Keno 3 Out Of 5 Numbers

Posted By admin On 02/04/22

According to data provided the hottest numbers in video keno are 3, 16, 44, 58, 61, 66, 67, 74 and 78. Video Keno Winning Patterns The game of video keno is centered on a big measure of unpredictability, because it is due to a RNG (Random Number Generator).

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.

  1. Check the latest Keno winning numbers here on PlayNow.com. There are thousands of Keno winners every day in BC. With the live draws happening every 3:30 minutes you could win up to $200,000.
  2. 5) Find out how many numbers you’ve hit in the free casino Keno game Finally, once you’ve completed all these steps the HTML5 game will draw numbers randomly and mark them colorful keno balls. The amount of numbers you’ve managed to hit along with the payout will be displayed in the side window.

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%.

Keno 3 out of 5 numbers texas lottery

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.

CatchFormulaCombinationsPaysReturn
3combin(20,3)*combin(60,0)1140$42$47880
2combin(20,2)*combin(60,1)11400$1$11400
1combin(20,1)*combin(60,2)35400$0$0
0combin(20,0)*combin(60,3)34220$0$0
Total82160$$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.

CatchFormulaCombinationsPaysReturn
4combin(20,4)*combin(60,0)4845$120$581400
3combin(20,3)*combin(60,1)68400$3$205200
2combin(20,2)*combin(60,2)336300$1$336300
1combin(20,1)*combin(60,3)684400$0$0
0combin(20,0)*combin(60,4)487635$0$0
Total1581580$$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.

CatchFormulaCombinationsPaysReturn
4combin(20,4)*combin(60,0)4845$1360$6589200
3combin(20,3)*combin(60,1)68400$20$1368000
2combin(20,2)*combin(60,2)336300$0$0
1combin(20,1)*combin(60,3)684400$0$0
0combin(20,0)*combin(60,4)487635$0$0
Total1581580$$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.

CatchFormulaCombinationsPaysReturn
5combin(20,5)*combin(60,0)15504$800$12403200
4combin(20,4)*combin(60,1)290700$9$2616300
3combin(20,3)*combin(60,2)2017800$1$2017800
2combin(20,2)*combin(60,3)6501800$0$0
1combin(20,1)*combin(60,4)9752700$0$0
0combin(20,0)*combin(60,5)5461512$0$0
Total24040016$$17037300

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

6 Spot

Multiplication
CatchFormulaCombinationsPaysReturn
6combin(20,6)*combin(60,0)38760$1500$58140000
5combin(20,5)*combin(60,1)930240$88$81861120
4combin(20,4)*combin(60,2)8575650$4$34302600
3combin(20,3)*combin(60,3)39010800$1$39010800
2combin(20,2)*combin(60,4)92650650$0$0
1combin(20,1)*combin(60,5)109230240$0$0
0combin(20,0)*combin(60,6)50063860$0$0
Total300500200$$213314520

6-Spot return = 70.99%

7 Spot

CatchFormulaCombinationsPaysReturn
7combin(20,7)*combin(60,0)77520$7000$542640000
6combin(20,6)*combin(60,1)2325600$350$813960000
5combin(20,5)*combin(60,2)27442080$20$548841600
4combin(20,4)*combin(60,3)165795900$2$331591800
3combin(20,3)*combin(60,4)555903900$0$0
2combin(20,2)*combin(60,5)1037687280$0$0
1combin(20,1)*combin(60,6)1001277200$0$0
0combin(20,0)*combin(60,7)386206920$0$0
Total3176716400$$2237033400

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

8 Spot

CatchFormulaCombinationsPaysReturn
8combin(20,8)*combin(60,0)125970$20000$2519400000
7combin(20,7)*combin(60,1)4651200$1500$6976800000
6combin(20,6)*combin(60,2)68605200$90$6174468000
5combin(20,5)*combin(60,3)530546880$9$4774921920
4combin(20,4)*combin(60,4)2362591575$0$0
3combin(20,3)*combin(60,5)6226123680$0$0
2combin(20,2)*combin(60,6)9512133400$0$0
1combin(20,1)*combin(60,7)7724138400$0$0
0combin(20,0)*combin(60,8)2558620845$0$0
Total28987537150$$20445589920

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

9 Spot

CatchFormulaCombinationsPaysReturn
9combin(20,9)*combin(60,0)167960$25000$4199000000
8combin(20,8)*combin(60,1)7558200$4000$30232800000
7combin(20,7)*combin(60,2)137210400$300$41163120000
6combin(20,6)*combin(60,3)1326367200$43$57033789600
5combin(20,5)*combin(60,4)7560293040$4$30241172160
4combin(20,4)*combin(60,5)26461025640$0$0
3combin(20,3)*combin(60,6)57072800400$0$0
2combin(20,2)*combin(60,7)73379314800$0$0
1combin(20,1)*combin(60,8)51172416900$0$0
0combin(20,0)*combin(60,9)14783142660$0$0
Total231900297200$$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.

