There was a murmur of excitement in the office last week when the Oz 7 Lotto division 1 was $50,000,000. Tonight, it has jackpotted to $90,000,000, which Golden Casket says “shatters all existing records”. The Sunday Mail duly fanned the flames of occasional, optimistic gambling.
Winning division 1 in Oz 7 Lotto requires picking the seven winning numbers from 45: 45,379,620 combinations. Since you can buy a 12-game ticket for $12.70, the entry cost to buy every combination is therefore a shade over $48,000,000. (There are tickets with more games, but I think they’re either system entries or quickpicks.) This suggests that a brute force attack may be efficient: i.e., buying every combination and making a profit. (This has been done before in Ireland, and I vaguely recall reports of it being done for some of the American mega-jackpots as well.)
So, I did some quick sums. The calculations are made easier by the fact that the total prize pool is specified by law and can be calculated based on the division 1 pool (Lotteries Rule 1998 (Qld) sch 6 s 18(1) (AustLII, OQPC), and the Golden Casket website has details about the number of prize winners in last week’s draw. I assumed:
There are half as many winners again in each division from last week’s draw (because more tickets are bought).
The overheads of the operation are $5,000,000 (about 10%), to cover the cost of actually putting in the 3,781,635 12-game cards and the cost of capital.
On my numbers (which could be wrong), the maximum potential profit is almost $71,500,000: a huge 135% return on investment. (It means that you win over half of the total prize pool.) But what really surprised me was how robust a proposition it is:
The main risk is another punter also winning division 1. If there’s another division 1 winner, the profit drops by $45,000,000: but that’s still 50% profit.
Even if there are three other division 1 winners, there is still a modest profit (about 7%). Four other division 1 winners gives a 1% loss.
If you assume you’re not the only one with this bright idea, and someone else has done exactly what you’ve done, you’ll still make a 37% profit (about $20,000,000), assuming no one else flukes division 1.
Even if there are two people (or syndicates) also buying all the combinations, it’s pretty much a break-even proposition: a loss of about $200,000, assuming no other division 1 winners.
So, in other words, for the venture not to be successful, basically there either needs to be four other division 1 winners (unlikely: there has been only 1 division 1 winner in Oz 7 Lotto in the past 13 weeks, and no winners in the past nine weeks), or two other similarly minded people or syndicates. They seem to be better than the usual odds when playing lotto.
Notably, last week (the $50,000,000 draw) was not nearly so robust. Assuming no other division 1 winners (which was the case), buying all the tickets would give a profit of about $22,500,000, or 42%. However, the operation is not profitable if either (a) there is another division 1 winner, or (b) if someone else also buys all the tickets.
In yesterday’s press, there was a report that there may be a further jackpot if there are no division 1 winners this week, and also that the prize pool may be larger depending on entries. This suggests that my projected returns for this week could be higher; and also that if it jackpots, the brute force attack becomes even more lucrative.
As far as I could see from my quick look through the Lotteries Act 1997 (Qld) (AustLII, OQPC), there’s nothing that prohibits this, though there might be something in the conditions of entry. (It’s hard to see a reason why there would be—the lottery is presumably fully funded, so there is no risk to the lottery operator.) What’s better is that section 152 of the Act prohibits a lottery operator from publishing the name or identifying particulars of a winner (see also section 225).
Of course, there may also be tax consequences. An enterprise to buy all the tickets in the lottery may well amount to a business, which I suspect means that the winnings will be taxed as income (rather than being tax-free), but I’m no tax lawyer. (The corollary is presumably that the expenses to earn the income are tax-deductible, which may ameliorate the tax impost somewhat.)
