Here are some thoughts I’ve had on how I would design a lottery if it were my job. I find computer programming and real game design to be more fulfilling than the design of these sorts of mind-hacking gambling games, which is why I would consort with a cactus before I’d ever work for Zynga. That said, someone has to do that job. Here’s how I’d do it if it were mine.

A toy example is the mathematically interesting, but impractical, “no-balls lottery” driven by “strategic luck” (to use a game-design term). It works like this: at each drawing, players choose a number between 1 and N (say N = 60). It costs $1 to play, and the payout for choosing the winning number is $N. Where’s the house edge? The winning number is not chosen at random; it’s the one chosen by the fewest number of people (with ties either split or resolved randomly). What’s cool about this lottery is that it has the appearance of being “fair” (zero expectancy, no house edge) but it produces risk-free profit for the house no matter what, because the winning choice will always be chosen by less than 1/N of the players. The more uneven the distribution of choices is, the better the house does. Game theory (Nash equilibrium) predicts that we’d see a uniform distribution of choices over time; I have no idea how it would actually play out. The house edge would unlikely be enough to cover administrative costs, but it’d be an interesting social experiment.

At any rate, the press loves lotteries. Not the small, reliable, boring kind, but the big ones. The $640 million jackpot for the MegaMillions has been a major news item of late– it’s the largest U.S. jackpot lottery in history. I even chose to play, mainly for epistemological reasons related to recent and extremely unusual events in my life that lead me to suspect supernatural trolling. Let me explain. There’s somewhere above a 99.999% chance (call this “prior” p) that the universe acts the way we think it does, and that there’s no correlation between balls drawn at a lottery and personal events in my life. It’s actually very likely that the correct value of p is much higher than 99.999%. I can’t put a true probability on it for the same reason I can’t put one on religious questions: probability enables us to reason about uncertainty of known structure, and this is about uncertainty of unknown structure. That said, there’s a 1 – p chance that the universe is deeply weird, that it has the tendency to troll the fuck out of people, and that playing the lottery right now (only right now, because this is a singular moment) might lead to profit. I don’t know what this “1 – p” is, but I’m willing to pretend, for the moment, that it’s high enough to buy a few lottery tickets.

(Technically speaking, the MegaMillions already has positive expectancy. This is practically irrelevant, as it is for the notorious St. Petersburg lottery. Almost all of that positive expectancy is concentrated in the extremely-low-probability jackpot and, between taxes, split jackpots, discount rates applied because lottery payouts occur over time and, far more importantly, the extreme concavity of the utility curve for money, I don’t know that it has a meaningful expectancy. I’m buying because, despite my scientific training, weird events cause lapses into superstition.)

A lot of people think the way I do, and the vast majority of them never win lotteries. People are very bad at managing low-probability events. Cognitive biases dominate. What actually ruined my interest in the lottery, as a child– my dad played about once a year, and let me pick numbers– was realizing that a Super-7 outcome of {1, 2, 3, 4, 5, 6, 7}, which “would obviously never happen” was precisely as likely as for me to pick winning numbers. (Actually, {1, 2, 3, 4, 5, 6, 7} is a bad play because of split jackpots. Dates are common fodder, so pick numbers 32 and higher if you want to minimize that risk.) Moreover, this type of magical thinking tends to surround the largest lottery jackpots, which appear “historic”. Of course, I know how silly it is to think this way, because large jackpots are nothing more than an artifact of Poisson processes and very long odds: it would be possible to build up a $5 billion jackpot (assuming people would play) just by designing the lottery so that the odds of winning are very small.

So if I were designing a lottery, how would I do it? Let me say that I’m ignoring the ethical question of whether I think gambling and the lottery are good things. I’m assuming the position of a person who thinks lottery gambling provides a social value. (My actual position is more uneasy.) I would not be happy to design some small scratch-off game. I’d want to build the lottery responsible for the first billion-dollar jackpot.

First, 7 balls is too many; the ideal number seems to be 5 or 6 (short-term memory). Two-digit ball ranges are also desirable, with 50 to 60 being typical. Numbers in the 50s seem moderate on account of the “inverse Benford effect”, whereby numbers with leading digits of 5 and 6 seem “moderate”. (Falsified financial figures tend to lead with ’5′ and ’6′ digits, although log-normally distributed real-world variables should lead with ’1′ over 30 percent of the time.) A typical 6-ball lottery, with 50 balls, gives odds of 15.9 million to 1. That’s clearly not enough. It might produce a piddling $30 or $40 million jackpot on occasion. Congratulations: you’ve earned ten months’ salary for an upper-echelon corporate scumbag (and by waiting in line for 3 minutes for that ticket, you’ve had to do more work than that well-connected blue-blooded shit has done in his whole life). Since it’s long odds that produce large jackpots, how do we push those odds into the billions?

The idea’s already there. Consider the 6-ball lottery that I described. The odds can be made 720 times longer by distinguishing or ordering the 6 balls. This is how the Powerball and MegaMillions work. One ball is distinguished as “special”. This makes the lottery more “fun”/engaging, and it makes the odds of choosing a perfect ticket longer. My target, in designing this lottery, is going to be to aim for odds in the 1- to 2-billion-to-1 range.

