Is It True Deuces ‘Never Loses?’

Jan 9, 2006 1:32 AM

One of the most popular strategies that keno players employ to increase their win frequency is to play deuces on a ticket. As you have seen from reading this column, if we add three deuces to a six spot, we can expand our total frequency of wins six-fold.

On the deuced ticket, we’ll hit a deuce and double or triple our money once every 5.8 games. On the straight ticket, we must hit a four out of six to accomplish the same thing, and this occurs only once every 35 games. That’s the good news. The bad news is, this comes with a cost, and we’ll cover that cost next week. The chart below gives you exact odds for various catches on such a ticket (a six spot grouped 2-2-2) and also compares these odds to a straight six spot ticket. The win frequency (freq. on the chart below) is always defined as the inverse of the odds for one.

For example, a catch of 4 out of 6 on a straight six spot shows odds for one against of 35.04. If you divide 35.04 into one, you will have the inverse .02853, which is the win frequency for that catch.


Three Deuces Straight Six Spot

Catch Freq. Odds for 1 Catch Freq. Odds for 1


0 0 0 0.16660 6.00 Catch 0 0.16660 6.00


1 0 0 0.36349 2.75 Catch 1 0.36349 2.75


1 1 0 0.24665 4.05421 Catch 2 0.30832 3.24

2 0 0 0.06166 16.2168


1 1 1 0.05192 19.2575 Catch 3 0.12981 7.70

2 1 0 0.07789 12.8383


2 1 1 0.02283 43.8013 Catch 4 0.02853 35.04

2 2 0 0.00570 175.205


2 2 1 0.00309 323.04 Catch 5 0.00309 323.04


2 2 2 0.00012 7752.84 Catch 6 0.00012 7752.84


There are several interesting things about this comparison. First of all, on the deuce ticket, there are more possible different catches (10 on the deuce ticket, 7 on the straight ticket), so many catches on it are correspondingly harder to hit individually than on the straight ticket. This is true where there are more than one way to hit a certain catch (2, 3 and 4 out of six).

Secondly, there are four catches on the deuce ticket that are identical to the straight ticket: 0-0-0, 1-0-0, 2-2-1, and 2-2-2. The odds on these catches are identical to their corresponding straight catches because there is only one way to hit each one of them on the way ticket, whereas you can hit a four out of six two different ways (2-1-1 or 2-2-0).

If you add together the frequencies for the two different four out of six catches on the deuce ticket (.02283 + .00570 =.02853) you will find that the total frequency is equal to the corresponding total catch on the straight ticket. This is true on any way ticket for corresponding catches.
Well, that’s it for now. Good luck! I’ll see you in line!

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