The Odds of Keno

Understanding Keno odds is an essential prerequisite to learning how to win playing online Keno. Read here for more info. Some math required.

Keno Odds – The Odds of Keno

Keno games the world around are all governed by the same laws of probability. The drawing of the 20 numbers from the pool of 80, whether done mechanically by balls in a rotating cage or blower, or done digitally by an RNG – Random Number Generator – should statistically generate the same results. The Keno odds are standard everywhere.

A Combination of Factors

To compute Keno odds, start with the draw. During the drawing, the first ball is any one of 80 possible numbers. The second ball, drawn from the 79 balls remaining, can be any of 79 possible numbers. Multiplying them means that the two numbers can be any of 80x79 = 6,320 possibilities. However, the order of the draw doesn’t matter; drawing 37 and then 63 or drawing 63 then 37 is the same outcome for Keno. So 6,320 is divided by 2 to give 3,160 combinations for two draws. The next ball, with 78 possibilities, increases that to 3,160 x 78/3 = 82,160 combinations. Continuing for seventeen more balls, the final result is 3,535,316,142,212,174,320, or three and a half quintillion, possible combinations of Keno numbers.

# of draws Combinations out of 80
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

But Wait, There’s More

Despite the astronomical number of combinations, Keno odds are much better in some ways. Consider the case of 1 spot (a player pick of a single number.) With 20 numbers drawn out of 80, then any 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 bet. After the first spot’s 75/25 split, there are 79 remaining numbers for the second spot. In case the first spot hit (matched,) there are 19 remaining drawn numbers and 60 undrawn. If the first spot missed, there are 20 drawn and 59 left that weren’t. In either event there are 79 possibilities. For the former case of a hit, the odds are 19:79, and in the latter (after a miss) odds are 20:79. After the 1:4 hit, the 19:79 second hit happens (1x19)/(4x79) of the time. That’s a 19/316 or ~0.0601 probability – just over 6%. The remaining 60/316 cases (0.1899 or 19%) result in a single hit (the first one) for the two spots. 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 (3x20)/(4x79), which is also 60/316 or 19%. This is again a single hit result, a miss followed by a hit, which combined with the previous odds for a hit followed by a miss leaves a total chance for hitting 1 spot out of two as nearly 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.