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

I think we need to step back and look at this from another angle. The odds on a ticket winning the lottery is 14 million to 1. If you buy 1000 tickets. each of them will have exactly the same winning chance as each other ie 14 million to 1.

In order to better our odds we need to be selective in how we choose our numbers. that is to say... there are 14 million different ways to pick a set of 6 numbers, in order to better our chances we need to lower these odds by picking DIFFERENT SETS OF NUMBERS from the pool of the 14 million available. If we had 14 million pounds to throw away we could go through every set - ie 1,2,3,4,5,6 1,2,3,4,5,7 1,2,3,4,5,8 all the way through to 44,45,46,47,48,49.

With a bit of thought behind our selections though we can drastically reduce the odds (though not drastically enough to make it a viable option). It is possible to guarantee for instance that we get at least 2 correct numbers for as little as £167 which is a little to expensive for my taste as we still haven't got close to guaranteeing a return of a tener, let alone the jackpot.

I think I will stick to the quid a week approach myself....

I would hate to be the person working on the fag counter when somebody decided to buy their lifetimes supply of tickets in one go. Or someone in the queue behind them!

I remember a few years ago a consortium of players tried to 'corner the market' on a lottery in New England. Each of the members invested something like $20,000. They made arrangements with a several stores in the area to process no other tickets but theirs. They were going to buy every combination. They had to wait for a jackpot of over $50 million to make this worthwhile. Unfortunately a couple of the lottery machines they had reserved went down whilst they were running their tickets through and therefore they did NOT get all the numbers...

Luckily they did get the winning number. I believe they also made several million from the partial winning combos as well.

Now most of the lotteries here in the states have either increased the number of balls to 54 or added a 'powerball' that increases the number of permutations to too many to make this feasible.

Here I am!

So, we're all a bit confused, and I think it has a lot to do with words. Damn words, always mix up good maths.

Instead of using chances, think about the probability of winning:

If you buy a ticket this week in a lottery that has a possible 14 million numbers, you buy one "chance" in 14 million. this is right.
Your probability of winning this week is hence: 1/(14 000 000)

If you do this next week, you will have the same probability of winning, 1/(14 000 000).

Say we consider what happens over the two weeks: I bought two tickets, both with probability of 1/14 million for a win. The probability I win this week OR next week is now 2/14 million, which does indeed come to 1/7 000 000.

Following this reasoning, if we do this every week for 2 500 weeks, our probability of winning this week OR next week OR the week after 0R...OR in our last week of playing is now (2 500)/(14 000 000) which simplifies to a 1/5 600 probability of winning at least once.

If we buy all the tickets in the same week, we will 2500 of the possible 14 000 000 possible tickets, so our probability of winning is also 2 500/14 000 000, exactly the same.

This method does not improve your "chances" of winning over your lifetime, it just improves your "chance" of winning this week compared to the guy who only bought one ticket this week.

You are exactly right, Count! (Ha ha ha...)

There isn't really a way of improving your chances of winning the lottery if you play week by week, it is a random sample (that's what makes it fair!). So every combination of numbers is equally likely, therefore each single ticket has the same "chance" of winning. The only way you will be more "likely" (have a greater probability) to have the winning ticket is to buy more of them. That's where the trap lies, and that is why mathematicians prefer counting cards at blackjack to playing the lottery...

Basically, in any random process (cards, lottery, raffles, roulette) the only way to improve your chances is to cheat.

Here in WA we have a lottery based on drawing a ball each from 10, three times (so we have 000, 001, 002, ..., 999 as possible tickets). It only costs 50 cents to enter, and the prize is 500 dollars. So if you bought every ticket, you could technically break even -- but only if they give each winner the full prize. That is a drawback of the 'one golden draw' method above. You might win, but you might have to share with another person who only spent 1 pound, where you spent 2500.

Hope things are clearer (sorry about the long post)

Ami of zx (maths )

Our "pick three" lotto costs a dollar to win five hundred!

Not pedantic at all "odds" I think are calculated by bookies based upon the "chance" they think you have of winning a particular bet.
As to the chance of winning a lottery with 2500 tickets surely its still 1/1400000 per ticket. You would have to have a different combination of numbers per ticket so 2500 combinations of six numbers. You may win a 5 ball ticket or lesser prizes thus getting all the "lifetime" winnings in one go so saveing the wait, but your "chances" per ticket are no better. You may get better odds as you have more chances of winning the big one.
Or am I just confused?

I dunno. I still think you can narrow down your chances of losing by putting all your money on the same lottery.

e.g. £14,000,0000 staked = guaranteed win but loss
£7,000,000 staked = 50/50 chance but still a loss
3,500,000 = 1 in 4 . . . . . . .

. . . . and down to £1 = 1 in 14,000,000

So it logically follows that you narrow the odds in one given draw by doing more combinations of numbers, whereas if you do one set of numbers every week, your chance of winning is always 14,000,000 to one in each draw.

Consider this. If you stake £13,999,999 you still have a chance to lose, right? That's because the remaining £1 stake has just as many chances of winning as the rest of the bets. Equal chances but increased odds, right? At least that's the way I see it.

I would say you would have a good chance of winning, as the odds of losing would be 1 in 14,000,000.

Its like this, i think, if you live to be 14 million weeks old and you pay for it all in one week then your guaranteed to win once without spending any more money. If you live less then your chances are less then guaranteed but still more then if you just pay once a week

also chances are when you compare the numbers of ways an event can happen to the total number of events. Odds are when you compare the number of ways an event can happen to the number of ways an event cant happen.like if your chances of winning a horse race are 1/5 then your odds are 1:4

As a life long lotto player, here's my two cents worth.

