The Parrondo Paradox And The Office Lottery Pool

There are pairs of losing games which if played one after the other become a winning combination. Whereas you would expect the combination of two losing games in sequence always tend to lose.
Michael Clark, Paradoxes From A To Z, (Second Edition), p. 155

As any reader of this blog will now know the Oracle of Ottawa loves his paradoxes! A paradox is the tip of the iceberg that we can see over the wall of the limitations of our existence. They are very important. A paradox is proof that such useless things as the study of philosophy can be very profitable indeed. Paradoxes also prove that we don't have such a solid grasp of our respective reality's as we are lead to believe. A paradox is an indicator of all the knowledge that we are not yet aware of.

What is the optimal algorithm?

One paradox that has captured the Oracle of Ottawas attention of late is known in the literature as the Parrondo Paradox. It is the work of one J. M. R. Parrondo. I will leave it to the reader to track down all the forms that this striking oddity can appear. It is not a waste of time and you will get a lot out of it.

Back in my working days I was in a very large office lottery pool in a government office somewhere in Ottawa. The guy that ran it was old Bob. The way an office lottery in Ottawa usaully works is that you cough up some money every week. All the winnings go into a pool that is distributed just before Christmas. We had a great run with this pool. All of us shared in a prize of a couple of grand once! It was just before the closing of my first home purchase and it came in mighty handy, paying my closing costs and enabling a larger down payment that of course lowered my monthly payment. The mortgage has been paid off for a while now, but the thought of how to maximize the office lottery has kept popping up in my thinking.

J.M.R. Parrondo

If you are running a large pool or are buying a lot of tickets on a regular basis, you want to, at the least, play the most plays for the least possible amount money. A possible way to do this is to split up the number of plays between two or more lotteries per play cycle. For example in the province of Ontario there are at least three weekly lotteries that I like to take a flyer on. I think of it as "Extended Diversification". I once saw in a serious Investment text book that you should put at least a fraction of one percent of your yearly take into such bets! My combination at present is Lotto-Max, Lottario, and Ontario 49. There are not too many lotteries anywhere you could possibly win a seven figure prize for 50 cents a play! It is quite weird, but I am most always cashing winners in and keeping the over all cost down.

Isn't that just extraordinary?!