President Donald Trump’s second impeachment begins Wednesday for his role in inciting an insurrection at the Capitol on Jan. 6, adding another ignominious stain to his legacy for historians to parse.
But another bit of the Trump legacy is on display this week as well, as the country’s two biggest lotteries swell to $550 million for Powerball and $750 million for Mega Millions, which draw on Wednesday and Friday, respectively.
Because of Trump, lottery math has changed, making a lower jackpot more mathematically advantageous and more attractive to play.
First, a little bit of background.
Math nerds often like to study lotteries and sweepstakes, and occasionally have figured out how to game them. But one element that has accompanied the conversation has been the expected value of a lottery ticket: what a $2 ticket is actually worth.
A $2 ticket is usually worth far less than $2, since its odds of winning (and being sole winner) multiplied by payoff is well under $2. (This number is called “expected value.”)
But since the pot rises over time as lottery players don’t win, a large enough jackpot theoretically means that a $2 ticket might end up being worth more than its price. This makes people perk up whenever the jackpot swells, as the implicit (“expected”) value of the ticket gets closer to its $2 sticker price.
In a simplified, tax-free example, a $2 ticket might have a 1 in 300 million chance of winning. So if you could theoretically buy every ticket out there, you’d come out ahead if the jackpot was worth more than $600 million. (It’s not this simple, because there are other prizes and jackpots with other payouts, but it’ll work.)
However, taxes complicate the calculations: if you win, you’re not actually going to walk away with $600 million because the IRS takes some of that jackpot, which changes the cutoff point for when a ticket is worth more than its $2 price tag.
Before Trump, when the top-tier tax bracket was 38.6%, the breakeven point was around $2.3 billion. The Trump administration’s 2017 tax cuts have rejiggered the breakeven calculation. The new top tax rate of 37% has moved the expected value down $200 million. And the number for a complete breakeven would fall to around $2.1 billion.
That number is huge, but getting to $2.1 billion from $550 million or $750 million doesn’t take that many weeks given that high jackpots attract more players. If no one wins, it’s not out of the question.
A lottery ticket’s value, however, also changes based on whether someone else picks the number. If you and your friend choose the same number, you’re effectively lowering the value because any jackpot would have to be split. That’s why choosing numbers that are less attractive (no birthdays, no “good looking” patterns) are a good move, since any series of numbers has the same mathematical probability as “1, 2, 3, 4, 5, 6.”