First of all, let's make the numbers simple. let's pretend there are ten numbers in the lottery and you have to pick the right one.

Each week, your chances of winning are 1 in 10.

If you bet two weeks in a row your chances of winning are still one in ten, because regardless of what number wins the first week, every number has the same chance of winning the second week.
(e.g if you bet number 1 in week one and it doesn't win, it has no better chance of winning in week two - you cannot be guaranteed to win if you bet number one ten weeks in a row).

However if you bet two numbers in the first week then your chances of winning in the first week are 2 in 10 , or 1 in 5. (Your chances of winning the second week are zero.)

If you bet all ten numbers then your chances of winning are 10 in 10, or certain (of course you might win less money than the bet cost, but that's another matter).

So it is certainly true that the more tickets you bet in a given week, the better your chances.

Now lets look at a real lottery, where there are more than ten numbers in the draw and to win you need to pick more than one correct number to win a prize.
Let's use the NSW lottery as an example (and let's forget about supplementary numbers for now)
There are 45 numbers, and if you pick 6 , 5 or 4 you win a prize.

If you make one bet each week, your chance of getting all six numbers is about 1 in 8 million (actually it's 1 in 8,145,060)

If you were to bet every week for 40 years, thats roughly 2000 bets, so if instead you were to put on 2000 bets in week one, your chance of winning that week would be roughly 1 in 4000.

As an added advantage, in the NSW lottery, if you can risk more money on a given week, you can reduce the cost of the bet (since each entry is subject to a 10 cent handling fee for the agent) - as an example, if you made 2000 bets all at once, you could enter about 110 "system 18" entries, so would save about 19 dollars in handling fees. Also by making more entries in a given week you increase your chances of winning "minor dividends" over making one entry each week.

In your simple example of a 1 in 10 chance of winning though, you still have a chance of multipe wins if you buy over multiple weeks instead of buying all the tickets in one go.

My calculations, literally on the back of an envelope and generated with the aid of a head cold suggest that if you buy one ticket for each of ten weeks your chances of winning n times p(n) are:
p(0) 0.348
p(1) 0.387
p(2) 0.193
p(3) 0.057
p(4) 0.011
p(any thing else) pretty small.

So, even in the simplified example you trade off the certainty of a single win in ten tickets for one weeek against the chance (about 0.265) of winning more than once with the risk (0.348) of not winning at all over ten weeks for the same outlay. The most likely single outcome though remains that of a single win (0.387).

Let's face it, if you buy one of every ticket in one week, it isn't a lottery any more.

To answer the orginal question, do you have a better chance of winning the lottery if you play all your tickets in one week rather than one ticket every week.
Here goes. Take your simple example of 10 balls where we pick 1 ball, and there is 1 winning ball
Odds of winning = 1/10 as we all know
If we look at playing this game 4 times in but with two methods

Method (i) We will pick 4 balls in week one
Method (ii) We will pick one ball a week for 4 weeks

Odss of method (i) are easy to work out, we obviously have a 4/10 chance of winnning or 0.4.

Method (ii) requires a bit more thought! P=Probability

P(winning) = P(win once) + P(win twice) + P(win 3 times) + P(win fours times)

This is complicated to work out. It's a lot easier to work out the probability we dont win, which for any given week is 9/10 0r 0.9
Therfore P(losing 4 weeks in a row)= 0.9 x 0.9 x 0.9 0.9 = 0.6561
And hence P(winning) = 1-P(losing 4 weeks in a row)
= 1-0.6561
= 0.3439

We can see have a better chance of winning if we put all our money on at the same time.

If my maths are wrong please tell me

If this theory was accurate which it isn,t and buying a second ticket would half the odds then you would only require to spend £50 to have an almost certain win as reducing 14,000,000 by half becomes 2 as in 2/1 odds within 23 conversions.
The odds are always 14000000/1 all you have done is purchase 2 chances at 14000000/1

I still say that if you flip a coin 100 times and it's tails every time that the chance of tails for the 101st is still 50 / 50.

No, sorry, geomac. You don't halve your odds of winning EVERY time you buy a ticket, just the first time. If you were to buy a third ticket, the odds would be 3 in 14,000,000. And so on. You could knock a nought off by buying ten tickets as 10 in 14,000,000 is equal to 1 in 1,400,000. Still pretty bad odds though. Even if you bought 7 million tickets, you would only have a 1 in 2 chance of winning.

Sorry to harp on. If you buy one lottery ticket a week, you're never going to increase the odds. I was reading the backlog and I read a post about that. You can't halve the odds by buying 2 tickets in 2 different lotteries. The odds would be 2 in 28,000,000 which is the same as the odds of you winning one lottery.

If you bought 50 grands worth of tickets in one lottery (I'm just focusing on winning the big money here, no smaller prizes) I calculate the odds of winning at 280 to 1. That's some crazy bet.

If you have enough money when you are still young to get substantially improved odds of winning the lottery, you shouldn't even contemplate it. Buy some ISA's or go on a fantastic holiday or something. The lottery operators don't need your money. I do. Send it to me.

It bears repeating, "I guess I think of lotteries as a tax on the mathematically challenged." - Roger Jones

Um, no. If you buy one ticket in two lotteries, you almost double your chances of a single win since there is a 1 in 14m chance each time. The difference in buying tickets in multiple lotteries, as opposed to multiple tickets in a single lottery, is that you increase your chances of multiple wins (at the expense of marginally reducing your chance of any single win).