When to buy a lottery ticket

For the past ten years or so someone I know has been dutifully buying lottery tickets. His return on investment so far has been at most 25 cents to the Dollar. This is how I tried to explain to him that lotteries are a sucker’s bet. “Look,” I said, “I’ll give you a much better deal than any lottery. Just give me $10 every week and I will return $5 of it to you.” But he remains unconvinced, and it’s not because he’s math challenged. He points out correctly that in some cases a $1 lottery ticket is worth more than $1. How does this come about? It happens when there are more Dollars in the pot than there are players. So if 1000 players each buy a one Dollar lottery ticket and the jackpot is,say, $2,000 then that $1 lottery ticket is worth $2.  But how can 1000 players putting in a Dollar each make a $2000 jackpot? It can’t, but if there’s money left over in the pot from previous no-winner lottery purchases the money piles up. In fact it happened in yesterday’s $640 million drawing in the U.S. “Mega Million” lottery.

There are quite a few flaws in this argument. The most fundamental one being that the expected return is more than the lottery ticket price only if you haven’t been buying lottery tickets in the no-winner rounds. In the simple example above, if there were, say, 3 previous no-winner rounds then a consistent player has already paid $3 into the pot–his lottery ticket price is effectively $4 ($3 losing tickets + $1 for the latest round).  One other flaw is specific to the rules of each lottery. For example, if the prize is to be split between 3 winners then the jackpot is effectively cut to 1/3 as far as each individual player is concerned (quiz: where is the weakness in my own logic on this point?). The rest of the flaws have to do with taxes and such. Bottom line, economics 101 tells you not to get into the lottery game.

But life isn’t all about basic economics.  For many, a Dollar is a smal price to pay for the thrill of hope and the incentive to daydream about a life of luxury. Consider it part of your entertainment budget. Also lotteries are a way of  raising funds for big projects. A million Dollars in one pile can do a million times more than a million separate Dollars buying random things (taking some artistic licence here). As I said, economics 101 tells you not to buy lottery tickets,  however advanced economics may have a different answer. If the lottery authorities use the money for worthwhile projects that wouldn’t be possible otherwise then there are benefits to the public and therefore ultimately to the individual. For example, the tomb of Ferdowsi in Toos was built with funds from a national lottery held in Iran in 1934. Above photo is of one of these historic lottery tickets discovered in the Golestan Palace archives. It may even be the winning ticket–not sure.

Have a lucky sizdeh bedar.




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