400 | $0 | $0 |
| 0 | combin(20,0)*combin(60,4) | 487635 | $0 | $0 |
| Total | 1581580 | $ | $1122900 |
The return of the 4 Spot ticket is 1,122,900/1,581,580 = 71.00%.
4 Spot Special
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.
| Catch | Formula | Combinations | Pays | Return |
| 4 | combin(20,4)*combin(60,0) | 4845 | $1360 | $6589200 |
| 3 | combin(20,3)*combin(60,1) | 68400 | $20 | $1368000 |
| 2 | combin(20,2)*combin(60,2) | 336300 | $0 | $0 |
| 1 | combin(20,1)*combin(60,3) | 684400 | $0 | $0 |
| 0 | combin(20,0)*combin(60,4) | 487635 | $0 | $0 |
| Total | 1581580 | $ | $7957200 |
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.
| Catch | Formula | Combinations | Pays | Return |
| 5 | combin(20,5)*combin(60,0) | 15504 | $800 | $12403200 |
| 4 | combin(20,4)*combin(60,1) | 290700 | $9 | $2616300 |
| 3 | combin(20,3)*combin(60,2) | 2017800 | $1 | $2017800 |
| 2 | combin(20,2)*combin(60,3) | 6501800 | $0 | $0 |
| 1 | combin(20,1)*combin(60,4) | 9752700 | $0 | $0 |
| 0 | combin(20,0)*combin(60,5) | 5461512 | $0 | $0 |
| Total | 24040016 | $ | $17037300 |
5-Spot return = $17,037,300/24,040,016 = 70.87%
6 Spot
| Catch | Formula | Combinations | Pays | Return |
| 6 | combin(20,6)*combin(60,0) | 38760 | $1500 | $58140000 |
| 5 | combin(20,5)*combin(60,1) | 930240 | $88 | $81861120 |
| 4 | combin(20,4)*combin(60,2) | 8575650 | $4 | $34302600 |
| 3 | combin(20,3)*combin(60,3) | 39010800 | $1 | $39010800 |
| 2 | combin(20,2)*combin(60,4) | 92650650 | $0 | $0 |
| 1 | combin(20,1)*combin(60,5) | 109230240 | $0 | $0 |
| 0 | combin(20,0)*combin(60,6) | 50063860 | $0 | $0 |
| Total | 300500200 | $ | $213314520 |
6-Spot return = 70.99%
7 Spot
| Catch | Formula | Combinations | Pays | Return |
| 7 | combin(20,7)*combin(60,0) | 77520 | $7000 | $542640000 |
| 6 | combin(20,6)*combin(60,1) | 2325600 | $350 | $813960000 |
| 5 | combin(20,5)*combin(60,2) | 27442080 | $20 | $548841600 |
| 4 | combin(20,4)*combin(60,3) | 165795900 | $2 | $331591800 |
| 3 | combin(20,3)*combin(60,4) | 555903900 | $0 | $0 |
| 2 | combin(20,2)*combin(60,5) | 1037687280 | $0 | $0 |
| 1 | combin(20,1)*combin(60,6) | 1001277200 | $0 | $0 |
| 0 | combin(20,0)*combin(60,7) | 386206920 | $0 | $0 |
| Total | 3176716400 | $ | $2237033400 |
The 7-spot has a return of $2237033400/3176716400 = 70.42%
8 Spot
| Catch | Formula | Combinations | Pays | Return |
| 8 | combin(20,8)*combin(60,0) | 125970 | $20000 | $2519400000 |
| 7 | combin(20,7)*combin(60,1) | 4651200 | $1500 | $6976800000 |
| 6 | combin(20,6)*combin(60,2) | 68605200 | $90 | $6174468000 |
| 5 | combin(20,5)*combin(60,3) | 530546880 | $9 | $4774921920 |
| 4 | combin(20,4)*combin(60,4) | 2362591575 | $0 | $0 |
| 3 | combin(20,3)*combin(60,5) | 6226123680 | $0 | $0 |
| 2 | combin(20,2)*combin(60,6) | 9512133400 | $0 | $0 |
| 1 | combin(20,1)*combin(60,7) | 7724138400 | $0 | $0 |
| 0 | combin(20,0)*combin(60,8) | 2558620845 | $0 | $0 |
| Total | 28987537150 | $ | $20445589920 |
8-Spot return = $20445589920/28987537150 = 70.53%.
