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?
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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.
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