We have spent a lot of column space discussing 7-spots in Keno. The reason is the 7-spot is the lowest number of spots you can play and get a really BIG win.
Several downtown casinos pay $16,000-$17,000 for a $1 7-spot, some pay $14,000 for an 80-cent 7-spot, and a few pay $15,000 for a $1.25 7-spot.
A 7-spot is six times as easy to hit as an 8-spot and the reward is often more than half of the reward. Still, the odds of hitting a SOLID 7 are close to 41,000-to-1, thus the use of ways to lessen the odds. (Of course, you pay for the privilege by paying for each way).
Use eight kings and play the sevens and you reduce the odds for a single 7-of-7 to hit to less than 7,000-to-1.
What about using 9-spots, all kings, and playing the sevens? There are 36 possible 7-spots with 9 kings. ((9x8)/(2x1)) = 72/2 = 36.
How did I come up with this? Simply, the number of possible 7-spots out of a nine-king ticket must equal the number of 2-spots out of a nine-king ticket as for each 7-spot you choose, two numbers remain.
Thus you have to compute how many possible ways can you choose two numbers out of nine. You choose one number and then you have eight left, thus 9x8.
But you can choose them in either order thus you divide by 2 to compensate so you have (9x8)/2 = 36.
In Binomial theorem choosing 7-of-9 looks like 9!/(7!2!) = 36 (9! = 9x8x7x6x5x4x3x2x1). (7! = 7x6x5x4x3x2x1). (2! = 2x1). The ! means factorial.
When you do the division you have 9!/(7!2!) = (9x8x7!)/(7!2!). If you will notice you have 7! in both the numerator and the denominator thus they cancel out and you have (9x8)/(2x1) = 36.
Now that we have done the math, how can we play so many ways and not go broke? The answer is compromise. Settle for a lower dollar win in exchange for having more chances to win.
As mentioned in many prior columns, The D has the highest return for low level tickets of any casino in Las Vegas and probably anywhere in Nevada. I say Las Vegas because I have yet to see ALL the pay books for all casinos in Nevada. If you have a pay book you believe I should examine please have it scanned and send it to the email address at the bottom of this column.
The D has the “Deano” rate returning an average of 85% before offers and comps are figured in. The base rate for the Deano rate is 40 cents with 10-cent ways allowed as long as the total ticket price is $4 or more. Thus you could play a ticket of 9 kings at 10 cents a way. You have a 9, nine 8s, and 36 sevens for a total cost per ticket of $4.50.
If this is too much play their Candyman rate. While the return on the Candyman rate is in the 75% range (better than many casinos) you can play for as low as a penny a way as long as the ticket price is $5 or more, whether that is derived from the number of ways or the number of games or a combination of the two.
Thus play a penny per way and play at least 12 games and you have satisfied the minimum ticket requirement. (45-cents-per-game x 12 games = $5.40.)
Of course if you play for pennies you get paid accordingly (pro-rated) on wins, though $175 for a 7-out-of-7 for a penny, I think, it pretty good.
Let’s say you hit 7-out-of-9 on an all king ticket for a penny. First of all you get paid $2.75 for your 7-of-9 hit. Then you have hit two 7-of-8s paying $17.50 each for a total of $35.
You also have seven 6-of-8s paying 75 cents each for a total of $7.50. Then you have hit one SOLID 7-of-7 paying $175 PLUS 14 6-of-7s paying $1.75 each totaling $24.50 AND 21 5-of-7s paying 15 cents each (subway fare many, many years ago in NYC) for a total of $3.15.
Thus your total win is $2.75 + $35 + $7.50 + $175 + $24.50 + $3.15 = $247.90 – not too bad for your 45 cents, which in the 1960s could take you, me and the keno writer from Brooklyn to Manhattan.
If you want to get your 2 cents worth (2 cents a way) at 90 cents per game the 7-of-9 would pay $495.80.
The odds of hitting 7-out-of-9 are 1699-to-1. The odds of hitting 8-out of-9 are 30,681-to-1 and the odds for a SOLID 9 are 1,380,688-to-1.
Let’s say you hit 8-of-9 for a penny a way. You then get paid $50 for your 8-of-9. You will also have a SOLID 8 paying $300, plus eight 7-of-8s paying $17.50 each for a total of $140.
Now for the super hit. You have eight SOLID 7s at $175 each paying a total of $1,400. Still remaining you have 28 6-of-7s paying $1.75 each for a total of $ 49.
Thus your 45 cents returns $50 + $300 + $140 + $1,400 + $49 = $1,939. (In 1939 I believe the NYC subway fare was a nickel, see http://www.nysubway.com/stories/subway-fares.html.)
Now what if you hit them all? It HAS happened! I have been in a casino when someone has hit a 10-of-10. With everything hit SOLID the calculation is easier, thus a good incentive to hit all your numbers, why not?
You get $350 for the 9-of-9 SOLID hit, you get $300 for EACH of the nine 8-out-of-8 hits totaling $2,700 and $175 EACH for the 36 7-out-of-7 hits totaling $6,300. Your total win for your 45 cents is $350 + $2,700 + $6,300 = $9,350.
Invest $45 for 100 games while you are there and you have 10 hours of excitement!
Pesach Kremen is a former UNLV Masters Gaming student, has won and placed in multiple local keno tournaments, and has written several academic papers on keno. Email: [email protected]