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Probability in Keno

Probability in Keno

If you want to learn how to win at online Keno, you need to understand the chances involved. Click for further reading material. Calculation is necessary.

The Chances of Winning at Keno

All Keno games adhere to the same probabilistic rules. Statistically speaking, it shouldn’t matter if the 20 numbers are drawn from the pool of 80 physically, using balls in a revolving cage or blower, or digitally, using a RNG – Random Number Generator. The odds of Keno are uniform worldwide.

A Confluence of Circumstances

The odds in Keno are determined by the draw. The first ball drawn might be any one of eighty different numbers. The second ball, picked from the 79 balls left, can be any of 79 potential numbers. There are 6,320 possible combinations of the two integers when multiplied together (80×79). Drawing 37 and then 63 is the same outcome as drawing 63 and then 37 in Keno, except the order of the draws does not matter. Therefore, there are 3,160 possible outcomes for two drawings if we divide 6,320 by 2. With the 78-possibility second ball, there are now 82,160 possible outcomes. With an additional 17 balls, the number of potential Keno combinations increases to 3,535,316,142,212,174,320, or three and a half quintillion.

1 80

2 3,160

3 82,160

4 1,581,580

5 24,040,016

6 300,500,200

7 3,176,716,400

8 28,987,537,150

9 231,900,297,200

10 1,646,492,110,120

11 10,477,677,064,400

12 60,246,643,120,300

13 315,136,287,090,800

14 1,508,152,231,077,400

15 6,635,869,816,740,560

: :

20 3,535,316,142,212,174,320

However, That’s Not All

Despite the huge number of possible outcomes, the odds in Keno are significantly better. Consider the scenario of 1 place (a player choose of a single number.) With 20 numbers chosen out of 80, then every single number has a 1 in 4 chance of being drawn, and a 1 spot play has one chance in four of winning.

Minimum play in many online Keno games is a 2-spot stake. After the first place’s 75/25 split, there are 79 leftover numbers for the second spot. In case the first location hit (matched,) there are 19 remaining drawn numbers and 60 undrawn. If the first location missed, there are 20 drawn and 59 left that weren’t. In either situation there are 79 choices. For the former instance of a hit, the chances are 19:79, whereas in the latter (after a miss) odds are 20:79. After the 1:4 hit, the 19:79 second hit happens (1×19)/(4×79) of the time. That’s a 19/316 or ~0.0601 probability – just over 6%. The remaining 60/316 occurrences (0.1899 or 19%) result in a single hit (the first one) for the two positions. For the latter case of a first spot miss, with its 3:4 odds, the chance of the second spot hitting is 20:79, for a possibility of (3×20)/(4×79), which is also 60/316 or 19%. This is again a single hit outcome, a miss followed by a hit, which combined with the prior chances for a hit followed by a miss leaves a total probability for hitting 1 location out of two as roughly 38%. The final case of a miss (3:4) followed by a second miss (59:79) is 0.5601 (56%).

Computing the third spot’s chances following the three outcomes above yields: 2-spots (19:316) versus (18:78) for a 3-spot or (60:78) for 2; 1-spot (120:316) versus (19:78) for a 2-spot or (59:78) for just 1; and no-spots (177:316) becoming 1-spot (20:78) or remaining no-spots (58:78). Total distribution is 3: 342/24648 (0.0139 1%), 2: (1140+2280)/24648 (0.1388 14%), 1: (7080+3540)/24648 (0.4309 43%), and 0: 10266/24648 (0.4165 42%). The procedure can be evaluated for the 10 spots playable in most online Keno gambling sites.

Keno Odds

Note the possibility of matching all 10 spots on a 10-spot bet is 1 in 8,911,700, nearly 9 million to 1 against.

Putting It All Together

These Keno odds are standard everywhere. Combining them with the tables for Keno payouts in any particular online Keno game can help in figuring out how to win at Keno.