Keno Calculator
Calculator Use
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.
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.'
A MULTIPLIER number will be drawn prior to each KENO! Drawing: None, 2X, 3X, 5X, or 10X. If you played the MULTIPLIER option and your KENO! Ticket is a winner, your base prize will be multiplied by the selected MULTIPLIER for that draw. You may choose to play both BULLS-EYE and MULTIPLIER with your KENO! If both BULLS-EYE and KENO!
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:
- For every drawing, a Bulls-Eye number is selected by the computer from one of the 20 winning Keno numbers drawn. If any of your numbers match the Bulls-Eye number, you win a Bulls-Eye prize in addition to any base Keno winnings. Bulls-Eye prizes cannot be multiplied. The cost of Bulls-Eye equals the cost of your base Keno wager in Step 2.
- 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.
- You’ll only need to step into Red Rock’s Keno Lounge to see why it’s widely regarded as the absolute best in Las Vegas. It hosts 20 seats, four writer stations, automatic ball drawing, and Jumbo Keno as a linked progressive on 6, 7, 8, and 9 spot tickets.
- Keno is a fun, fast-paced game where you choose up to ten numbers and win based on how many you match. Win $1–$100,000 Cost: $1 – $20 per game; Packaged Keno To Go lets you purchase 20, 40, 60, 80 and 100 games for just $.25 per game, then watch drawings wherever and whenever you want. Win $.25 – $25,000. 20 games for $5 40 games for $10.
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.
Best 7 Spot Keno Numbers
If odds are stated as an A to B chance of winning then the probability of winning is given as PW = A / (A + B) while the probability of losing is given as PL = 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
Odds and Probabilities in Keno
There are 2 equivalent formulas using combinations to calculate probabilities for the game of Keno.
The two variables involved in the calculation are:
- n = Number of selections made by player
- k = How many of the player's selections match the drawn numbers.
1) The following formula uses the total number of combinations (i.e. denominator) from the houses point of view. There are 80C20 ways for the house to draw 20 from 80 numbers.
| Probability(n, k) = | nCk x (80-n)C(20-k) |
| ----------------------- | |
| 80C20 |
2) The following formula uses the total number of combinations (i.e. denominator) from the players point of view. There are 80Cn ways for the player to draw n from 80 numbers.
| Probability(n, k) = | 20Ck x 60C(n-k) |
| ----------------------- | |
| 80Cn |
3) Both of the above equations can be reduced to the same equation involving factorials given below.
| aCb = | a! |
| --------------- | |
| b! x (a - b)! |
Therefore:
| Probability(n, k) = | 60! x 20 ! x n! x (80 - n)! |
| ---------------------------------------------------- | |
| 80! x k! x (20 - k)! x (n - k)! x (60 - n + k)! |
Video Keno Odds Chart
Calculating the House Advantage in Keno
To calculate the return to the player, sum the returns (equal to probability multiplied by the pay-out) for each possible outcome. The house advantage is determined by subtracting the return to the player from the bet amount and is usually expressed as a percentage. The table below calculates the player's return using formula 2 above for the Spot 9 pay outs given in the example section of the Standard Rules page. The house advantage in this case is 100 x ($1 - $0.669665) = 33.03%.
| Result Details | ||||
|---|---|---|---|---|
| Match | Collect ($) | Frequency | Probability (%) | Return |
| 0 | 0.00 | 14,783,142,660 | 6.374783835335 | 0.0000000000 |
| 1 | 0.00 | 51,172,416,900 | 22.066559430007 | 0.0000000000 |
| 2 | 0.00 | 73,379,314,800 | 31.642613522274 | 0.0000000000 |
| 3 | 0.00 | 57,072,800,400 | 24.610921628435 | 0.0000000000 |
| 4 | 1.00 | 26,461,025,640 | 11.410518209547 | 0.1141051821 |
| 5 | 5.00 | 7,560,293,040 | 3.260148059871 | 0.1630074030 |
| 6 | 20.00 | 1,326,367,200 | 0.571955799977 | 0.1143911600 |
| 7 | 210.00 | 137,210,400 | 0.059167841377 | 0.1242524669 |
| 8 | 2,500.00 | 7,558,200 | 0.003259245500 | 0.0814811375 |
| 9 | 100,000.00 | 167,960 | 0.000072427678 | 0.0724276778 |
| Total | 231,900,297,200 | 100.000000000000 | 0.669665027234 | |
Related Pages
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. The best way to take advantage of Keno's chance-based platform is to know what the odds are for each selection (our Keno odds calculator can help with that). Keep this page handy while you are playing Keno so you get the best chances of winning. Start playing right now by selecting an online casino from our reviews here on ReviewPokerRooms. We list the top-rated online casinos that offer the highest internet security encryption and 24/7 customer service so you always have the help you need at any time of the day or night.
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