Saturday, 21 July 2018

What's the betting?..

THIS POST is prompted by being asked what the odds of successfully predicting England's mood over the course of an eight-year period are, and, in providing an answer, realising that it also casts further light upon the Lottery that we call Democracy.

If that seems like a stretch, bear with me...

A lottery never delivers what it promises to those that participate in its draws. It is the only game in which its organisers bear no risk - and that is why all lotteries were once illegal.

In the same way, politicians bear no risk in the process of being elected; because, like any lottery, they only face competition from other 'lotteries' whose promises are more appealing to potential players than theirs.

Lotteries compete by offering a larger Jackpot than their rivals, and attract players fooled into thinking that, if they win, they are guaranteed that stated prize. They aren't. They will have to share it with anyone else matching the same numbers (it's a lottery, stupid) - and none of the prizes are contractually guaranteed.

Lotteries maintain trust by robbing smaller prize winners of what they were promised in order to keep the promise of the Jackpot. Rarely are Jackpots lowered. If absolutely necessary, because of disastrous ticket sales, the organisers might make up the difference from their vast profits (but are far more likely to virtue signal their good causes that the lottery supports - and change the game).

You see? It all fits...

You have to be dumb to buy a lottery ticket. You have to be even dumber to continue playing, week after week, after week. (But, you have to be in it, to win it, right? Like that isn't true of every type of game).

Don't be dumb and desperate. If you're desperate: change the game.

We all like a flutter, right? We all have that loose change weighing us down at the supermarket checkout that, somehow, is always added to when we settle the bill. But why buy a lottery ticket or scratch-card, when you can equally put that loose change in your favourite charity's collection box - or pop next door to the bookies to play an honest game where the organiser shares your risk?

You can play the lottery in a betting shop, just as you can in the supermarket - and you can also choose to play the game in any manner that you wish. You can back singles, doubles, triples, four-folds, five-folds, six-folds - or any combination you care to perm.

How did you finally match those three numbers on the lottery last time? Did you do the sensible thing and play a perm? (Any six from seven, right? And it cost you £7). How much did you win/share?..

The odds against you matching those 3 numbers from a field of 49, using your perm, were: 525:1 (which is why it probably took you so long to achieve it). In fact, it would normally take a dire run of 375 draws before your accumulated lack of winning tipped your 'luck' into the 50/50 arena. So, how does it feel to have potentially risked £2,625, in return for what? A tenner?..

Jeez. Are you dumb, or what?..

To add to your humiliation, just think of the number of times you matched one, and two numbers - but have never been rewarded in return. Do you see where all that Jackpot money comes from now? The little guys. The poor. The desperate. The little people that can't afford to play your perm and can only scrape enough to play one or two lines that equally match one or two numbers.

You claim to be intelligent, right? But even you kept playing your dumb 525:1 odds of matching THREE - because matching those ones and twos encouraged you to think that matching that magic six was just as likely.

Dimwit. The odds of you matching all six numbers from your carefully crafted perm is: 1,997,687:1 - and it would take you multiple lifetimes of dire disappointment to reach that magic 50/50 tipping point.

So: what does it feel like to be told you'll probably never live long enough to even get a sniff at the swag stolen from all the poorest players?

Where's your charity now, huh?..
  • Lotteries aren't fair. Bookmakers are.
  • Lotteries don't take any risk. Bookmakers equally share yours.
  • Lotteries steal from the poor. Bookmakers set a fair price that is paid to each player, in direct proportion to the risk they are prepared to bear.
  • Lotteries guarantee nothing. Bookmakers guarantee they will pay you the price agreed if you win any bet placed with them.
  • Lotteries share prizes between players matching the same numbers. Bookmakers don't share winnings - what they contract to pay, you get (along with your stake money). Bookmakers don't charge you for winning - it is the losers who settle the bill.
You stand to lose whomever you play with - the real odds always remain the same; but you know where you stand with a bookmaker before you place your bet - and you can guarantee that a bargain struck will be a bargain honoured. Lotteries are just lotteries - you never know where you stand.

