Another OLG Paradox Of Probability

In stochastic processes the future is not uniquely determined, but we have at least probability relations enabling us to make predictions.
William Feller, An Introduction To Probability Theory And Its Applications, Third Edition, Vol. I, p. 420

The Oracle of Ottawa has the grand pleasure to be a resident of Ottawa, Ontario. And in the Province of Ontario we have a wonderful organization known as the Ontario Lottery And Gaming Corporation.  The OLG is a house of many games. One of the most interesting is a sports game known as Pools. It is just like an office sports pool that you play at work, but Pools is an office pool that has as its "subspace" the whole population of Ontario! (population, 13,505,900)

Lesson? - Probability is Spooky...

  As you can well imagine, things can get pretty exciting well into the NFL football season, where by one of the most popular bets in Ontario is the weekly series of NFL games. There can be up to 16 games, from Thursday night to Monday night. For five dollars you can take your best shot, straight up, and come Tuesday, the winner(s) are announced. If you can pick 14-16 NFL games, straight up, you could turn $5.00 into several hundred thousand dollars! And it being Canada, this will all be sweet and tax free.

HP-11C - Good tools are very important...

If the Oracle of Ottawa's old brain is working correctly, The weekly NFL Pool was the first and only Pool in the Province of Ontario. Then of course came the weekend NHL hockey Pool, then the MLB baseball Pool. With a hold back of any where from 40% - 60% the good old OLG ran with a really good thing until at the time of this writing, there are pools offered every day.  Which is proper and fitting, fair and wide open.

Most of the time, the results are to be totally expected. Such as the days when 14 baseball games are on the list, and the results are that only 2- 4 people were able to pick 12 of the 14 offered games. For this awesome feat, the reward can be several thousand dollars! This, for those that know of such things, fits the normal curve about just right. And tomorrow there will another list. Now remember, this is a pool, you do not have to get all the games right, you only have to be the punter or punters that gets the most games right, result, you get all the money, Sweet!  

William Feller - Awesome beyond words...

For example, early last week, there was a card offered of a mere 10 night MLB games. If you have tried it Dear Reader, you know that handicapping MLB baseball is all but impossible. But on this day one punter in Ontario got all 10 games, and in turn took all the pool money, which was north of $20,000 bucks Canadian, great work, if you can snag it!

On Thursday last was offered Card #99, it consisted of all the pre-season NFL games from August 15, 2013 to August 17, 2013 a small list of only 14 pre-season NFL games. If you think that major league baseball is hard to cap, you also know that regular season NFL games is an awesome feat of capping prowess. But who in heavens name would be crazy enough to even try to cap 14 pre-season NFL games? Surely a total impossibility?


Then the little fridge light came on in the Oracles brain, give it a random guess, by a very possible stroke of luck, the Oracle could possibly pick say 12 out of 14 games and share the prize with say at least six other randomizers. Well it was this fine Sunday morning when the Oracle checked his ticket and discovered that he only could guess 7 out of 14. Pure text book expectation. But the Oracle of Ottawa was shocked to discover that 66 punters in Ontario were able to predict 14 out of 14 pre-season NFL games!! The odds of performing such a feat of picking 14 of 14 games are 1: 16,384! That means that about 1,081,344 tickets at five bucks each would have to be sold, more or less. For a gross pot of $5,406,720 +/-. before withholding percentage of the house take, assuming 40%, would leave a prize pool about 3,244,032, which would have meant 66 prizes of $49,152! The actual prize that was awarded to these awesome subset of punters was a mere $555.30 each!! Hmmm...

This of course means, and makes very much sense, that only a very very small subset of the population of the Province of Ontario actually played. But excuse me! Sixty six people of this small subset were able to pick all 14 of 14 winners!???  While the greatest capper in America alive today Kenneth Massey, could only manage a paltry prediction of 10 out of 14!? If one was really cynical one would blurt out that the only way this could possibly happen is if you were somehow able to buy your tickets after all the games were actually played! But the Oracle of Ottawa wouldn't think of doing a nasty thing like that....