I've often written on my blog about how poorly the human brain intuitively understands probability. My very basic understanding from statistics courses (and a vague interest) is the reason I don't buy lottery tickets. Yes, your chances of winning a jackpot if you don't play are zero, but your chances of winning if you do play are so close to zero it makes no difference. I might do better wandering around town hoping to find a few million dollars lost in a bag on the street (which has happened, here in Vancouver).
People who know me are tired of my saying that if I ever do buy a lottery ticket, my numbers will be consecutive: 1, 2, 3, 4, 5, 6 for the Lotto 6/49, for example. Those are just as likely to be a winning combination as anything else. Here's proof: not just one, but four people in New South Wales, Australia just won a jackpot using the numbers 1 through 10 as their picks, getting more than $2 million Australian each.
I think it was my friend Karen who pointed out that choosing consecutive numbers (or any other set that might be easy to think of, or might have some meaning to people) isn't the smartest strategy. Why? Because, as for those Australians, it's more likely that several players will choose them, and that you'll have to split any winnings you do get. That's because, unlike the numbers that win, many numbers that players pick are non-random. Going with a random set of numbers (the same ones or different ones, whatever) each draw would bring the best likelihood—still trivially small—of keeping it all yourself, or splitting with fewer co-winners. Nevertheless, I'd take $2 million and the good story.
But if I have a few bucks to spend, I'll probably still get myself a burger.
Back in the days when the UK lottery was popular, this was a frequently discussed subject.
The lottery corporation actually released some stats... I forget the exact numbers but they claimed that, on average, several HUNDRED people every week chose 1,2,3,4,5,6 and so a full jackpot would only net you ten thousand pounds or so each.
As you say, the smart (*) thing is to pick your numbers to minimize the chances of picking the same numbers as someone else... shunning popular numbers or patterns. You're right, you can't increase your chance of winning, but you can increase your payout should the (very unlikely) occur.
A year or two into the UK lottery, they introduced a new way to play where you could let the machine pick your six numbers for you randomly. If you were going to play, this was the smarter way to do it as it reduced any chance of "clumpiness" in your numbers.
The other trick worth remembering is to pick a couple of numbers above 31. Many people use dates for their lottery numbers and so there's a higher chance of collisions with the lower numbers.
(*) less smart than not playing the lottery at all of course.
I think our 6/49 and other lotteries have always (or at least for a long time) had that "quick pick" system. And a lot of people do use it, simply because it's easy and fast.
Easy, fast and also the best way to maximize your 'winnings'. Although really you're probably just minimizing the time you waste :-)
My guess is that rollovers probably dropped after the lucky dip feature was added to the UK lottery.
In the UK my department had a lottery syndicate. Everybody threw in £1 a week and someone took the cash over the road and bought us 40+ tickets (before lucky dip, that took a LOT of work LOL)
It was quite interesting looking at the results... those with limited understanding of maths thought of it as "boosting our chances"... I looked at it more as "losing money faster". The UK lottery runs the same system as the 649 so every week we'd pretty much expect a "3 numbers" win or two paying back £10. After a couple of months the excitement wore off and people started to grumble about it (what? You expected to be living in the Bahamas by now?). There was a certain amount of blackmail in the way the syndicate ran... maybe this would be the week that the syndicate won £10,000,000... wouldn't you hate to be the guy that missed out... maybe you'd be the only person in the office on Monday?
I dropped out after about 3 months and every week I'd proudly announce how much more money I had than the people still in the syndicate :-) - a couple of times they got 4 numbers on a ticket but dividing that money by the number of people in the pool, and taking into account the number of weeks they'd lost money, they never clawed back to break-even.
Now Premium Bonds... that's an entirely different story.