I’ve run across an interesting set of "twin" keno tickets. Both have 22-way sixes. The first ticket has ten numbers on it, while the second has 11. The first ticket has three deuces and four kings (2-2-2-1-1-1-1). The second has four deuces and three kings (2-2-2-2-1-1-1). As you can see, if you take both tickets together, there’s an agreeable symmetry.
Let's look at the ten-spot first. With a grouping of 2-2-2-1-1-1-1, we have a one-way 10, four-way 9, nine-way 8, 16-way 7, 22-way 6, 24-way 5, 22-way 4, 16-way 3, nine-way 2, and a four-way 1. It has a total of 127 ways. An interesting way to play this ticket would be to play a dollar on the ten, and 50-cent ways on the sixes and threes, for a $20 ticket. If I hit one of the 16 threes, I’ll win $20 and change at most keno games, covering my wager. There are three different varieties of sixes on this ticket. The 2-2-2 is one six; the 2-2-1-1 ways account for 18 ways; and the 2-1-1-1-1 ways account for the remaining three ways.
The 11-spot, grouped 2-2-2-2-1-1-1, has a one-way 11, three-way 10, seven-way 9, 13-way 8, 18-way 7, 22-way 6, 22-way 5, 18-way 4, 13-way 3, seven-way 2, and a three-way 1. It, too, has a total of 127 ways, just as the ten-spot. On this ticket, I’d either play the eleven for $1, with 50-cent sixes and threes for an $18.50 ticket; or I might play 50-cent sixes and fours with the $1 eleven for an admirable $21 ticket. There are only two varieties of sixes on this ticket, namely the 2-2-2 for a four-way six, and 2-2-1-1 for an 18-way six.
Traditional keno wisdom says you have a better chance of hitting a solid six on the 10-spot than on the 11-spot, because "fewer numbers are better." Here are the odds for one of hitting on each ticket for a six-spot:
Ten Spot, Grouped | Eleven Spot, Grouped | |
2-2-2-1-1-1-1 | 2-2-2-2-1-1-1 | |
6/6 | 453.817 | 417.612 |
5/6 | 30.034 | 29.057 |
4/6 | 5.277 | 4.895 |
3/6 | 2.099 | 1.820 |
It’s clear from this chart that it’s much easier to hit a solid six, five of six, four of six, and three of six on the 11-spot than it is on the 10. In fact, you’ll hit a solid six, on average, 36 or so games sooner playing the 11-spot. It seems the conventional wisdom is wrong, at least on this point.
Consider the 15-spot ticket, grouped 5-4-1-1-1-1-1-1. There are 6 sixes using 5-1, 15 sixes using 4-1-1, and one six using all six kings, for a total of 22 sixes. Its twin, a 13-spot ticket grouped 5-2-1-1-1-1-1-1, has 6 sixes using 5-1, 15 sixes using 2-1-1-1-1, and one six using all six kings. You can see why I call these tickets "twins." The groups and the ways are all the same except for the substitution of a group of four for a group of two.
But which of these two tickets offers the best chance of hitting a solid six? In this case, the ticket with the 13 spots, with odds of 499 for one of hitting a solid six, versus odds of 571 for one of hitting the same on the 15-spot ticket. It is, interestingly enough, slightly easier to hit a five out of six on the 15-spot than on the 13-spot!
This brings us to the best 22-way six. Take 16 numbers and group them 3-3-3-3-1-1-1-1. Besides having an excellent symmetry in groups, this ticket has a 22-way 10, a 28-way 9, a 36-way 8, a 28-way 7, a 22-way 6, a 24-way 5, a 17-way 4, an eight-way 3, a six-way 2, and a four-way 1. Besides the 22 sixes, I particularly like this ticket for its eights, sevens and fives. You might try a 28-way 7 and a 22-way 6 for 50 cents a way, for a commendable $25 ticket. After all, if you hit a solid six, you’ll have at least one six out of seven, and one more number could get serious!
TWENTY-TWO WAY
SIX COMPARISON
GROUPING ODDS FOR ONE OF
6/6 | 5/6 | 4/6 | 3/6 | |
3-3-3-3-1-1-1-1 | 398.66 | 23.38 | 3.99 | 1.63 |
2-2-2-2-1-1-1 | 417.61 | 29.06 | 4.90 | 1.82 |
2-2-2-1-1-1-1 | 453.82 | 30.03 | 5.28 | 2.10 |
5-2-1-1-1-1-1-1 | 499.61 | 32.62 | 5.73 | 1.92 |
5-4-1-1-1-1-1-1 | 571.21 | 30.51 | 4.51 | 1.61 |
Quite a few keno players play the 22-way 6. Most of them play the 10-spot (2-2-2-1-1-1-1). By playing the 16-spot, on average you’ll hit a solid six some 55 games sooner than on the 10-spot. If you’re playing 50 cents per way, this means you’ll hit your solid six some $600 sooner tHan when playing the 10-spot. On a ticket that will pay you $700 to $900 on a solid hit, it makes some sense to switch!
Well, that's it for now. See you in line!