h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: How To Improve Your Chances Of Winning The Lottery - A1025191
Author: Sir Kitt - U180224

I've been thinking of submitting this for a while. I don't get on H2G2 as often as I use to. It may be a few days before I'm back to take any comments.

I happen to like this entry. Both useful in the sense of providing a genuinely better chance at winning the lottery, and at the same time demonstrating to people who play the cumulative foolishness of their investment. Wouldn't be even more of an improvement if you got together with some friends and everyone did this method the same day?
-MotDoc

Alas this does not increase your chance of winning the lottery. It increases your chances of winning it IN ANY ONE week, but solely by putting more money on.

Incidently buying 2 tickets does not double you chances of winning.

I may be wrong, not having taken statistics in a long time, but I believe that buying two tickets would double the chance of winning. If your chance of winning with one ticket is 1/20,000,000 than your chance of at least one ticket winning if you have two tickets is 1/20,000,000+1/20,000,000=1/10,000,000.

Also, it should increase your chance of winning unless you always choose the same numbers every week. If you play a random number each week than the probability should always reset, leaving you with no greater chance the next week, whereas if you buy them all at the same time each non-winning number would narrow the remaining possible numbers down and thus increase the chance of any one winning.

It makes no difference to the probability what numbers you pick - whether you have random numbers or the same ones each week - even if you win one week and then keep the same numbers you have the same chance of winning the next week.

I like this entry.

Buying two tickets does in fact double your chances of winning the jackpot (assuming you put a different set of numbers on each ticket).

The method outlined here doesn't improve your chances _over your lifetime_. It just moves the possible win forward in time to now, when you can enjoy it, rather than 25 years from now (assuming you are playing for 50 years). You make this point in the entry, but it might be important enough to deserve a change of the title of the entry.



I saw an interesting point made in a book on probability about the Lottery. It suggested that you should by your ticket on the day of the draw rather than a few days in advance, because this improves your chances. The reasoning is that if you buy your ticket a few days before the draw, you are more likely to be killed by being run over by a bus than to win the Lottery.

Glad you like the entry. I wasn't sure about the title, but I don't want to make it any longer. Any suggestions?

SK

http://www.fool.co.uk/news/comment/2003/c031202d.htm?ref=emaillunchhtml

loose > lose

Thanks Zarquon, typo corrected.

SK

I'm not quite sure about it - would it be relevant to add a link to A1084673?

May I make an observation here? If you only play the lottery on rollover weeks, then it's much closer to being "fair". I.e. normally you get back about 50p on average for every pound you put in, but on rollover weeks you get back more than that.

You should wait for a rollover week before buying your 2500 tickets - the odds will be the same, but if you win you get more money.

I'm not sure about this, but maybe you could even make an (almost) guaranteed profit on a rollover. E.g. if the jackpot had gone up to more than 14 million, buying all 14 million distinct tickets would be a profitable strategy. (There's a chance that lots of other people would have bought the winning ticket too, but you've got that whatever you do. Maybe you want to mention something about picking numbers that other people are less likely to have chosen.) I seem to recall a newsgroup discussion on refinements of this strategy like trying to cover all combinations of five numbers - I'll see if I can track it down.
Ekaterin.

To make the outcome a better deal, in the one-fell-swoop approach, pick a week with a *HUGE* payoff!

Punctuation suggestion: 'Put the whole lot on in one week and win or lose never, but never play the lottery again.'
'Put the whole lot on in one week and (win or lose) never, but never play the lottery again.'

Waiting for a huge payout is just being greedy.

I'm not sure about the punctuation thing. I not really keen on using brackets in text like that.

SK

You seem to start with a false premise: "Every week the chances of winning the Jackpot are 14 million to 1, hence every week you lose a pound"

Every week except for that one in 14 million. But even then you may not lose your pound every week - you could win one of the smaller prizes. I'd be interested in seeing the entry cover how these smaller prizes affect (or don't affect) your chances of making a profit...

Good point, Archangel

I've reworded the line you are concerned about to take accont of the minor prizes. Of course you are bound to pick up quite a few minor prizes with this method, but it's the jackpot we're really interested in.

SK

Looking at the prize breakdown, can you really afford to discount the 'minor' prizes so casually when you'r etalking about buying so many tickets? Given that we're buying 2,500 tickets, how many of those tickets could we expect to match 3 balls? Or 4? Or 5? Or 5 and the bonus ball?

I think (although, it has to be said, without bothering to do the maths) that it's entirely possible for you to win a substantial amount of money - possibly as much as you'd win by matching six balls - without actually winning the jackpot.

By my calculations the ares:

3 balls 153:1
4 balls 7062:1
5 balls 317814:1
I'm not sure how to work out the odds for 5+bonus ball

So for your £2500 the odds would reduce to:

3 balls 1:16.66
4 balls 2.8:1
5 balls 127:1

The 3 ball prize is £10, so you could expect to make £160-£170 on them. The other prizes are not fixed but 4 ball usually pay in the order of £50 and 5 ball around £1300. So you would have to be lucky to get one of those and you'd still make a net loss. 5 and the bonus would get you in to profit paying around £100 000 or so. Which would be nice but no where near as nice as the jackpot.

If some one can help me out with odds for 5 + the bonus I'll have a look at working them in somewhere.

SK

5 plus bonus would be the prob of getting 5 out of 49 times the prob of getting 1 out of 44 I think...

That's what I thought at first, but the same odd as getting six balls. The bonus ball is drawn after the six main balls so it would be one from 43 balls. But even that is times the odds of getting 5 would gives 13.7 million to 1, which still seems to high.

You can never find a tame mathematician when you need one.

SK

Yeah, I was wrong, the prob will be:

1 out of 49
times
1 out of 48
times
1 out of 47
times
1 out of 46
times
1 out of 45
times
1 out of 43