9 Spot
| Catch | Formula | Combinations | Pays | Return |
| 9 | combin(20,9)*combin(60,0) | 167960 | $25000 | $4199000000 |
| 8 | combin(20,8)*combin(60,1) | 7558200 | $4000 | $30232800000 |
| 7 | combin(20,7)*combin(60,2) | 137210400 | $300 | $41163120000 |
| 6 | combin(20,6)*combin(60,3) | 1326367200 | $43 | $57033789600 |
| 5 | combin(20,5)*combin(60,4) | 7560293040 | $4 | $30241172160 |
| 4 | combin(20,4)*combin(60,5) | 26461025640 | $0 | $0 |
| 3 | combin(20,3)*combin(60,6) | 57072800400 | $0 | $0 |
| 2 | combin(20,2)*combin(60,7) | 73379314800 | $0 | $0 |
| 1 | combin(20,1)*combin(60,8) | 51172416900 | $0 | $0 |
| 0 | combin(20,0)*combin(60,9) | 14783142660 | $0 | $0 |
| Total | 231900297200 | $ | $162869881760 |
9 Spot Return = 70.23%
10 Spot
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For some reason there is a $2 minimum beginning with the 10-spot. Here is the return table for a $2 ticket.
| Catch | Formula | Combinations | Pays | Return |
| 10 | combin(20,10)*combin(60,0) | 184756 | $50000 | $9237800000 |
| 9 | combin(20,9)*combin(60,1) | 10077600 | $8000 | $80620800000 |
| 8 | combin(20,8)*combin(60,2) | 222966900 | $2000 | $445933800000 |
| 7 | combin(20,7)*combin(60,3) | 2652734400 | $260 | $689710944000 |
| 6 | combin(20,6)*combin(60,4) | 18900732600 | $40 | $756029304000 |
| 5 | combin(20,5)*combin(60,5) | 84675282048 | $4 | $338701128192 |
| 4 | combin(20,4)*combin(60,6) | 242559401700 | $0 | $0 |
| 3 | combin(20,3)*combin(60,7) | 440275888800 | $0 | $0 |
| 2 | combin(20,2)*combin(60,8) | 486137960550 | $0 | $0 |
| 1 | combin(20,1)*combin(60,9) | 295662853200 | $0 | $0 |
| 0 | combin(20,0)*combin(60,10) | 75394027566 | $0 | $0 |
| Total | 1646492110120 | $ | $2320233776192 |
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.
In this Article we Present to You an Extensive list of the Most Commonly Used Terminology in Keno!
Today, you can play keno both offline as well as online. If you are new to Keno, you would do well to know the different terms used in the game. What is an ‘all or nothing’? Or a ‘ball game’? What does someone mean when he uses the term ‘buy-in tournament’? This article provides a glossary of these and some other terms used in Keno.
The Most Important Keno Terms to Know
Keno: This is today’s version of an ancient Chinese lottery. You get to draw 20 numbers out of a total of 80 (nowadays the total is 120), and you win if you are able to correctly guess the numbers drawn.
All or Nothing: This is a term used in Keno to represent a ticket that pays only if you draw all the numbers picked, or if you draw none of the numbers picked.
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Ball Game: This is the most common form of Keno nowadays. In this form of the game, plastic balls represent the numbers.
Blank: This is a term used to represent an unused Keno ticket.
Blower: The blower is part of the machine that is used to dispense the plastic balls used in Keno. With the blower, the game operator can force the balls into a tube, using air.
Buy-in Tournament: This is a type of Keno tournament where you have to pay a pre-determined fee upfront. Once you pay the fee, you are eligible to play in a specific number of games or play a set number of tickets. In a buy-in tournament, you get to keep any money you win.
Cage: The cage is no longer used in Keno games today. Basically, it was a wire cage used in the earlier days to hold Keno balls. Today, you mostly find plastic hoppers. The term ‘cage’ also denotes a specific area in a casino where only employees are allowed, and where you can find Keno workers.
Catch: This is a term used to denote a number that you have called in a Keno game.
Catch-all: This is a type of Keno game where you have to get all the numbers marked on your ticket. Another game is Catch-zero, where you must ensure you do not get any of the numbers that you have marked on your ticket.
Close: This is a term used to identify that period in time when the casino stops writing any more Keno tickets. The time period usually stretches from just prior to the draw till immediately after the draw.
Fractional Rate Ticket: This term is used to represent a ticket that you can play for a fraction of the standard rate.
High End Ticket: This term is used to refer to a Keno ticket that pays you more if you catch a high number of spots. However, if you catch a lower number of spots compared to the standard ticket, you win less or even no money.
High Roller Ticket: This is a Keno ticket whose minimum pricing is high.
House Edge: This term is used to represent the percentage of bets that the house, i.e. the casino, can hope to win over time. The standard house edge is 30%, though this number is not necessarily the same for all casinos.
Keno Glossary – Summing Up
Odds Of Winning Keno
The above are some of the terms that you will encounter when you start playing Keno. You would do well to read up more about the large number of terms related to Keno before going ahead and trying your luck at the game. We have further glossary lists on our site so check them out!