# The Math Behind James Holzhauer’s Streak-Ending Final Jeopardy! Wager

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Monday’s Jeopardy! game was destined to be exciting. James Holzhauer, who had become famous for winning by enormous margins, was within \$60,000 of reaching the all-time winnings record.

But it wasn’t to be. Holzhauer lost both the game and his chance to take over the \$2.52 million record set by Jeopardy! legend Ken Jennings in 2004.

At a glance, Holzhauer seemed to stray from his big money strategy in the final round. He uncharacteristically wagered just \$1,399. Up to that point, his final wager for his previous 32 games averaged nearly \$29,000.

Even host Alex Trebek was clearly surprised. “A modest one for the first time,” he remarked, as Holzhauer revealed the amount.

Why put up so little? To throw the game in deference to Jennings? Or to use a number that had personal significance, just as he had previously wagered family members’ birthdays and other important dates?

No. The \$1,399 wager was specific and deliberate because, mathematically, it was his best play.

Despite a strong start, Holzhauer failed to land on either of the two Daily Doubles in the second round. Daily Doubles are key to his strategy, allowing him to make big bets and pull ahead of the other contestants. This time, competitor Emma Boettcher found those Daily Doubles, wagered aggressively, and took first place.

As Trebek revealed the final Jeopardy! question, the standings were Boettcher at \$26,600, Holzhauer at \$23,400 and third contestant Jay Sexton at \$11,000.

Imagine that Holzhauer wagered everything. A correct response would have put him at \$46,800. So Boettcher sensibly put \$20,201 on the line, ensuring that if she answered correctly, she would win with \$46,801.

On the other hand, if Holzhauer wagered it all and responded incorrectly, he would be left with nothing. If Boettcher were incorrect, she would still have \$6,399.

So Holzhauer had no chance to win against Boettcher unless she answered incorrectly and he had wagered only a small amount, to keep his total north of \$6,399.

To determine how much that small amount should optimally be, Holzhauer need to ensure that third-place Sexton, with \$11,000, could not come out ahead if he doubled his score to \$22,000. Holzhauer could wager \$1,399 of his \$23,400 and, if he flubbed, still beat Sexton by \$1.

In the end, all three contestants responded correctly. Sexton wagered \$6,000 for a third place finish of \$17,000. Holzhauer took second with \$24,799. As runners up, they will only take home \$1,000 and \$2,000, respectively.

Boettcher’s win seemed to shock the typically unflappable host. “Oh gosh!” Trebek exclaimed, as he declared Boettcher the new champion. “What a payday—\$46,801. What a game! Oh my gosh!”

As Trebek signed off the game, Holzhauer walked over to Boettcher to give her a high five. As a professional sports gambler, he had consistently proven that he had the guts and the math chops to always make the surest possible Jeopardy! bet. This game was no different.

Correction, June 4

The original version of this story misstated the amount of money with which contestant Jay Sexton finished. It was \$17,000, not \$22,000. The original version of this story also misstated in one instance James Holzhauer’s score leading into Final Jeopardy. It was \$23,400, not \$24,400.