gambling

[Bloganuary] Not The Lottery

This post is part of my attempt at Bloganuary 2024. Today’s prompt is:

What would you do if you won the lottery?

I know what I’d do, and I’ll get to that. But first, let me tell you about the lottery game I play.

"LOTTO Schleswig-Holstein" player slip with two "series" of numbers selected: in game one, all the numbers ending 7, and the lucky stars 1 and 2; in the second game, the first five numbers (the lucky stars aren't visible). — “Why yes, my numbers are 1, 2, 3, 4, 5, with lucky stars 6 and 7. What do you mean, they’ll never come up? They’re just as likely as yours!”

Not the lottery

I don’t generally play the lottery¹. I’ve made interactive widgets (now broken) to illustrate quite how many losers there are in these games and hopefully help highlight that while “it could be you”… it won’t be.

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.

Dan poses in the centre of a group of seven other Three Rings volunteers. — 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.

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!

⁵ Y’know, to keep in the fridge in the treehouse.

Note #11720

#challengerobin continues unexpectedly into a new day as I bet Robin a tenner that he can’t jump a river without getting his feet wet.

A Russian Slot Machine Hack Is Costing Casinos Big Time

This article is a repost promoting content originally published elsewhere. See more things Dan's reposted.

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…

Brendan Koerner (Wired)

Non-transitive Games

Non-transitive dice

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:

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…)

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!)

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

A coin being flipped. — 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.

Play “Penney’s Game”

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!

Not the lottery

Winning the lottery

Footnotes

Non-transitive dice

Penney’s game