Lotteries have been with us for most of recorded human history, dating back at least to the Han Dynasty in China, when proceeds may have helped finance the Great Wall. They were also present at the very start of this country, when King James created a lottery to raise money for the new settlement at Jamestown, Va., in 1612. The dream of drawing a lucky number still has an allure: About half of Americans said in a 2016 Gallup poll that they’d bought a state lottery ticket within the past year. Many myths surround these games of chance — and their winners and losers.

Myth No. 1

Playing makes economic sense when the jackpots get big.

It seems intuitive: The higher the potential winnings, the more sense it makes to spend a few dollars to try your luck. Writers in outlets from Forbes to Money.com have claimed that when the Powerball winnings reach a certain threshold, the expected value — the payout times the probability of winning — exceeds the price of the ticket.