Musings On Extended Diversification

To my mind losing is always better than never trying, because you can never tell  what may happen.
Jean Chretien, Straight From The Heart, p. 195

Every year in Canada due to the two national lotteries there could be created up to 154 new millionaires per year! But due to the prizes building from week to week and not being won and then having, say, a 40 million dollar prize go to a group of 35 people, you could on average count on 154 as being a pretty stable estimate.
Now this is not counting the smaller provincial lotteries that often award prizes over a million dollars. So therefore the number of newly minted millionaires could climb to over 200 in any given year.

Is this process solvable??

Take a six column 1 to 49 drop ball lottery. The odds to beat can be as high as 1 : 15,000,000 or more depending on variations built into the game. The Oracle of Ottawa often ponders how so much randomness can be squeezed into such a small 'space'. Now essentially this is a closed process. Yet it is deemed in all the texts as fruitless to even begin thinking about a way to 'solve' this process.

William Feller - Made math cool...

I often tell any youngsters that will listen, and there isn't many, that the most exciting field they could probably enter is the mathematical field of probability. If you want to get the biggest bang for your education nickels a degree in probability and statistical inference would be a fine place to start. For a life long pursuit that will have many more doors open as the future unfolds, all very hard to beat...

Is this data random? - Can you prove it?

 For example take the old card shuffling problem. This is a problem that is still yielding really weird and totally unexpected results! Who knew? But for a mere mortal or a really sharp kid read about one William Feller!
If you can get hold of a copy of 'An Introduction to Probability and Its Applications, Volume I, just dip in any where... You will soon find why that it is regarded as the greatest book on probability ever written. Why the bit on coin tossing is still rippling through the world. Some of the stuff in that book is so weird and so totally unexpected that it is at first read just incredible.... But the best piece of gold I mined from this work is to break the process down into smaller independent processes... Try it before you scoff...

Yes, all that is all very interesting, but these games are for silly poor people and ignorant rubes... A middle class or better off person does not buy lottery tickets or bet on sports, or go to the track or the card tables at the local casino... Well not so fast! And I have a reference! You should budget a very small amount for such things! See 'Investments' by Sharpe, Alexander, Bailey and Fowler, Second Canadian Edition, Chapter 26.   
Read this carefully. You can't win if don't have a ticket!

Many professional Mathematicians have been clobbered by this one! Now do you see the power?

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?!