First, I think we’re ready for two distinguished balls, one red and one green. In fact, we’ll need that to get the kinds of long odds we want. The range for each is going to be 1 to 31. Why 31? Because, from a design perspective, it fits. One of the most common sources of lottery numbers is dates, so why are we cluttering up the card with these higher, less useful, ungainly numbers? For the other four balls, however, we need a wider range: 1 to 80. Yes, 80 puts us afoul of the “inverse Benford effect”, but we’re selling a premium product, so 80 is appropriate.  How many possible tickets are there? 80!/76!*4! * 31 * 31 = 1,519,898,380. With 80% of ticket revenues going into the non-discounted dollar amount jackpot (which means we’re actually only putting about 50% in, because we’re paying an annuity over about 25 years) we’ll be seeing billion-dollar jackpots on a regular basis. Not only that, but we’ll be seeing $1-billion non-split pots on a regular basis. For the first time ever, we’ll be minting billionaires from a lottery.

Of course, it’s the jackpots that bring ticket-buyers in, but it’s the small prizes that keep them coming back. The prize is a free ticket if you hit either the red or green ball (16:1), $100 if you hit them both (961:1). (A $100 payout on 1 in 1000 tickets, for jackpot lotteries, is unheard-of.) We’re paying 16 cents on each ticket there, but I think it’s worth it to keep continued engagement. We also want to make the second-to-top small prize large: $1 million for a ticket that matches the 4 white balls and one of the colored balls. The odds of that are 25 million to one, so we’re paying 4 cents per ticket there. We can shave expectancy on the middling prizes, which will be low compared to the odds against them. No one really looks at those, anyway. It’s the frequently-won small prizes, the second-best prize, and the jackpot, that actually matter.

Here’s why I think we should do this. Here’s the real ideology behind what I’m suggesting. I don’t care much either way about lotteries. Nor do I have a need to make that kind of money off people who, in general, need it more than I do. I do think Instant Games are a bit unethical (pathological gambling, and the fact that winnings almost always go into buying more scratch-off tickets, often on the same day) but also I think that, compared to alcohol, tobacco, and trans fats, lottery tickets are one of the less harmful things sold in most convenience stores. This said, the lottery I described is a starter in giga-lotteries: 1.5-billion-to-1 odds, three-digit millionaires and billionaires being made out of random people on a regular basis. Sure, the odds are very long, but most lottery players don’t give a damn about the odds: they’ll play as soon as they see $500-million jackpots, for the novelty. I do it, just to see the huge numbers. It’s gossip. But to paraphrase Justin Timberlake, a billion dollars isn’t cool (or won’t be, after it becomes commonplace). You know what’s cool? A trillion dollars. Or, at least, $85 billion or so. U.S. lottery revenues are about half that, but I think we can do more. Way more, once we establish a lottery where billion-dollar jackpots are the norm.

I don’t care here, as I said, about revenues. My goal isn’t to make money off of peoples’ cognitive biases with regard to low probabilities. It’s not to get rich. (Since I can’t legally implement this idea– only governments can– I never would.) Making money isn’t the goal. We should shove as much of our ticket revenue into the jackpot as possible. Rather, the goal is to make huge fucking jackpots. Two distinguished balls (one red, one green) is just the start. For the real act, we can have six different colors (white, red, gold, blue, green, and silver). This colorful lottery will be so engaging and so well-hyped (once $10-billion jackpots are old hat) that we can charge $5 per ticket. The ranges on each ball will be 1 to 84. We’ll need a lot of high-profile small prizes, and a two- or even three-tier jackpot system will be in order, as the odds of a perfect ticket will be 351 billion to 1. Top-tier jackpots will swell and swell and swell, building for months and growing exponentially. We might have to make this a world lottery to get a winner a couple times per year or so. But at some point, however, someone out there will win a huge amount of money. It will take a long time to get there, but a trillion-dollar jackpot will, at some point, happen.

What’s the redeeming social value of a trillion-dollar jackpot? Complete and total humiliation of the world upper class. Mockery of the world’s most destructive dick-measuring contest. A person, chosen completely-the-fuck at random, being catapulted to the top of the Forbes 500 for no fucking reason whatsoever. So fucking awesome. I would buy $1000 of these fucking lottery tickets every month and hand them out to the most undeserving randoms, solely in the quixotic, long-shot pursuit of the noble goal of humiliating every single private-equity asshole on Park Avenue at once by having a lottery player out-win all of them by orders of magnitude.

Is this evil? I’m not sure. I don’t actually want to see this experiment happen. I fully support humiliation of the existing upper class, but this sort of extreme lottery would just create a new upper class. The only difference is that this would be an elite made for no reason, as opposed to our current elite, which exists for mostly bad reasons. Moreover, I just don’t think it’s the best use of my time and talent to encourage mathematically naive people to pump trillions of dollars into a process of no social value.

The objection I have to it, again, isn’t gambling: we gamble all the time. Every blog post I write has an effect on my career– mostly positive, in that I can establish myself as knowledgeable about technology, progressive management, mathematics, software engineering, and computer science– but potentially negative, as well. This post, in which I describe the application of game design talent to an extremely perverted social project, is probably riskier to me than buying a few hundred lottery tickets. And this blog post, unlike the MegaMillions, has no chance of ever earning me $640 million.

There is another problem with this trillion-dollar lottery (TeraTrillions, and I am fucking trademarking that name). I am afraid that someone would fucking Occupy that shit.