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). 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.

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 = ј. The expected return is thus ј * 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.

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

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.

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## Keno patterns

### 1. Keno numbers. How to find the pattern?

You have to know that Keno game uses an RNG system when extracts the numbers; this means is extracting random numbers, without any connection with previous or next extractions. Yet, as in any game, there are different patterns which can be observed after a long game monitoring. The keno algorithm creates some patterns to be followed by gamblers, which advantages are offered to those players who know how to identify them. If a gambler is able to understand the way in which program is generating those random numbers, then he can take advantage of the game and will easily win at keno. These patterns can be found only after careful study of various game sessions and they’re called in gambling terms -“pattern numbers”. These could be “hot” and “cold” numbers, mostly and can be found in the database of some casinos or in gambler archives. Keno statistics show that often between 5 and 8 numbers from the previous extraction are repeated.

### 2. Selecting Keno Patterns

Selecting patterns in a game are the most intriguing action, as request lots of patience and study. Choose consecutive numbers when you’re playing keno or bet on “hot” and “cold” numbers. Keno patterns involve mostly the way in which numbers extracted in different sessions and places are repeated. Keep looking for numbers repeated over and over, as these numbers offer a bigger chance of winning. Some players use their favorite numbers to bet, as family’s birth dates, ages or significant dates in their lives.

### 3. 4 card keno patterns

For the 4 card keno, the gambler will choose between 2 to 10 numbers, but playing on 4 tables at the same time. Playing 4 cards Keno is much better as your winning chances are higher; you can “hit” seven spots on half of these cards (2/4), which will offer you a pretty good jackpot. This is the pattern of winning at 4 card Keno: playing of various combinations of numbers, “reduced” from a bigger number. Actually is about overlapping numbers on the cards. Splitting the numbers among those 4 cards will offer a better chance of winning. Choose numbers in a quick succession like 20, 21, 22, 23; a total of: 26, 28 and a total of: 36, 37. It will be played at 3/3 (3 numbers of 3) with big chances to get out a single number.

### 4. 20 card keno patterns

Basically, the 20 card Keno is similar with the 4 card Keno, the only difference is related to the number of numbers played. Play up to 20 numbers on your cards, deduct combinations of number, and play on more than 3 spots. Actually, the biggest winner is starting with 5 spots, but this will make difficult the way in which the numbers are distributed. Working with 20 numbers split within 20 cards it is a little bit difficult, but as long as your winning chances have a better way of improvement, why not? After all, this is the best way of enjoying Keno! Share on three simple numbers vary between 63 and 70 (or others, depending on previous extractions). Find the combination of numbers that was repeated more often in the last 10-20 draw, then play 5 or 10 consecutive draws with a 4/6, 5/8, 6/10, but do not climb more than 6 / x (the more likely the smaller amount), i.e. calculating the minimum rate to win some (always keep you win).

### 5. Multi card keno patterns

As long as you’re playing with multiple cards, your chances if winning are balanced; even the odds are reduced, yet you will be able to open the path towards greater winnings. Choose to split the keno table into imaginary pieces to have a better view over it. Do whatever is necessary to keep your attention focused on all cards. These are the 5 hot numbers (often drawn): 23, 34, 72, 1 and 4.

### 6. Popular keno patterns

Keno gamblers really enjoy playing with various strategies or just following classic and popular patterns of the game. Either they’re playing using dates related to their families, either they’re using statistics and databases, observations by determining which numbers were often extracted, what is important in this game is to have fun. Focusing on the winning only, will have a negative result in this game. Just to combine fun and gambling, close your eyes and play with numbers randomly chosen.

### 7. Methods and patterns in keno

In a keno game, there is only one truth: the biggest prize is won with the highest number of picked numbers. In this case, a total of 20 numbers (which have been established that is impossible). From 6 to 10 picked numbers, any player has the opportunity to win at keno; up to 15 numbers can hit the jackpot. All keno gamblers (bingo and lottery too) have their own “lucky” numbers, on which they often play. You have to bet on big amounts if you want to win big rewards; playing on lower values will reward you with smaller gains. Here are according to statistics the hottest numbers in keno: 61, 66, 67, 74, 3, 16, 44, 58 and 78.

### 8. Keno winning patterns

The game of keno is based on a high dose of unpredictability, as it is the result of an RNG; random numbers are hard to be predicted, especially they’re the result of computer choice. Some players like to observe, determine and play with those numbers called “hot” numbers while others prefer to use complicated software programs, which they like to call “computer predictors”.

### 9. Lucky keno patterns

In a Las Vegas @#Casino#@, a player hit the biggest keno jackpot ever using the age of his wife, children, and his own birth date. The total value of the prize was $6.4 million and at the press conference, the winner said did not use any strategy, juts followed his favorite numbers, which in this case was “keno lucky numbers”.

### 10. Most common keno patterns

As it might see, there are different types of patterns used by the keno gamblers when they’re betting. When they’re playing using various dates related to their families, they should replace date of birth with the year of birth, as this offer a better option (the date of birth is only up to 31). Or can play using other dates related to themselves or their families as driver license number, passport dates, address’s numbers, etc.

### 11. Best keno patterns to play

The best way to win at Keno is by playing using verified numbers, as “hot” numbers. Or just play with the dates you like or use every time. Also, a better option is to use computer algorithm, which is able to make proper calculations and offer an increased chance of hitting big prizes. You have to figure out which is the best option for in the Keno game and used on a long time run. And do not forget to have fun, as Keno is before all, a game made to offer relaxation. Play on keno using these numbers, as they’re among the best: 61, 66, 67, 74, 3, 16, 44, 58 and 78. As long as you will follow these keno patterns, your chances of winning will be at the highest rate.

You have to know that Keno game uses an RNG system when extracts the numbers; this means is extracting random numbers, without any connection with previous or next extractions. Yet, as in any game, there are different patterns which can be observed after … ]]>