If you were going to run a syndicate with 27 entrants, would you be better off buying these 27 tickets or a random bunch of 27 tickets in terms of getting a jackpot?
Or is there no difference in terms of likelihood of getting a significant win?
Or is there no difference in terms of likelihood of getting a significant win?
In fact the only thing you can do in the lottery is to avoid "popular" sequences like birthdays etc, so that if you do win you don't have to split it with a bunch of people.
A lottery in the Philippines famously had 433 winners, who all played 9, 18, 27, 36, 45 and 54. (https://www.cnn.com/2022/10/06/asia/philippines-grand-lotto-...)
If you permute the numbers with a substitution cipher (randomly chosen), maybe? Personally, I'd prefer a ticket selection like this that covers all the numbers over 27 random selections that may leave some numbers open, etc; but I wouldn't be surprised if you run the numbers, assuming no prize sharing, and get the same results on any distinct 27 tickets.
Or to put it another way, this system ensures you only lose £52 a week maximum before any additional free lucky dips or rolldowns.
If what you're concerned about is maximizing the odds of getting a jackpot, all you need to do is pick 27 different numbers. Say, 1-2-3-4-5-6 through 1-2-3-4-5-32.
If what you're concerned about is maximizing the odds of getting a jackpot that you don't need to share with anyone else, you shouldn't play any numbers that you think anyone else is likely to play, such as the numbers in this paper, six numbers that form a straght line on the play slip (vertical, horizontal, or diagonal), any six consecutive numbers, the winning numbers from any recent drawing[1], or famous lottery numbers like 4-8-15-16-23-42 (the mystical numbers from the TV show "Lost.")
If what you're concerned about is guaranteeing a small win of some kind, then use some rotation of the numbers in this paper.
If what you're concerned about is minimizing the variance in the outcomes you achieve, then you'll want a more complicated formula for picking tickets, taking into account the values of the prizes for matching 2, 3, 4, 5, or 6 winning numbers. And if you're specifically looking for a set of tickets that's robust to operational interruptions in your ticket purchasing (what happens if the lottery system goes offline when you've bought ten of your 27 tickets, and you can't buy the last 17!?)[2].
But if one of the things you care about is the fully-loaded cost of buying 27 tickets, you'll almost certainly want to buy 27 random tickets, because picking specific numbers takes mental and physical effort, and 27 random tickets are unlikely to have enough overlap that it will have a significant impact on your likelihood of winning a large prize. The main downside of buying 27 random tickets is that it makes checking whether you won take more effort than if you already had your list of numbers.
And on that note, if what you care about is the fully-loaded cost of buying and redeeming your tickets, one of the best things you can do is the opposite of what this paper is about: you want to MINIMIZE the likelihood of winning a prize. Going to the store to cash a ticket takes effort, but it isn't much more effort to claim 27 prizes vs one single prize. So if you have a choice between a 1-in-27 chance of collecting 27 $2 prizes vs a 100% chance of collecting one $2 prize, you're better off with the former, simply because you can probably avoid an extra trip to the store.
[1] Unless you think there's a problem with the RNG system. IIRC about 15 years ago there was a state that drew the same lottery numbers 3 days in a row because they introduced a new computer PRNG and part of their runbook introduced the same seed for every draw; after the third consecutive draw they fixed the issue.
[2] I've had this happen to me, though the problem was that my bank froze my account partway through buying tickets, and I was buying a lot more than 27 tickets. The most famous/infamous lottery syndicate in modern history, a group from Australia that tried to buy every combination in the Virginia lottery in the early 1990s, also ran into logistical issues and was unable to finish buying their complete set of tickets, but they got lucky and hit the jackpot anyway.