Mark Z., Lottery Master

by IIG

February 2008 — Mark Z. from north of the border claims that he will predict the winning numbers in the Canadian Lottery. He has sent in a formal application, and we are trying to calculate the odds of him doing this by chance before we accept his testing protocol. In meantime, the IIG Steering Committee wonders what he wants with our $50,000 if he can win the lottery.

A month later, Mark clarified his original claim:

"From my past experience I hope to provide you with [a] quantity of correct predictions for Ontario "Pick 3" lottery, which in 2-3 times will exceed the random level. For "Pick 3" lottery increase[ing] the number of right guesses in 2-3 times makes the game profitable. But not so strong, because organizers returns [sic] to players only 50% of collected money. An [sic] therefore even 3 times increase of correct predictions means simply 150% profit. In another words to make $50,000 I will have to spend about $33,000."

We responded the only way we know how:

"I'm a little confused about your claim."

Adding:

"Why don't you predict one of next week's Pick 3 numbers now and give us a quick demonstration of your ability[?]"

We received no such prediction from Mark.

Later, we sent Mark a statistical analysis from our own resident number-cruncher Stu Lengel. That letter went out on April 8th, and we have not received a reply from Mark:

Hello Mark,

My name is Stuart Lengel, stuart@iigwest.org.  I  have been assigned as the lead investigator to process your participation in our $50,000 Dollar Challenge.  I  was an Aerospace Scientist for 25 years and used statistics frequently to establish the reliability of our products in demanding  applications so I am familiar with the mathematics used here.

Prior to establishing a test procedure that we can both agree on, I would like to go over some of the basics, as I see them, and then we can go from there.

If  I understand your application and follow up email you are going to send us:

1. Fifteen 3-digit numbers at least 2 hours before the numbers are drawn on the Canadian Pick-3 lottery for that day.

2. With these numbers you claim you can achieve a win rate of  2 to 3 times the calculated rate and would achieve this rate with a level of significance of 90% during a 2 month preliminary test and a level of significance of 99% during the actual test period. which you think would take place over approximately one year.  Further, during this year you expect you will be able to send us your predictions approximately 6 days out of 10.

Using basic calculations and ignoring probability curves:

1. The chances of winning are 1 in 1000.
2. You are going to send us 15 numbers per day which makes your standard chance of winning 15/1000 = .015  or 1.5 times per 100 plays.
3. You expect to win 2 or 3 times more than the standard rate, so over the same 100 days you would expect to win 3, 4 or 5 times.
4. Now the problem is this.  If I develop a binomial curve using this data,  (Sample size – 100;  % lose – 98.5; % win -  1.5) and establish its distribution, I find that over many trials with a sample size of 100  I can expect to get  22% with no wins, 34% with one win, 25% with 2 wins, 13% with 3 wins, 5 % with 4 wins and 1% with 5 wins.
5. In other words – just using normal binomial calculations without an improvement factor, it can be expected that one would get 3, 4 or 5 wins over 100 trials 19% of the time, or approximately 1 time in 5.

Because of the length of each trial, and the fact that even under normal circumstances your winning numbers would occur 1 time in 5, I see no practical way of testing your assertion that you can achieve 2 to 3 times the expected win rate using you improvement factors with a pick 3 lottery. I am sure you understand we would have to have a really significant win ratio before we entered into an agreement with you.  Perhaps a pick five or pick six lottery would offer the winning percentage we would expect. Also if the "daily time period for picking winning numbers" is fairly long, maybe winning streaks while playing Blackjack or Roulette could be developed?

I wait your reply.