When you participate in a lottery, you are playing against the whim of the organiser. When you bet with a bookmaker, you are playing a fair and honest game.

Here's why - and we'll use an imaginary Wheel of Fortune game (seems appropriate) to illustrate how I arrived at those Twitter odds.

Let's take the Wheel and its thirty-six sections as a sequence of thirty-six numbers, and the five Pentacle points as a selection of five numbers, drawn at random from the field of thirty-six. The chance of randomly matching one number from our five choices is 5/36, or 6.2:1 (13.89%).

(If you are interested in calculating that 'tipping-point,' it is the power to which the chance of not winning is raised to reach <=0.50 - and the chance of not winning, of course, is one minus the chance of winning).

That's all the parameters we need to devise a lottery and ensure it makes a bundle of cash from those too poor to afford a perm large enough to stand a fair chance of winning; but the key to understanding how a bookmaker thinks is to recognise that matching five numbers is not all that has been achieved. Those winning five numbers have also matched 5 singles; 10 doubles; 10 triples; 5 four-folds; and the five-fold. (Combinations, get it?).

So, why shouldn't the winner get paid for what he has actually achieved? That's only fair, right?

Of course it is - and the first thing we need to establish is what is a fair price, based upon the actual, real-world odds, that would permit every possible permutation and combination to be played - whilst also ensuring that each player (including the bookmaker) were correctly rewarded for their individual risks.

You see, it is all about percentages. If you want to bet me £1 against my £3, then it's only fair that you should bear the greater risk. I'll take a look at the real situation, and if I think I stand a 75% chance of taking your money and keeping mine: I'll give you those odds. If you win, I'll give you my £3 and your money back; but, if I win, I'll keep your £1.

That's how it works.

So, what would be a fair price for accurately predicting England's mood over 8 years?

We've already calculated it: 5/36 or around 6:1. That's the fair price of correctly predicting just one Pentacle point - because it is the real odds of the event actually occurring by chance. (That is, the chance of the predicted mood being correct at the specific time).

So, what would be a fair price in return for correctly predicting all five points? Well, if I'd placed a £1 five-fold bet at a price of 6:1, I'd get £6^5 (£7,776) plus my £1 stake back. That's the simple answer (provided the bookie didn't take the time to fully understand what he was getting into by reading my book).

It also assumes that I would be so confident as to just cover the five-fold, and not consider the other opportunities on offer. What about all those singles, doubles, trebles, and four-folds that I would also match if my selection won? How much would it cost to cover all those possibilities?

Well, let's work it out...
  • There are five singles in a five-fold, each paying 6:1.
  • There are ten doubles in a five-fold, each paying 36:1.
  • There are ten trebles in a five-fold, each paying 216:1.
  • There are five four-folds in a five-fold, each paying 1,296:1.
  • The five-fold pays 7,776:1.
There are 31 bets there, so the perm would cost £31 - and I'd just need a double to cover my stake and make £17.

If the five-fold comes in: I would have stood to make £16,806.

It soon mounts-up, doesn't it? But here's the thing: apart from the single, none of those other betting odds reflect the real world.

These are the real-world odds that you would actually be up against: -
  • For the single: 6.2:1
  • For the double: 62:1
  • For the treble: 713:1
  • For the four-fold: 11,780:1
  • For the five-fold: 376,991:1
The difference is because of the fair price we have chosen, which is the overall odds of correctly predicting a single number given five random choices from a field of 36. In actual fact, it depends upon how many numbers have already been drawn, and how many unmatched numbers you have left to compare with the next drawn number. So, it's not really true to say that the odds of matching all five numbers are 13.89%^5 - in reality the odds are 5/36*4/35*3/34*2/33*1/32; and the odds for other combinations actually vary.

Don't make the mistake of thinking that fair betting odds reflect the real world. They don't.

The truth is that the real world isn't fair. Neither are lotteries - and nor are career politicians...

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