eBay UK have changed their terms to (a) remove seller fees for most private sellers, but (b)
instead of paying-out immediately, payouts are four times a year (or on-demand).
That sounds like they’re trying to keep money in their ecosystem. The hope is, I guess, that by paying sellers in virtual “eBay Pounds” rather than actual money in the first instance
they’ll encourage those sellers to become buyers again (either of other listings, or of eBay’s postage and other services). You can cash out anytime you like, but you can never leave.
You see the same technique used e.g. by the National Lottery, who pay out “small” winnings into your online account, knowing that the vast majority of winnings are on the order of only
a few times more than the value of a ticket, and so players will be more-likely to “re-invest” if they’re not paid-out directly.
But if I ever happen to be somewhere that the lottery results are being announced, I sometimes like to play a game I call Not The Lottery.2
Here’s how you play:
Set aside the money it would have cost for a ticket.
Think of the numbers you’d have played.
When those numbers don’t come up, congratulations: you just won not-wasting-your-money!3
Want to play Not The Lottery retroactively? Cool. I’ve made and open-sourced a tool for that. Hopefully it’ll load below
and you can choose some numbers (or take a Lucky Dip) and have it played through the entirety of EuroMillions history and see how much money you’d have won if you’d only played them
every week. Or, to look at things from a brighter perspective, how much you’ve saved by not playing. It’s almost-certainly in the thousands.
Loading game… please wait… (if it never loads, Dan
probably broke it; sorry!)
Winning the lottery
But that’s not what the question’s really about, is it? We don’t ask people “what would they do if they won the lottery?” because we think it’s likely to happen4
We ask them because… well, because it’s fun to fantasise.
And I sort-of gave the answer away on day 20 of Bloganuary: I’d do my “dream job”. I’d work (for free) for Three Rings, like I already do, except instead of spending a couple of hours a week on it on average I’d spend about ten times that. I’d use the
luxury of not having to work to focus on things that I know I can do to make the world a better place.
If money was no object, I’d spend more time with these happy folks (and many more besides), making volunteering easier for everybody.
Sure, there’s other things I’d do. They’re mostly obvious things that I’d hope anybody in my position would do. Pay off the mortgage (and for all the works currently being done to
infuriate the dog improve the house). Arrange some kind of slow-access trust or annuity for the people closest to me so that
they need not worry about money, nor about having to work out how to spend, save, or invest a lump sum. Maybe a holiday or two. Certainly some charitable donations. Perhaps buy
really expensive ketchup: the finest dijon ketchup5.
But mostly I’d just want to be able to live as comfortably as I do now, or perhaps slightly more, and spend a greater proportion of my time than I already do making charities work
better.
I don’t know if that makes me insufferably self-righteous or insufferably simple-minded, but it’s probably one of those.
Footnotes
1 I’ve been caught describing it as “a tax on people who are bad at maths”, but I don’t
truly believe that (although I am concerned about how readily we let people get addicted to problematic gambling and then keep encouraging them to play with dark patterns that hide
how low the odds truly are). I’ve even been known to buy a ticket or two, some years.
2 While writing this, I decided to retroactively play for last Friday, having not seen
whatever numbers came up. I guessed only one of them. Hurrah! That means I saved £2.50 by not playing!
3 There are, of course, other possible outcomes. You could have missed out on winning a
small prize – the odds aren’t that low – but the solution to this is simple: just keep playing Not The Lottery and you, as the “house”, will come out on top in the end.
Alternatively, it’s just-about possible that you could pluck the jackpot numbers from thin air, in which case: well done! You’re doing better than Derren Brown when in 2009 he
performed a pretty good magic trick but then turned it into a turd when he
“explained” it using pseudoscience (why not just stick with “I’m a magician, duh”; when you play the Uri Geller card you just make yourself look like an idiot). Let’s find a way
to use those superpowers for good. Because what you’ve got is a superpower. For context: if you played Not The Lottery twice a week, every week, without fail, for
393 years… you’d still only have a 1% chance of having ever predicted a jackpot in your five-lifetimes.
