Given all the market and economic drama over the last few weeks, I thought that I should take a breather from the heavy stuff and update a post that I wrote a few years ago about winning the lottery.

And to do that, I’m going to credit a book called: “Alex’s Adventures in Numberland” – which I have plagiarised before (see: Have You Really Done The Math? #SavingsAreImportant).

**The Big Question: How Can You Win The Lottery?**

The short answer: buy all the tickets.

*drops mic, walks off stage*

**The Better Question: When Is Buying All The Tickets A Good Idea Though?**

Surprisingly, “buying-all-the-tickets” is not always difficult in practice. The famous example: Stefan Klincewicz, the half-Polish accountant, put together a syndicate to buyout the Irish lottery in 1992.

Successfully.

Having said that, the success does depend on the way that the lottery is constructed, and you’ll need to spend some time with the permutation and combination functions on your calculator.

**The Math**

Most lotteries invite you to play a variation of this game:

- There are 49 balls in the swirling cage
- You have to pick 6 of them.
- And it doesn’t matter what order you select them in.

There is obviously the big prize for guessing all 6 numbers. But there are other lesser prizes for getting three or four or five of the numbers correct.

If you look at the big prize on its own, there are 13,983,816* possible combinations that you would have to buy in order to guarantee having the winning ticket. Other important facts about the winning ticket: on average, the winning ticket gets around 52% of the “prize pool”**.

*If you’re interested in the complicated math, if I just had to pick 6 balls from a basked of 49, then I would have 49 options to pick from for the first, 48 for the second, and so on – meaning there would be 49×48×47×46×45×44 different permutations of numbers. However, those permutations would include choices like 1-2-3-4-5-6 and 1-2-3-4-6-5 as two different combinations – and we know that both of those would be the same if I picked them for the lottery (ie. the order doesn’t matter). So I’d need to divide my total number of permutations by the number of different ways that 6 numbers can be combined – which turns out to be 6×5×4×3×2×1. Thus: 49×48×47×46×45×44 ÷ 6×5×4×3×2×1 = 13,983,816 possible numbers.

**Here’s a link to the calculation of the prize pool for the UK National Lottery.

But good news: there are still those prizes for having 5 numbers right, and 4 numbers, and 3 numbers. So if you were to buy every possible ticket combination, you’d pick up those prizes as well. And given that the winning ticket is 52% of the prize pool, that’d leave 48% of the prize money for the smaller prizes.

Armed with that information, you can now make some fairly rational decisions based on the price of a lottery ticket and the size of the sweepstakes.

For example, if each lottery ticket costs £1, and the winning ticket gets £1.5 million – then that means it would cost you about £14 million to win about £3 million. So a complete no brainer – because paying £14 million in order to win £3 million is a guaranteed £11 million loss.

But let’s say that the lotto ticket costs £0.50, and the big prize is worth £5 million. Well, now it would cost you £7 million to win about £10 million*? That’s sounding more like it…

*about £5 million for winning ticket and another £5 million for the lesser tickets.

So where is the catch?

Well, at those stakes, you’re going to get a whole lot of other people buying tickets. So you won’t get all the winnings…

That said, the size of the lesser-prizes-pool is usually linked to lottery ticket sales (I’ve seen some lotteries talk about 45% of the ticket price going into the pool) – so whatever else happens, you should get back a good part of your initial contribution. But getting back 45% of your “investment” is not a great proposition – you should only be buying up lotteries if you don’t expect to lose money.

I’m also leaving out my least favourite thing: the admin. Individual ticket sellers are going to have some limits around what they can sell, so you’re going to have to mobilise teams of ticket purchasers. And then you’re going to have to split 14 million numbers between them. When they’re done, you’re going to need to store 14 million tickets. And this is all going to have to happen in a fairly co-ordinated fashion – otherwise the lottery operator will pick up on what you’re doing and suddenly “*the lotto server is offline, our technicians are attending to the problem…*”

**So What Did Stefan Klincewicz Do?**

Stefan did indeed mobilise teams of purchasers. But he was also dealing with the Irish lottery – which only had 36 balls in the ring, taking the number of possible combinations down to 1,947,792. Each ticket cost £0.50, and the big prize was £1.7 million (owing to several rollovers from previous weeks).

So to be clear, for less than £1 million, he could buy up a lottery worth around £2.5 million*. Unfortunately for the syndicate, two other people also got jackpot tickets, so it had to split the £1.7 million three ways. However, once his syndicate had also collected the smaller prizes, they’d made money. Some good money. Around £300,000 over and above the cost of all those tickets (so I’ve read).

*just the big prize was rolling over, not the smaller ones – so there was some distortion in the prize-pool.

Stefan went on to form multiple syndicates, and go in search of lotteries where the size of the sweepstake was significantly larger than the cost of buying the lottery out. His general rule, in order for the bet to be a good one, was that the sweepstake had to be about three times the cost of buying all the possible combinations. He won a further 7 jackpots, and then retired on the money.

**The Lotteries Respond**

It’s not that clear whether Mr Klincewicz retired because he was bored, or if it was because the lotteries got a bit clever.

Today, some of the big lotteries will allow the first five numbers to be drawn in any random order, but you have to get the bonus ball (pulled from a separate drum of 36 balls) right. That is, you have to get the number right, and you have to say that it was going to be the “bonus ball”.

This takes the number of combinations up to 68,647,824. So that slight alteration changed the odds so dramatically that it made it near physically impossible buy all the tickets.

Of course this is in addition to the “let’s add more balls to the drum” and “let’s increase the ticket price” options – both of which the Irish Lottery put in place after the Klincewicz syndicate hit them.

**To Sum Up…**

You can win the lottery and still not make enough money for it to have been worth your while.

But sometimes, winning big can be your foregone conclusion.

*Rolling Alpha posts opinions on finance, economics, and the corporate life in general. Follow me on Twitter @RollingAlpha, and on Facebook at www.facebook.com/rollingalpha.*