CatchFormulaCombinationsPaysReturn
10combin(20,10)*combin(60,0)184756$50000$9237800000
9combin(20,9)*combin(60,1)10077600$8000$80620800000
8combin(20,8)*combin(60,2)222966900$2000$445933800000
7combin(20,7)*combin(60,3)2652734400$260$689710944000
6combin(20,6)*combin(60,4)18900732600$40$756029304000
5combin(20,5)*combin(60,5)84675282048$4$338701128192
4combin(20,4)*combin(60,6)242559401700$0$0
3combin(20,3)*combin(60,7)440275888800$0$0
2combin(20,2)*combin(60,8)486137960550$0$0
1combin(20,1)*combin(60,9)295662853200$0$0
0combin(20,0)*combin(60,10)75394027566$0$0
Total1646492110120$$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.

12

12 Spot Game
Probability of winning a prize in this game = 1:15.73
MatchOddsWin
121:478,261,833.14$1,000,000*
111:5,978,272.91$25,000
101:184,230.29$2,500
91:10,482.07$1,000
81:980.78$150
71:142.30$25
61:31.05$5
01:43.05$4

11

11 Spot Game
Probability of winning a prize in this game = 1:7.63
MatchOddsWin
111:62,381,978.24$500,000**
101:945,181.49$15,000
91:35,244.06$1,500
81:2,430.62$250
71:277.18$50
61:49.50$10
51:13.50$1
01:30.57$2

10

10 Spot Game
Probability of winning a prize in this game = 1:9.05
MatchOddsWin
101:8,911,711.18$100,000***
91:163,381.37$10,000
81:7,384.47$500
71:620.68$80
61:87.11$20
51:19.44$2
01:21.84$2

9

Keno 3 Out Of 5 Numbers

9 Spot Game
Probability of winning a prize in this game = 1:6.53
MatchOddsWin
91:1,380,687.65$40,000
81:30,681.95$4,000
71:1,690.11$200
61:174.84$25
51:30.67$5
41:8.76$1

8

Numbers
8 Spot Game
Probability of winning a prize in this game = 1:9.77
MatchOddsWin
81:230,114.61$15,000
71:6,232.27$1,000
61:422.53$50
51:54.64$10
41:12.27$2

7

7 Spot Game
Probability of winning a prize in this game = 1:4.23
MatchOddsWin
71:40,979.31$5,000
61:1,365.98$100
51:115.76$20
41:19.16$3
31:5.71$1

6

6 Spot Game
Probability of winning a prize in this game = 1:6.19
MatchOddsWin
61:7,752.84$1,600
51:323.04$50
41:35.04$7
31:7.70$1

5

5 Spot Game
Probability of winning a prize in this game = 1:10.34
MatchOddsWin
51:1,550.57$450
41:82.70$20
31:11.91$2

4

4 Spot Game
Probability of winning a prize in this game = 1:3.86
MatchOddsWin
41:326.44$100
31:23.12$4
21:4.70$1

3

What Numbers Come Out The Most In Keno

3 Spot Game
Probability of winning a prize in this game = 1:6.55
MatchOddsWin
31:72.07$25
21:7.21$2.50

Does 3 Numbers In Keno Win

2

Keno 3 Out Of 5 Numbers Texas Lottery

2 Spot Game
Probability of winning a prize in this game = 1:2.27
MatchOddsWin
21:16.63$5
11:2.63$1

1

KenoKeno
1 Spot Game
Probability of winning a prize in this game = 1:4.00
MatchOddsWin
11:4.00$2.50

