A Tax on the Mathematically Challenged

Statistical logic is often forgotten in the face of emotional decisions.  This is one reason I do not play the lottery.  Sure, over the years, I’ve been given scratch-off game cards for birthday presents.  I will admit that I’ve scratched off the silver paint with all the excitement of an 8-year-old at Christmas. And usually, I have the same disappointment of the 8-year-old when he realizes the brightly decorated package contains socks.

In general, I consider the lottery as a Tax on the Mathematically Challenged.  But even the smartest people continue to play the game as they let their emotions (and the hype) drive their decisions.

Consider a 6 number lottery.  Each number can be from 1 to 50.  If no number can be repeated, the chance of guessing the correct 6 numbers in no particular sequence is about 1 in 16 Million.

I have a friend who is a Really Smart Guy.  He has an advanced degree and understands statistics quite well.  He was explaining to me with great excitement how he only plays this type of lottery when the payout exceeds the risk.  That is, when the prize is greater than $16 Million, he puts in his dollar as he calculates that the large payout multiplied times the small chance of winning exceeds his $1 investment.

I may have ruined his day when I pointed out that more than one person could win the lottery, and reduce the payout, destroying his statistical logic.  In fact, as the payout increases, more and more people play the lottery, increasing the chance of having to share the winnings and reduce the amount he might win.

Perhaps I should have remained silent and let him have his fun.

You will find many websites that explain how you’re less likely to win the lottery than get hit by lightening, crash in a plane, or have a car wreck, and that you would be better off putting your investment into insurance against those types of events.

However, if after all of this information, you are still set on playing the lottery anyway, there is a way to reduce the chance of sharing the prize and increase your chance of a winning payout by applying a little game theory. 

As all numbers are equally likely to be selected, select numbers that other players are less likely to pick.  People are often superstitious in their selection of lottery numbers, picking dates that are associated with birthdays, anniversaries or historical events.  This means they pick months (1-12) and days (1-31).  If you instead select all of your numbers to be in the range of 32 to 50, you are just as likely to win, but less likely to have to share the prize with others.  Unless of course if everyone reads this blog and all start to pick numbers in the 32 to 50 range!