As for Godot or an All-Ireland win for Mayo, the wait for a Lotto jackpot goes on. Once again – and for the 53rd time in succession – there was no jackpot winner in Wednesday’s draw.
When the jackpot was last won, on June 5th, daily Covid cases were in three figures, July’s heatwave was ahead of us, and we might not have guessed that we would spend the autumn engrossed in a blood-soaked TV show based on Korean childhood games. But unlikely things have a habit of happening, especially when they have plenty of opportunities to do so.
Some coverage of the rollover saga has emphasised the sheer unlikelihood of winning the Lotto jackpot. With six numbers to choose from a total of 47, there are 10.7 million ways that the winning numbers can be drawn. So each line bought on a Lotto ticket provides a one-in-10.7-million chance of a win.
This streak of rollovers is highly improbable, being in the range of unlikelihood of picking up a deck of cards and dealing a full house (about 700:1) or four of a kind (4,000:1)
But the odds of a jackpot win in any given draw depend entirely on how many distinct lines are bought. The National Lottery does not publish these details, but there are statistical clues that allow estimates to be made.
Noting that the number of match-four winners in each draw should be proportional to the overall number of lines sold, Dr Michael Cronin of UCC estimated sales for the two previous draws at 1.74 million and 1.36 million. This translates into an estimate for the odds of a win – and so the odds of a rollover.
Looking back to the beginning of June, this approach gives the average chance of a win as being 12 per cent (and so there also being an 88 per cent chance of a rollover).
Extrapolating from annual report sales data also gives a figure in this region. On this basis we can estimate the odds of 53 rollovers in succession as being about 1 in 1,000. But numerous caveats apply: it seems all but impossible to determine how many duplicate tickets may have been sold for a given draw, for example, or to gauge the effect of popular numbers arising in the actual draw.
A 2016 study of the Dutch lottery confirmed that players frequently use their birthday when selecting numbers, disfavouring numbers from 32 upwards. Similarly, the numbers 3, 7 and 11 were selected about 60 per cent more often than 37 and 38.
The odds, then, could be significantly longer, but they are probably not significantly shorter than one in 800.
Suffice to say that this streak of rollovers is highly improbable, being in the range of unlikelihood of picking up a deck of cards and dealing a full house (about 700:1) or four of a kind (4,000:1). But this raw improbability must be considered in light of the fact that the Lotto has been running for 33 years, and so has had a great many opportunities to roll over 53 times in succession.
Allowing a probability of 12 per cent for a jackpot win in any given draw, we find that the percentage chance of the jackpot rolling over 53 times in succession at least once in this period of time is well into double figures. So this event initially appears eye-catchingly improbable but looks less so over a 33-year window.
So how to win that €19 million jackpot? This is simple: buy lots of tickets. When will it be won? This is less simple. The game has no memory, and the odds of a win this weekend are no different from in that first rollover draw, in June
Any firm statement about this would require complete data rather than the estimates used here. It may be worth noting that there has been no intervention from the National Lottery regulator (who protects the interests of players), as there was in 2019, when anomalies arose with scratch-card games.
So how to win that €19 million jackpot? This is simple: buy lots of tickets. When will it be won? This is less simple. The game has no memory, and the odds of a win on Saturday, December 11th, are no different from the odds in that first rollover draw, on Wednesday, June 9th. This could go on and on.
National Lottery advertising seems to be pushing heavily the message that the Lotto is not just about the jackpot, and indeed prize money in excess of €1 million per draw has been distributed among match-five and match-five-plus-bonus winners since the jackpot was capped at the end of September.
But there is a sense that a jackpot win would come as a relief. (A "must-be-won" draw has been ruled out by the National Lottery, citing the regulatory framework.) Equally, it seems unlikely that the game can be changed at short notice to make it more likely to produce a jackpot winner. So sales it must be.
Incentives tied to further supporting the National Lottery's good causes may be worth considering. After all, we broke Revolut in our enthusiasm for donating to the Late Late Toy Show appeal without so much as a cent in it for ourselves.
Brien Nolan is an associate professor at Dublin City University's school of mathematical sciences
