I mentioned to a colleague that I’d bought two lottery tickets for last weeks Euromillions draw instead of my usual 1 to double my chance at winning. He said “Yeah, that’s not how it works.” I’m sure he is right – but why?
In: 7847
There are almost 14million combinations for the lottery so the odds of the jackpot for 1 and 2 tickets is;
1/14000000
2/14000000 = 1/7000000
The odds are halved with a second ticket so you were right originally
Well, your coworker gets it wrong. Every combination of numbers has the same chance of winning. So if you’ve got 2 tickets instead of 1, your chance of winning is 2/x and not 1/x, which is in fact a doubling of your chances.
Even if those tickets are for 1,2,3,4,5,6 and 1,2,3,4,5,7, or 1,2,3,4,5,6 or 10,11,12,13,14,15, doesn’t matter.
[removed]
You can buy as many lottery tickets as you want, and you’ll multiply your chances to win by as many. This is exactly how it works and your friend is wrong.
The problem, however, is that the tickets are not free, and the odds are not in your favor.
The theoretical “worth” of a ticket is the amount it can potentially win you, multiplied by the chance to win. If every ticket gives you 1% chance of winning a 100€ prize, then the theoretical worth of the ticket is 1€. (This is simplified; statistics are a complex field, and the devil is in the details of how the lottery works. But that’s the general idea.)
In order for a lottery to be viable for organizers, tickets are sold for more than their theoretical worth. A ticket giving you 1% chance of winning a 100€ prize would be sold for 2€ or 3€, or more. So when you buy one, you pay more than you “should”. If you bought *all* the tickets in the lottery, you would absolutely win the grand prize, but you would still lose money.
Buying a lottery ticket is saying “I am playing against the odds. I am buying a very small chance at winning a large sum of money. I am paying too much for that chance, but I’m willing to pay it because it’s fun, it’s not that expensive, and if I get extremely lucky I could win big.” You’re really paying for the thrill of the draw; but if we take that out of the equation, you’re making a bad deal, and the lottery is taking advantage of you.
So if you buy *two* lottery tickets, you’re making a bad deal *twice*. The lottery will have no quarrel with you. It is up to you to decide whether the excitement of having twice as much chances of winning, no matter how small these chances are in the first place, is worth the price of the extra ticket.
A single ticket has one chance in 139,838,160 to win. Two different number choices indeed double your chance, to one in 69,919,080. So, by purchasing your second ticket, you’ve gone from the chance that you’d be hit by lightning _fourteen_ times, to a paltry _seven._
you are definitely correct.
Each ticket / number / combination… has the same chance of being the winning ticket. Buying 2 means you have twice that chance.
Of course, this is assuming that you are not blind picking the tickets, i.e. the 2 tickets bought have different numbers.
It could be that your colleague was referring to the fact that since the chance of winning is so so low (0.00000…%), doubling that has little to no effect
Imagine that instead of millions of numbers, the lottery just had you pick from 3: 1, 2, and 3. If you bought a ticket with the number 1, you chances would be 1/3. If you bought 1 and 2, you’d have two out of the three, so your odds are 2/3; that’s double 1/3 and you’ve doubled your chances of winning.
But that’s too easy to win, so they add a fourth number. You buy 1, and your chances are 1/4; buy 2, and your chances are 2/4. 2/4 is still 2 times 1/4, so your odds of winning are doubled are by getting 2 tickets, even if your overall off are lower (2/4 instead of 2/3).
In fact, you can increase the size to any number of possibilities, N, and 2/N will always be twice as big as 1/N.
[removed]
If you try to guess which number i am thinking of in a 1..10 range and say 1 number it’s a 1/10 chance. If you say 2 different numbers it’s a 2/10 chance which has a better chance to be correct ( in this case, twice as likely)
He’s wrong, you are right. As long as the entries on each ticket are unique.
If the lottery was drawing a single number between 1 and 10, and each ticket lets you pick 1 number.
1 ticket would give you a 1 in 10 chances of winning.
2 unique tickets would give you 2 in 10 chances of winning.
Wow, some of the examples others have used are ridiculously complicated…and wrong, lol!
Latest Answers