More Lottery Nonsense

11 January 2014

By Donald Catlin

I recently received the following email from one of my readers S. Paul Smith

Hi

I found your website and liked very much the “lottery nonsense” article. The only thing that could slightly increase your chances is to play multiple games at once (picking several different series in the same game).

I have a question regarding the odd/even distribution in a 6/49 though. There are many people who say it is less likely to win with all numbers being even or all odd. I think that’s true, even if it only increases your chances slightly. What do you say?

Thanks for your time.

I wrote back to Paul as follows:

I assume that by 6/49 you mean a lotto type game with the player picking 6 numbers from 49. Is this correct? I’m not sure what the term “odd/even distribution” means. Are you suggesting that if the player picks all odd or all even numbers that his chance of winning increases? If not what are you suggesting?

I received the following reply:

Hi,

Thanks for your response. Yes I meant picking 6 out of 49 numbers. As for the “odd/even” I have seen several people claiming that if you pick 3 odds and 3 evens instead of all even or all odd that that you chance of winning would slightly increase. I would like to know if mathematically this makes sense or is it nonsense too.

Well Paul, I’m afraid it is nonsense. Every six number combination is as likely to be drawn as any other. The various lotteries go to great lengths to insure that this is true including frequent testing and replacement of balls. The choice of numbers doesn’t matter. The only biases are in the players’ minds. For example, many players would never play 1, 2 ,3, 4, 5, 6 because they feel it is very unlikely to be hit. It is unlikely but no more so than any other six number combination. These kinds of biases are what lead to odd/even speculation such as that you describe.

Let me see if I can make this crystal clear to you. Suppose that the balls were formed without numbers on them but were of 49 different colors Your wager is on a set of six colors. Would you feel that some sets of six were more likely than others? I don’t think so. See you next month.

Don Catlin can be reached at 711cat@comcast.net