So I have heard the passed along story of an individual who was put in charge of buying all the lotto tickets for a workplace lotto share. In case you are not aware, the way this works is that everyone puts in money (usually equal amounts) and a great number of lotto tickets are bought. If there are any winnings, the winnings are split amongst those who contributed money (in equal shares if everyone contributed equally, or otherwise proportional to the contirubtions.)
In this particular story, the individual in charge went to the local store and purchased the tickets. When filling out the tickets(do you remember when you had to do them by hand with pencil?) he chose combinations with conecutive values. When he brought back tickets with combinations like 12-13-14-15-16-17, his coworkers were outraged. “How could he possibly have chosen combinations like this that weren’t as random as other combinations, and thus had less chance to win?” they thought. He was shunned and not allowed to participate in the lotto pool again.
Unfortunately, this would be the common reaction in our generally statistically ignorant society. What they fail to realize is that those numbers have just as likely a chance of coming up as any other combination of 6 “random numbers”.
Allow me to prove to you that not only was this man’s method just as good as picking any 6 “random” numbers, but actually BETTER, if you can believe it, than the alternative.
As humans, we make associations, and generally those associations are good. From a very young age, we associate the smell of food cooking as good but touching a hot stove in an attempt to sneak a taste as bad. In that case, however, the association of the sequence of numbers with non-randomness is harmful to thinking logically about the situation.
The lotto machine doesn’t know what numbers are written on the balls. It shoots 6 balls out of its chute and if the numbers on those balls match your numbers you win. But after the first number, say a 7, comes up, the odds of a numbered ball appearing that is adjacent to 7, either 6 or 8, is just as likely as any other number, and so on, with every consecutive number.
Look at it another way. Let’s replace the number you choose with a color, and then color one of the balls with each color.
Thus, instead of picking between numbers 1-10 for a lotto, let’s say you have to choose between: Red, Yellow, Blue, Orange, White, Green, Pink, Black, Purple, and Brown.
Would it be just as likely that Orange, Pink, and Brown came up as Red, Yellow, and Blue? The answer is yes. The difference here, is that our brain doesn’t see an irrelevant ordering of the possible outcomes, it just sees a list of 10 colors.
So we have established that the odds are the same. But didn’t I claim that the man’s method was actually better than what most people do. Here goes.
Random numbers chosen by human’s aren’t ever truly random. If you don’t believe, try the following. Write down 8 random numbers from 1-100. It’s okay…I’ll be waiting for you to scroll down when you are done.
Got them? Good. Now, look through them and determine how many are odd. We would expect 4 to be even and 4 to be odd, but is that the case. Unlikely. Also, given that there are 25 prime numbers from 1-100, we would expect 1/4th or 2 out of your 8 numbers to be prime. I’ll bet you chose more than 2 primes. For reference, the primes up to 100 are 2, 3, 5, 7, 11, 13, 17, 18, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
For more on why this is the case, check out this cool site: http://scienceblogs.com/cognitivedaily/2007/02/is_17_the_most_random_number.php
Anyway, what we have determined is that people are more likely to choose a combination like 7, 11, 25, 31, 36, 41 when choosing “random” numbers, than a combination like 1, 2, 3, 4, 5, 6. Some would say 1, 2, 3, 4, 5, 6 is the type of combination of numbers only an idiot would choose.
In reality, however, keep in mind that in the event of more than one person having a winning lotto ticket with all the numbers matched, the prize is split amongst all winners. If every combination has the same odds of winning, but UNequal chances of being chosen by humans, and thus different chance of being split, than based on a comparison of expected values, it would seem that it is actually the BETTER choice to choose number combinations that people would not pick.
The man was 100% in the right, but in the minority of those who realized it.
Think about that the next time you are choosing those 6 magic digits that stand between you and a life of luxury.
* All of this is a moot point, however, when the truly wise realize the expected value of the lotto yields a payoff percentage of only about 61% and that the best choice one can make, statistically, is to not play the lotto at all.