Lottery Odds

[phl666]

If the chances of winning the Lottery are 14 million to 1, does that mean that if I bought two tickets, the odds are 14 million to 2 (i.e. 7 million to 1)?

[Guinevere]

Many years have passed since I learnt about probability at school.  But the idea is that an event's result does not have any effect on the next event's result.
For example:
You can toss a coin 50 times and each time it could fall heads up.  The chances of it falling heads up the next time are still 50/50.  You could toss a coin 5 million times and each time it could land heads up.  The 5-million-and-1st time you toss the coin, the chances of it falling heads up is still 50/50. 
It will even itself out eventually but this could take an eternity.
So, your 1st lottery ticket has a 1 in 14 million chance of winning.  If it loses it has no effect on the odds of your next ticket which still has a 1 in 14 million chance of winning.
I'm pretty sure this is correct.  Basically the odds on winning the lottery suck!

[Loosehead]

You are not comparing like with like Guinevere. You are correct with individual events so the chance of rolling a 6 is 1 in 6, if you roll again the chance of rolling a 6 is still 1 in 6. So if you have 1 possible set of 14m possible outcomes then yes this time you have 1 in 14m and the same next time etc. Now back to the dice, if you want to roll a 6 or a 3 then you have a 2 in 6 chance, so moving to the lottery again, if you have 2 sets of a possible 14m then you have a 2 in 14m chance ie 1in 7m.

[landie]

It's pretty obvious to me that, the more tickets you buy the greater are your chances of winning.

If 14 million tickets are normally sold you would need to purchase a further 14 million yourself to have a 50% chance of a share of the jackpot. Assuming that the 14 million regulars still buy the same amount.

You would need to purchase 28 million tickets to have a 66.6% chance (you would hold 28 out of 42 million tickets) On the other hand there may be no matching tickets out of the entire 42 million.

[twiglet4frog]

i suggested earlier about the percentage thing and was criticised (in a nice way admittedly) that i had it wrong because of the number of winners. but can i point out the QUESTION that was asked was the chances of WINNING and doesnt say anything about the chances of winning the WHOLE jackpot or the amount won, so effectivly the number of winners is regardless in the question asked as it is only asking the chance of actually winning (single or shared) and whether u are the only one or there are 100 winners u are still a winner

[*mystical*]

If we are talking about lottery in ''the real world'' can you really put odds on it? there are other things to concider such as luck!!!

[jean88]

There are endless probabilties. Have any of you seen the movie BRUCE ALMIGHTY, how would this affects it.....!!??

[Bangkok]

wowo, your extrapolation goes a little wrong, as the pattern is not halving the odds each time, it is 14,000,000 divided n+1, where n is the previous number in the sequence.  So it would be....

1 Ticket = 1 in 14 Million
2 Tickets = 1 in 7 Million
3 Tickets = 1 in 4,666,666
4 Tickets = 1 in 3,500,000
5 Tickets = 1 in 2,800,000
6 Tickets = 1 in 2,333,333

 

The absolute reduction in the odds decreases over time, so the difference to the odds of buying 1 or 2 tickets is far greater that 100 or 101.

[chazza]

Landie thats wrong.

 

The 14 million refers to the number of combinations, not the number of people buying tickets.

 

If only 1 person in the UK bought a ticket, they would still only have a 1 in 14m chance of winning, as that is the probability of choosing the correct numbers.  No matter how many people enter the lottery, your chances of winning with one ticket are always the same.

[Royal Pollen]

Thats right Chazza

1    is    1 in 14,000,000

2    is    1 in 7,000,000

3    is    1 in 4,666,666 not 1 in 3,500,000 as Wo Wo claimed

To half the odds and double your chances of winning you have to buy twice the amount of tickets each time

Like i said

4 tickets is     1  in    3,500,000

8 is                1    in 1,750,000

16    is            1    in    875,000

23 Tickets only gives you a  1   in 608,695 chance of winning

32    is    437,500..........and on and on   7,000,000 million tickets give a 1 in 2 chance of winning so long as all your tickets are unique

[Royal Pollen]

Look, Wo Wo thinks that 23 tickets gaurentees you a win. If that was the case why dont we all go spend �23 on Sat or whenever they run it nowadays and all be Multi-Milionaires???????

The reason is that it 23 doesn't but 14,000,000 tickts does as 7,000,000 gives you a 1 in 2 chance or 50% or a very bad investment as the Lottery only pays out a fraction of the money it takes in.

[landie]

chazza, I based my assumption on the normal prize fund. It is a good indication of how many tickets have been sold.

[Octavius]

You have one chance in 13,983,816 of holding the winning ticket. This probability is 0.0000000715
The more tickets you buy, the greater your chance of winning, of course.

Suppose you buy 50 tickets (which will cost you �50). Your chances of winning go up ...they're now a whopping 50 out of 13,983,816, for a probability of 0.000003575 (not much of an improvement!)

The probability of matching NONE of the six numbers is about 46.3% this means about half the time, NONE of your numbers will match!

Similarly, the probability of matching ONE of the six numbers works out to be 0.413, or 41.3% ... this is the probability of matching ONE number.

The probability of matching TWO of the six numbers works out to be 0.132, or 13.2% ... this is the probability of matching TWO numbers.

None of these results pay anything at all. If you add the three probabilities, you get 98.1%.  This means that 98% of the time, you won't win anything!

The first winning ticket is the one where you match THREE numbers. The probability of this occurring (using the method above once again) turns out to be 0.018, or 1.8%, or about 2 out of 100, or about 1 out of 50. This means you must spend about �50 on average, to hope to win the �10.

Are you beginning to get the picture? Your chances of winning the big prize are next to nothing, and the chances of winning even �10 are only one in fifty.
Yet people win all the time, of course, because millions of tickets are sold every week, and somebody has to win the prizes. It's just not very likely that it will be any one person in particular (ie: you!)

[kempie]

"... and somebody has to win the prizes."

Not if everyone selects non-winning numbers.

[chazza]

But landie you say that if you buy 28 million tickets you have a 66.6% chance of winning.

 

If there are only 14 million possibilities then surely if you buy anything over 14m tickets (with different numbers)  you have a 100% chance of winning as you have every combination of winning.

 

Thats where your theory falls down!

[Octavius]

Yes, and you would have spent �14m to win (possibly a share as others might have duplicated your winning line) in an average of about �4.5m 

[Octavius]

Yes, and you would have spent �14m to win (possibly a share as others might have duplicated your winning line) in an average of about �4.5m, but at least you have won .... haven't you....?  Or have you lost (more than �10m)..? 

[kempie]

It appears I must reiterate a point I made at the beginning of this thread.

landie is confusing a lotto with a lottery. The prize under discussion is a lotto.

[landie]

Kempie, I refer you to the question 'as asked'.

[kempie]

... which states "14 million to 1", a figure which relates to The National Lottery game of Lotto.

[landie]

Which also uses the word 'lottery' You could sell 60 million tickets and not get a match.