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

If you buy 1 ticket you have a 1 in 14,000,000 chance of winning
If you buy 2 tickets you have a 2 in 14,000,000 change of winning
This is not the same as 1 in 7,000,000

I am so confused, dow this work or not?

I believe that 2 chances in 14,000,000 are indeed mathmatically equivalent to 1 chance in 7,000,000.


However, now I'm straining my brain to see how this method improves ones chances at all. ok:

Overall chances per life time weekly method
(1 in 14,000,000) per week times 2500 weeks = 2500 in 14,000,000* = 1 in 5200

Overall chances per life time one glorious shot method
(2500 in 14,000,000) per week time one week = 2500 in 14,000,000 = 1 in 5200

(*the pool of possible numbers doesn't change weekly, unless they do to your lotto what they did to ours and increase the number of numbers because, get this, "there were too many winners" )


I agree with the conclusion that if you are 'going' to win it will most likely(1 in 2500 chance if you are destined to win it will be on the first week) move the date up to an early time in your life. But I don't see how it changes the overall lifetime odds a bit.

I could be wrong, I'm sure a pedantic finite mathmatician will be along soon to sort this out for us.

From what I remember from statisical analysis the chances remain at 1 chance in 14,000,000 for each ticket and the number of tickets you buy does not change that. Since you only can only win from one ticket, 1 in 14,000,000 are your odds. Your *opportunities* to win at those odds are increased with every ticket but your odds do not change.

Such is life.

True the chances per drawing don't change, but that is why I stated it as overall chances per lifetime....

The more I think about this the more confusing it gets...


:::::::::::::::::::::::thinks out loud:::::::::::::::::::::::


Does that 14,000,000 remain the same over 2500 drawings?...
True: each drawing will have odds of 1 in 14,000,000
but are 2500 1 in 14,000,000 chances the same as 2500 chances in 14,000,000?

I don't think it is exactly...

When you buy 2500 tickets (assuming they all have different number combinations of course) you are 'reserving' all those different combos. In other words you are taking them out of the possible losing combo category. But with the one ticket per week mode there are always 13,999,999 losing combos to one winning one... But of course this is still comparing the chances of one ticket to 2500.

Ok... lets try it from a different angle.. the coin toss.

Everyone knows that even if you have flipped a coin heads up 2499 times in a row the next flip still has a 1 in 2 chance of coming up heads.

However what are the chances of flipping a coin 2500 times heads up? Or,to put it another way, what are the chances of getting at least *1* tails in 2500 flips...[Rosencrantz?...Guildenstern?] "Pretty flippin' good" I should think!!! But by my maths above (which I now think has some flaw) that would be 2500 chances in 2. Which doesn't sound possible...


... Hey, I think that is correct!... It just doesn't 'sound' right. Which means that either way for the lottery, you have 2500 chances in 14,000,000!


Ok... Where's the maths to double check my work?

Every ticket you buy has a 1 in 14 million chance, so if you buy 2500 tickets you get 2500 in 14 million chances, this holds whether you buy them all in one week or whether you buy them over your lifetime, so long as all the tickets you buy in one draw are different. However, if you buy all the tickets in one go, you eliminate the possibility of more than one win, so you increase your chances of winning exactly one time. I don't think you actually alter your chances of holding a winning ticket.

How do you calculate that you have a 1 in 14 million chance of winning, i.e. all 6 of your balls being drawn out of 49? I make the odds a lot longer than this.

(49*48*47*46*45*44=10,068,347,520)

Nephew Who running in double precision mode

I am a nomath either.
First I would like to know what the prizes are say:
1 prize of 1000000,
10 prizes of 10000,
100 prizes of 100 and
1000 prizes of 1 (== 1 ticket)
One ticket each quik for 1111 prizes out of the 14000000 makes 1 out of some 12600 for any prize but this is for any of the prizes.

Doing this 2500 times gives chances of
2500 out of 14000000 = 1 out of 5600 for a 1000000 prize (~178.57)
2500 out of 1400000 == 1 out of 560 for a 10000 prize (~17.857)
2500 out of 140000 === 1 out of 56 for a 100 prize (~1.7857)
2500 out of 14000 ==== 1 out of 5.6 for a 1 prize (~0.17857)
This will learn us you will totally win an average of 198.39 ticket.
But there is a minute chance of winning 2 500 000 000 in total.
(1 out of 35 000 000 000)


Buying 2500 tickets at once increases the average win
2500 out of 13998890 = 1 out of 5599 for the 1000000 prize (~178.60)
2500 out of 1399889 == 1 out of 559.9 for a 10000 prize (~17.860)
2500 out of 139988 === 1 out of 55.99 for a 100 prize (~1.7860)
2500 out of 13998 ==== 1 out of 5.599 for a 1 prize (~0.17860)
This will learn us you will totally win an average of 198.43 ticket.
There is a little chance of winning 1 111 000 in total
(1 out of 15 554 000 000)

Like in the entry noted >-You loose-< , about 2300.

Wasn't it one of those *only one winner* type lotteries? Their the most common here and it makes the odds/chances a lot easier to calculate.

Sorry, forgot to change the title.

Traveller in Time on his head
"Well that just reduces the difference to about, well actually very closely, no it is: Zero, then there is no gain for all investment at once, just a tiny chance against a minute chance.

Anyway the entry states 'a few minor prizes', as if there are more. But like many entries this one does not provide much background information about the topic."

I assumed (no ass/you/me jokes!) that it was referring to a number of lotteries, thus the plural.

The principle applies to all lotteries. Just the odds may change. I still disagree with the entry's idea that this somehow 'improves' the odds, however slightly. I'm still waiting for that maths to settle this.

Although you are correct in your assumption that "combinations" are based upon factoral mathematics... your maths is a tad wrong. The way to work out the odds of winning the main prize in the lottery is done thus: 49! / (6! x 43!)

That is to say: Factoral 49 (the total number of balls in the lottery) divided by ( Factoral 6 (the number of balls you need to win the main prize) multiplied by Factoral 43 (the number of balls remaining in the hopper)) which equates to 13,983,816 (a gnat's whisker short of 14 million).

In Football Perms (perm is used incorrectly - they should be called combinations) a popular bet is 8 from 10 which gives us 10! / (2! x 8!) which is 3,628,800 / ( 2 x 40,320) = 3,628,800 / 80,640 = 45 lines

Thanks, it is a long time since I studied statistics.

It must be true though, that if you buy a lot of tickets for one lottery, instead of one a week over numerable lotteries, that you have a better chance of winning (though still very small), because you are narrowing the odds with every ticket you buy against a rigid set of numbers.

Noooooooooo! Every ticket has the same odds as the last (or next). You may have more oportunities to win but the odds stay the same.

If it was a roulette wheel with 14 million possible outcomes-

A very big roulette wheel.

Would it be better to stake all your money on several thousand squares, or have several thousand goes and just cover one square each time?

Several thousand squares would have *individually* the same chance. Having several thousand squares would increase your chances of winning but not your odds.

I am sorry, but I think several bookmakers would argue with you about that one!

It may just be pedantics, but there is a difference between *chance* and *odds*, you must see that?