The Debate: The more you play the Lottery the more likely you are to lose

Buying more lottery tickets is a sure-fire way of losing more money, and philosophically speaking, it doesn’t even increase your chances of winning.

Think of it this way. If you have two tickets in your hand, which one is more likely to win? Neither, right? They both stand the same chance. And just because you have two tickets in your hand it doesn’t increase the likelihood that one of them will win, it just means you paid out (or lost) twice as much.

Yet conventional wisdom dictates that whenever a jackpot swells above a certain life-changing amount we should increase the number of tickets we buy in order to be in with a better chance of winning. Office whip-arounds are set up, syndications are born, and we all take turns to sneak out of the office and buy five times as many tickets as we would do on any other occasion.

And with jackpots becoming increasingly monstrous the instances of this happening appear to be going up. According to one news report high-earners in Canary Wharf have taken to bulk-buying lottery tickets whenever the jackpot gets above £70m to £80m in the EuroMillions, with local shops forced to take on extra staff to cover the surge in demand. Peter Wagg, owner of the News of the Wharf store, told the Financial Times that one City worker bought £15,000 worth of “lucky dips” tickets on one occasion and paid in bundles of £50 notes. No news of a jackpot winner was reported in the area after the draw.

Surprising, you may think, yet had the same man stood outside the shop and flipped a coin 15,000 times would you expect the fact that he is tossing it so many times to alter the result? Of course not, but that is the very reason people crowd around roulette tables at a weekend convincing themselves that after landing on black five times the ball must surely now land on red. It might, it might not. It has a 50/50 chance. And that doesn’t alter whether it is the first spin or the 5,000th.

As anyone who has ever set foot into a philosophy class will know, the probability of something occurring does not increase as you use it. The mathematicians will no doubt scoff, but there is reason to believe that. My brother put it to me recently that he doesn’t know anyone who has won the lottery, nor does he know anyone who knows anyone, but he still chips in for his work’s syndicate, which flies in the face of his realisation that more does not necessarily equal more likely. So why do we do it?

Well, there are some grounds to believe that your odds of winning go up the more tickets you buy, but you should be careful which theory to believe. For example, the notion that if you buy one ticket you have a 1 in 45,057,474 chance of winning and if you buy two tickets you have a 2 in 45,057,474 chance of winning is just crude mathematics, because if two variables are independent you can’t sum the probability. Math that can be used to determine your odds of winning  a raffle (where all prizes must go) can not be used to determine your odds of winning the lottery (where there does not have to be a winner).

You might, however, want to look into theories around binomial distribution, but you will find that not only is the theory seriously complex, its findings also show that while you are more likely to win at least once by playing more, you’re also expected to have lost more money, which is a factor people often neglect to account for.

So in summary, think twice before buying more than one lottery ticket. Or perhaps just think once. But know the more you buy the more likely you are to lose.

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2 Responses

  1. David

    Cutting edge stuff 🙂

    There is not, however, a more certain proposition in mathematics, than that the more tickets you adventure upon, the more likely you are to be a loser. Adventure upon all the tickets in the lottery, and you lose for certain; and the greater the number of your tickets the nearer you approach to this certainty

    Adam Smith, in, er, 1776.

    But there’s a great chapter in the brilliant “How Not To Be Wrong” by Jordan Ellenberg about how it can work if the lottery people screw up.

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