4 What if we lived in a world where we did use statistics to think about the
hypothetical questions we ask people? Would we ask “what would you do if you were stuck by lightning?”, given that the lifetime chance of being killed by lightning is significantly
greater than the chance of winning the jackpot, even if you play every draw!
In early June 2014, accountants at the Lumiere Place Casino in St. Louis noticed that several of their slot machines had—just for a couple of days—gone
haywire. The government-approved software that powers such machines gives the house a fixed mathematical edge, so that casinos can be certain of how much they’ll earn over the long
haul—say, 7.129 cents for every dollar played. But on June 2 and 3, a number of Lumiere’s machines had spit out far more money than they’d consumed, despite not awarding any major
jackpots, an aberration known in industry parlance as a negative hold. Since code isn’t prone to sudden fits of madness, the only plausible explanation was that someone was cheating…
Have you ever come across non-transitive dice? The classic set, that you can get in most magic shops, consists of three different-coloured six-sided dice:
A “Grime’s” style set of 3 non-transitive dice. Notice the unusual numbering.
There are several variants, but a common one, as discussed by
James Grime, involves one die with five “3” sides and one “6” side (described as red below), a second die with three “2” sides and three “5” sides (described as
green below), and a third die with one “1” side and five “four” sides (described as blue below).
They’re all fair dice, and – like a normal six-sided dice – they all have an average score of 3.5. But they’ve got an interesting property, which you can use for all kinds of magic
tricks and gambling games. Typically: the red die will beat the green die, the green die will beat the blue die, and the blue die will beat the red die! (think Rock, Paper,
Scissors…)
Seemingly paradoxically, the dice will generally beat one another in a circular pattern.
If you want to beat your opponent, have them pick a die first. If they pick green, you take red. If they take red, you take blue. If they take blue, you take green. You now have about a
60% chance of getting the highest roll (normally you’d have about a 33% chance of winning, and a 17% chance of a draw, so a 60% chance is significantly better). To make sure that you’ve
got the best odds, play “best of 10” or similar: the more times you play, the less-likely you are to be caught out by an unfortunate unlucky streak.
But if that doesn’t bake your noodle enough, try grabbing two sets of nontransitive dice and try again. Now you’ll see that the pattern reverses: the green pair tends to beat the red
pair, the red pair tends to beat the blue pair, and the blue pair tends to beat the green pair! (this makes for a great second act to your efforts to fleece somebody of their money in a
gambling game: once they’ve worked out how you keep winning, give them the chance to go “double or nothing”, using two dice, and you’ll even offer to choose first!)
When you pair up the dice, the cycle reverses! While red beats green, double-green beats double-red!
The properties of these dice – and of the more-exotic forms, like Oskar van Deventer’s seven-dice set (suitable for playing a game with three players and beating both of your
opponents) and like the polyhedral
varieties discussed on Wikipedia – intrigue the game theorist and board games designer in me. Could there be the potential for this mechanic to exist in a board game? I’m thinking
something with Risk-like combat (dice ‘knock out’ one another from highest to lowest) but with a “dice acquisition” mechanic (so players perform actions, perhaps in
an auction format, to acquire dice of particular colours – each with their own strengths and weaknesses among other dice – to support their “hand” of dice). There’s a discussion going on in /r/tabletopgamedesign…
I’ve even written a program (which you’re welcome to download, adapt, and use) to calulate the
odds of any combination of any variety of non-transitive dice against one another, or even to help you develop your own non-transitive dice sets.
Penney’s game
Heads or tails? Image courtesy David M. Diaz.
Here’s another non-transitive game for you, but this time: I’ve made it into a real, playable game that you can try out right now. In this game, you and I will each, in turn, predict
three consecutive flips of a fair coin – so you might predict “tails, heads, heads”. Then we’ll start flipping a coin, again and again, until one of our sequences comes up. And more
often than not, I’ll win.
If you win 10 times (or you lose 20 times, which is more likely!), then I’ll explain how the game works, so you know how I “cheated”. I’ll remind you: the coin flips are fair, and it’s
nothing to do with a computer – if we played this game face-to-face, with a real coin, I’d still win. Now go play!