How to Play

  1. Choose how many numbers (spots) you want to play by marking in the appropriate box.
  2. Select the amount of money you want to wager per game ($1, $2, $5, $10 or $20) by marking in one of the Amount Bet boxes.
  3. You can play up to 30 consecutive games by marking the appropriate box under Number of Games Played.
  4. Pick the numbers you wish to play from a field of 80 by marking in each of the boxes, keeping in mind the number of spots chosen above. IMPORTANT: KEEP MARKS INSIDE BOXES. Use only PENCIL OR BLUE BALL-POINT PEN to mark the betting slip. You may also let the Lottery computer choose your numbers by marking in the Quic Pic (QP) box.
  5. Mark the “Y” box if you wish to play KENO BONUS. If you play KENO BONUS the total wager amount will double.****
  6. Give the completed betting slip to an ON-LINE Lottery Sales Agent.
  7. The Sales Agent will give you a separate ticket as your receipt. IMPORTANT: CHECK YOUR TICKET! BE SURE THAT IT REPRESENTS THE NUMBERS AND DRAWING(S) THAT YOU WANTED TO PLAY AS IT IS YOUR ONLY PROOF OF PLAYING THESE NUMBERS.
  8. The Lottery suggests for your own protection that you sign the back of your ticket to identify ownership.

KENO BONUS

KENO BONUS gives you a chance to increase your KENO winnings by 3, 4, 5 or 10 times. To play KENO BONUS, mark the “Y” box on your bet slip. The cost of your wager will double. If you purchase the additional BONUS play for a drawing and win, you may multiply your winnings if a multiplier number (3, 4, 5 or 10) is drawn. The overall odds of having a multiplier number (3, 4, 5 or 10) are 1:2.3.

MultiplierOddsExample Winning Amount if KENO BONUS
Not PlayedPlayed
No Bonus1:1.75$5$5
3x1:3$5$15
4x1:15$5$20
5x1:40$5$25
10x1:234$5$50

KENO BONUS is not available for the 10-spot, 11-spot, or 12-spot KENO games. A KENO BONUS wager is only valid when played in conjunction with a valid KENO wager.

Rules

Keno 3 Out Of 5 Numbers Online

  1. Bets are not effective until accepted by the Lottery’s on-line computer processing system prior to the drawing of the winning number and in accordance with Lottery rules. Bettors acknowledge that on-line Lottery sales agents are acting on behalf of the bettors in entering bets into the Lottery’s on-line KENO computer processing system.
  2. Present your completed bet slip to your Lottery Sales agent for processing. You will receive a ticket. CHECK YOUR TICKET IMMEDIATELY TO VERIFY THAT THE SELECTIONS ON YOUR TICKET MATCH THE SELECTIONS REQUESTED ON THE BET SLIP.
  3. Present winning ticket to any on-line KENO sales agent for payment of prizes up to and including $600. Claims for more than $600 will be paid by the Lottery Commission after claim form is filed. Under unusual conditions, fixed prizes may be reduced according to the rules and regulations. All cash prizes must be claimed within one (1) year following the draw date.
  4. Your ticket is a bearer instrument. Unless signed by owner, prize may be claimed by anyone in possession of winning ticket. SIGN YOUR TICKET IMMEDIATELY. Bettors agree to abide by Lottery Commission rules and regulations. Applicable rules are available for inspection by bettors by contacting the Lottery Commission at. 150 Mount Vernon St. Dorchester MA 02125
*
Maximum overall prize payout for matching 12 out of 12 is $2,000,000 for any single game. If there are more than two ($2) dollars bet on the winning numbers, the payoff for each one ($1) dollar bet equals two million ($2,000,000) dollars divided by the number of dollars wagered.
**
Maximum overall prize payout for matching 11 out of 11 is $2,000,000 for any single game. If there are more than four ($4) dollars bet on the winning numbers, the payoff for each one ($1) dollar bet equals two million ($2,000,000) dollars divided by the number of dollars wagered.
***
Maximum overall prize payout for matching 10 out of 10 is $2,000,000 for any single game. If there are more than twenty ($20) dollars bet on the winning numbers, the payoff for each one ($1) dollar bet equals two million ($2,000,000) dollars divided by number of dollars wagered.
****
KENO BONUS gives you a chance to increase your KENO winnings by 3, 4, 5 or 10 times. To play KENO BONUS, mark the “Y” box on your bet slip. The cost of your wager will double. If you purchase the additional BONUS play for a drawing and win, you may multiply your winnings if a multiplier number (3, 4, 5 or 10) is drawn. The overall odds of having a multiplier number (3, 4, 5 or 10) are 1:2.3. KENO BONUS is not available for the 10-spot, 11-spot, or 12-spot KENO games. A KENO BONUS wager is only valid when played in conjunction with a valid KENO wager.