Keno or yes and blackjack insurance

8 December 2016

By John Grochowski

QUESTION: I like to take an occasional break and play keno. It is a game where I can play a quarter at a time and take a little time off. You can bet anywhere from one to 10 numbers at a time. I know the best pay tables for the number groups I play, but I do not know the intricate math to know which number group has the best payoff percentage. It seems to be 9.

ANSWER: Most video keno machines are set up so the differences in payback percentages are fairly narrow, except that you get the lowest return for picking only one number. Typically, a one-coin bet will bring a three-coin return if your number comes up. The overall return is 75%.

The percentage rises when more numbers are picked. Let's use a real world example, a machine where a pick 2 brings 15 when both numbers hit; pick 3 brings 2 for two numbers and 46 for three; pick 4 brings 2 for two, 5 for three and 91 for four; pick 5 brings 3 for three, 12 for four and 810 for five; pick 6 brings 3 for three, 4 for four, 70 for five and 1,600 for six; pick 7 brings 1 for three, 2 for four, 21 for five, 400 for six and 7,000 for seven; pick 8 brings 2 for four; 12 for five, 98 for six, 1,652 for seven and 10,000 for eight; pick 9 bring 1 for 4, 6 for 5, 44 for six, 335 for seven, 4,700 for eight and 10,000 for nine; and pick 10 brings 5 for five, 24 for six, 142 for seven, 1,000 for eight, 4,500 for nine and 10,000 for 10.

With those pay tables, payback percentages are 90.2% on the two spot, 91.6% on the three spot, 92.0% on the four spot, 91.9% on the five spot, 92.7% on the six spot, 92.4% on the seven spot, 92.3% on the eight spot, 92.0% on the nine spot and 92.6% on the 10 spot.

Note that on this machine, the paybacks are clustered around 92%, and the differences are measured in the tenths of a percent.

There are both higher and lower payers among video keno machines, but within any given machine, the payback percentages tend to be similar once you pick more than one number.


QUESTION: I was looking at some statistics on blackjack, and saw that you get a blackjack an average of once per 21 hands. So does the dealer, so the times both you and the dealer would get a blackjack are 1 in 21 times 21, or 1 in 441.

In deciding whether to insure a blackjack, do either of those numbers matter, 1 in 21 or in 441? Either way, I thought they were pretty interesting.

ANSWER: Neither is really relevant to the insurance decision. You already know you have a blackjack, so that takes care of your 1 in 21 chance. You also know the dealer has an ace up, or else insurance wouldn’t be offered. What’s relevant is the chance the dealer has a 10-value card face down. With a full deck, that’s a 30.8% chance, a figure that varies according to other cards that have been dealt.

Insurance pays 2-1, so if the you know one-third of the remaining cards are 10-values, insurance is a break even bet. With more than a third of remaining cards being 10s, insurance is a bet with a player edge. With less than a third – the standard situation – insurance favors the house and you should skip it.