Professional gambler James Holzhauer has been laying waste to the game of Jeopardy for weeks now, amassing a fortune of more than a million dollars across only 17 games (for context, all-time record holder Ken Jennings totaled just over $2.5 million over 74 games). By now there have been innumerable articles about the various strategies Holzhauer uses that allow him to win, which include, roughly in order of importance:
Aggressive Daily Double betting (extremely uncommon, enabled by Holzhauer’s background and comfort with betting big sums)
Daily Double hunting (a not-uncommon approach by players who are smart enough to pull it off)
Value building (going after harder, more valuable clues first in order to have a good-sized pile of cash by the time you happen on a Daily Double; this is less common)
Just generally being very knowledgeable (in a very recent episode he mentioned he did much of his preparation by studying in the children’s section of bookstores, which is so fucking smart, frankly, and entitles him more to this incredible fortune than anything else he’s done)
And of course, buzzer skills (Jeopardy’s best-ever buzzer player was not Ken Jennings, but the other player who faced down IBM’s Watson alongside Jennings, Brad Rutter)
I’ve been watching Jeopardy since before I can remember (thanks, Dad), and I might love Jeopardy strategy and theorycrafting almost as much as I love trivia itself. Watching Holzhauer is almost pleasant, in a way that watching players with otherworldly bodies of knowledge is not. If you’ve watched one of those players with a super-deep well of information, you know the feeling of having your mind constantly blown throughout an episode, like in most Tournament of Champions episodes. Holzhauer knows some niche stuff and is incredibly solid on classic subjects like geography, but he is not encyclopedic. This is reflected in his play: He hardly ever buzzes in on a clue he doesn’t know (he has a 97-percent correct answer rate, and a higher Coryat score than Jennings), but he regularly loses out easy-ish clues to other players, sometimes seemingly on the buzzer and sometimes because he just doesn’t know. He is mellow and unflappable and it never feels like he is specifically railroading his opponents, yet when you look down at the end of a round he has 30 times as much money as the other two players.
For these reasons, I think there is another factor in Holzhauer’s success that speaks to his savvy for odds. It has to do with the value of clues relative to how often a player can expect to get them right, and using harder clues to shore up the chances of getting easier ones correct.
Holzhauer often starts rounds with the hardest bottom row of clues, which so far has been taken as a value-building strategy to amass money with which to Daily-Double (he can’t be Daily-Double-hunting down there, because Daily Doubles are most likely to appear in the next two rows up, particularly in the $800/$1600 row). According to historical data, players get these bottom-row clues right less than half the time; the top two rows in double Jeopardyhave an 82 percent and 70 percent correct-answer rate, while the bottom row has a 44 percent correct answer rate. Barring Daily Double hunting, which is executed by cherry picking across rows 3 and 4 first, Jeopardy players almost exclusively go from the easiest to the hardest clues, probably on the idea that it is good to “warm up” on the format or structure with lower-value clues in order to give oneself the best odds at the highest-value ones.
Holzhauer turns this strategy on its head, and it seems to work just fine for him; he does not need the warm-up, maybe. But I submit one of the major reasons it works is not that he knows everything, or enough that clue difficulty will never get to him; it’s that he is burning clues he has less of a chance of getting anyway on the grasping-the-format part of approaching a category, to ensure he doesn’t waste clues he would otherwise nail as long as he doesn’t get tripped up by the particulars of the answer clues.
Jeopardy categories are not often straightforward; the clever, sometimes borderline-awkward phrasing is part of what makes clues tough. This goes double for categories that integrate wordplay, like portmanteaus or themes (all answers are palindromes, all answers end in “ized”). Learning to read through formats and pick out the right context clues is as important, if not more, than just knowing a boatload of facts.
It happens often that players take a clue or two to latch on to the format, meaning they lose the gimmie $200-to-400/$400-to-800 clues on technicalities, and then ramp up on the next two rows before fizzling on the last clue. Starting with the hardest clues feels counter-intuitive — why waste the most valuable clues? What if you would have known the answer if only you’d already understood the format? — but by considering raw odds of getting a correct answer and by constraining all the uncertainty to the hardest clue, Holzhauer may be leaving overall less money on the table.
This is borne out by more Jeopardy statistics that relate clues’ value and the rate at which they are answered correctly or incorrectly, on average, in order to get a “payout” value. According to one data scientist’s analysis, a $200 clue has a $177 payout; in other words, your expectation of getting it right, and thus getting money out of it, are pretty high, because it is an easy clue. $2,000 clues, by contrast, have a $1,006 payout, because the raw odds of getting them right are much lower. This means that a $400 clue ($342 payout) and an $800 clue ($623) are actually together nearly as valuable ($963) as a $2,000 clue when you consider how certain you are to get them right, even though they are worth much less on the board.
It also means that, according to this analysis, the $1,600 clues are of about equal value in terms of payout ($1,003) to the $2,000 clues, and the $1,200 clue, while worth substantially less on the board than the $2,000 clue, is actually only about $150 less valuable ($857 payout) when you consider your chances of getting it right. Furthermore, while the $400 and $800 clues are of equal value to the $1,200 clue on the board, they are actually more valuable in terms of total payout ($963 vs $857). In other words, it is actually smarter to do what you can to guarantee your correct answers on the easiest clues rather than burn them on figuring out the format or topic and then rolling the dice on hopefully knowing the correct answer on the harder clues.
A valid counterargument here is that Holzhauer is not an average player and he is not accurately represented by average odds; he is definitely getting more clues right at a much higher rate than the norm. But while this probably raises his overall odds, it doesn’t necessarily eliminate the relative value of clues when you consider ones he has the best shot of getting right versus ones that are more of a risk. It all suggests to me that it would be an extremely valid Jeopardy strategy, particularly for a tricky, format-forward category, to start with the hardest clue first, the one you will probably not get anyway, as a chance to glimpse the format, before tackling the easier clues.
I could see someone getting through all this and saying, “but then he would just be throwing $2,000 aWAY,” and yes, that’s one way of looking at it. You could also probably arrange the data a little differently and get different values than above. But “ you’re throwing $2,000 away” is also precisely what the Jeopardy board wants us to think. It’s possible that by rising above the game-logic that the board is trying to push, Holzhauer might be proving out one of the most innovative winning strategies good old Jeopardy has seen in a long time.
