Usually when you see an article or some link about “beating the lottery”, you know it’s going to be a scam site, so there’s no point in clicking on it. You can’t beat the lottery, you just can’t. Right?

That’s certainly the popular wisdom, and the attached article (I used to hate the Huffington Post, but it’s become a little less sleazy and irresponsible of late, I find) walks through some of the history of how it is just a tax on the poor, the underrepresented, etc. And if someone found a way to “beat” the system, it would be illegal, right?

Well, apparently not. Based on some articles that ran in the Boston Globe, a down-home, blue collar guy in a white collar job (working for a cereal company on packaging), was fond of puzzles. And he loved math, so he would read, take courses, constantly learning new things. And then, one day, he was reading an ad for a new state lottery when he noticed something odd. It was your standard “pick-six” numbers out of a possible 49 for up to a $5M pay-off. Nothing unusual there. But they were adding a feature — if the big prize wasn’t won, it would roll-over, and roll-over (similar to most lotteries) BUT with one key difference — after a few weeks, if the big prize wasn’t won, they would do something called a “roll-down”. They would take all that big prize money and pro-rate it across all the smaller prizes. So, for example, the smallest prize of $5 could win $50 that week, if nobody won the big prize.

While that seems like no big deal, it drastically alters the math for your “return on investment”. So if you think of your chance of winning $10 in a game that only has ten tickets that cost a $1 each, then your expected return for your dollar “bet” is only $1. How does that work:

Expecting winnings = the prize money x the likelihood of winning = $10 x 1 in 10 = $1

So, statistically speaking, if you played over time, you would come out even. You would pay a $1 and expect to get a dollar back. Even Steven. And lotteries take that into account when they design the games. The math is NEVER in your favour. For example, your normal “return” calculation would look like this:

Expected winnings = HUGE prize x low odds of winning = $50M x 0 = $0

It isn’t zero, admittedly, but it is so low, it doesn’t change your payout calculation other than to say your return would be somewhere around one-thousandth of a penny. Over time, you would be guaranteed to lose money. Lotteries are rigged so the house always wins and suckers can’t game the system.

However, the rolldown would change that calculation, if for example, every sixth game, the payout was $20:

Expected winnings = $20 x 1 in 10 = $2

Or, put differently, if you could buy all ten tickets for $1 each for $10, your guaranteed payout would be the $20 and you’d be up $10. The math works because the winnings that week are NOT based on your normal return, they add in winnings from previous weeks that went uncollected. This means the state isn’t losing money — they already got their take. This is more like previous people didn’t win, so you can win THEIR money as well as the money from this week.

The problem though, in a state lottery, or any lottery where there are millions of combinations of tickets and millions of players, you can’t buy all the tickets, of course, but you also can’t buy enough tickets to even out random chance. So in the above example of $20, if you only buy 1 ticket, then your odds of winning don’t change, and it could take ten times before you “hit” — on average. But it could be 20 times or 2 times…if it is only twice, you’re way ahead. If it is 20, you come out down $10. The example in the article is with coin tosses, but the basic idea is that you need enough tickets to offset the random fluctuations of chance so that your investment matches the statistics (i.e. you need enough coin tosses for statistics to prevail).

How many tickets? The more you buy, the more it evens out the fluctuations. The main guy in the article starts at $3500 on $1 tickets. And he lost $150 or something. Next time, he went larger, $10K, $15K, etc., and evened it out. So he was making almost 50% return. Then he took on investors and jacked it up to $100K and more.

But the time investment was huge — he had to stand at a terminal all day long printing tickets. And only for “roll-down” pots. It wsa the only time the payouts were in your favour. And over time, the lottery officials would notice and kill it.

So he started playing another similar game in another state, and the newspaper article profiles other “investor” groups who noticed the same design flaw. However, to be clear, they weren’t cheating. They were just doubling down their bets when they knew the odds and payouts were more favourable. They weren’t rigging the game (although one group did that a bit, albeit not illegally). They weren’t cheating. They also weren’t anonymous — the lottery knew what they were doing and wasn’t stopping them. Because they were playing like everyone else — press the button, buy some tickets, take your chances. They were just doing it on a MASSIVE scale. Which the lottery officials didn’t mind because 40 cents of every bet was going into revenue for the state. The tax part of the winnings.

Overall, a really cool article. Even if the HP is mostly piggy-backing on stories written elsewhere, it’s decent reading.