This column provides informative commentary on financial matters and is written by Patrick van Beek, managing Proprietor of Caribbean Actuarial & Financial Services.
Derek Gomes, a financial services professional, often sits quietly at his desk, chin cupped in hands, brows furrowed and beading perspiration with a pensive expression on his face. What could be causing such contemplation? Is he worried about a financial crash, stock market tumble or another large insurance claim? No, he is considering his choice of numbers for next Lotto game.
Lotto, the flagship game of the Guyana Lottery Company Ltd involves buying a ticket for $100 and picking six different numbers from between 1 and 31 inclusive. Gomes enters nearly every draw, which occurs twice a week, often buying three or four tickets. At the draw, six numbers are drawn randomly from the 31. If the six numbers picked match the six numbers drawn, the player walks away with the jackpot unless more people also choose the winning numbers, in which case it is split equally between them. The jackpot is a minimum of $4 million and increases each week that no one wins; Gomes says it currently stands at around $19 million. There are smaller prizes for getting four of the six numbers, five of the six numbers, and five of the six numbers along with the bonus ball which is an additional number drawn after the six.
Asked what the odds of choosing the winning numbers are Gomes gets pretty close to the mark with a guess of 760,000 to one. He appreciates these are exceedingly long odds, but rationalises them by considering other long odd situations: "The man who dies in the plane crash is not comforted by the statistic that more people die in car crashes." He hopes for the lucky break since the big prize would make a big difference and "unless you play you don't have any hope of winning". So much so that Gomes puts his spending on Lotto tickets at the top of his weekly expenditure.
Gomes has various systems he uses to choose his numbers. One way is the quick pix, in which the numbers are chosen at the Lotto terminal randomly. Another is the lucky dip, where he picks the numbers from a bag. Clearly he has no delusions that there is any system which can be used to try and predict the numbers yet he still feels some superstition. "I like to change a set of numbers if they win". If the numbers are truly random then they have exactly the same chance of coming up next time regardless of whether they have been seen before.
I have analysed the odds of winning any prize in the various games and the expected payout, which is the amount you would expect to be won per ticket over the long term. As the table shows, the expected payout as a proportion of ticket receipts is pretty consistent at about 47%-48%. The exceptions are Lotto, and Play de Dream, where there is a 44% and 50% payout ratio respectively.
However, Lotto is the only game where the jackpot increases. In fact if the jackpot exceeds $73,628,100 then the expected payout ratio on the jackpot becomes more than 100%, which means if you could play the game with that level of prize indefinitely you would expect to make money. Unfortunately you would expect to break even after about 7,080 years so this is not really practicable.
Odds and Payouts assuming $100 is spent on each game
* Assuming $19M jackpot, $208,760, $38,660 and $1460 prize structure
A better tactic, which has been employed in some of the largest lotteries in the world like the double and triple rollovers in the state lotteries in the USA, is to buy every possible ticket combination. In Guyana this would involve 736,281 tickets at a cost of G$73,628,100. The big risk is that someone else guesses the numbers, in which case you have to share the prize, so you could end up with less than you spent on the tickets.
This is a lot of capital to risk if the jackpot is only marginally greater than the cost to buy all the tickets.
However, if the prize gets to 2-3 times more than this, the odds of there being so many winners that the prize becomes diluted to less than what was paid to buy all the tickets, becomes so remote that barring someone else buying all the tickets as well you are almost certain to make a profit.
Of course it is quite common that the bigger the prizes, the longer the odds, so more tickets can be bought, which makes actually buying all the tickets an administrative nightmare.
The expected payout of a jackpot on the Lotto does not exceed that of Daily Millions Plus until the jackpot reaches $11.2 million, so going on jackpots alone statistically you are better off playing Daily Millions Plus up to that point and then switching across.
When I pointed out the odds of winning a prize on Daily Millions Plus was far better than the Lotto, Gomes was of the opinion that a million dollars would not be enough to make a difference and he did not consider the consolation prizes to be prizes at all.
He has matched four numbers on the Lotto about 10 times, not bad going if you consider the odds are 164 to 1. But this is to be expected if you buy seven tickets a week over a five-year period or so.
It seems that even people who are well aware of the odds and expected payouts are happy to play the lotto. The fact is that they are willing to lose a small amount for the extremely small change of an extremely large payout.
Coupled with this comes the excitement involved in almost any game of chance.
I have to admit that when I took part in the syndicate at my work for the Christmas lottery in Guernsey, I could not help myself from thinking, "what if we win?"
It certainly made watching the draw exciting, so if nothing else there was entertainment value to be had from the whole experience. And no, we didn't win!