Feb. 2nd, 2014

chris: (crisis)
Meg's sister Sarah has been staying with us for the winter, since just before Thanksgiving. As usual, she has brought joy and laughter to our house. She has an exciting deadline to meet in the US, so unfortunately her time in the UK has had to come to an end. Accordingly, the last couple of weeks have been sad. The most faintly silver of linings of the recent Polar Vortex and its impact on Atlanta has been that her original flight home was cancelled and thus we got three extra days of sister time for free, but even that has come to an end. Today has been as sad as we feared - and, with taking her to Manchester to check in early for a morning flight, a tiring day as well. There is space in our house, but this does not make up for the space in our hearts. Long distance things don't get easier.

I have, as often is the case, retreated to find comfort in mathematics. The football pools were one of the foremost forms of gambling in the UK until the National Lottery launched, nearly twenty years ago. Simplifying, participants attempted to predict which (association) football games from a list would end as a draw - ideally, a score draw (1-1, 2-2, etc.) rather than a 0-0 draw. If a participant picked eight such games from a list of fifty-some - and some weeks there might only be four to find, whereas other weeks might have four times as many - then they would share a prize made up of a reasonably high proportion of the total entry fees. A scoring system shared some of the entry fees as consolation prizes ("second dividend", "third dividend" and so on) among players whose selections were near misses.

The relative difficulty of determining which matches would be drawn in this way made picking such a winning line a very difficult challenge, and a great degree of public interest was placed in trying to make accurate selections. There was a considerable degree of luck in the enterprise and its prominent place within public life was more a historical accident than anything else. Accordingly, it would be usual for participants to select more than eight matches and submit every possible combination of eight matches from the larger number selected. This was, technically imprecisely, referred to as a full permutation. However, the more possible matches were covered in this fashion, the more attempts at the competition were required and the greater the cost. In fact, the number of attempts required increased very rapidly as more matches were named.

The mathematically interesting part was a little bit complicated. )

Another discovery on a related search that I considered interesting was this index comparing different UK bookmakers' football gambling offerings in the year 1960. If Ray Winstone had wanted to "have a bang on that" at the age of three, what options might have been available to him? Again, they're quite intricate and interesting from a gaming perspective. Even then it was possible, though highly unlikely, to win many thousands of pounds for a stake of just pennies - and pre-decimalisation pennies, at that. There's also a degree of commonality in appearance between these bookmakers' coupons and the standard format of the football pools coupon that survived over the decades.

The conclusions I draw are again pretty technical and I'm going to assume a degree of familiarity with the terminology. )

None of which will help you make money betting on football, of course, and will only confirm how strongly the oddsmakers of the world tilt things in their favour. Still interested me, though.

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Chris

November 2016

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