The Game

It may be the most ubiquitous game we have. Every element of the TV product, from the music to the characters to the viewing experience to the commentary, has transformed it over the decades into an American cultural institution and a weekly family ritual across the country, a hit among all ages and demographics. The rules are never explained because explaining is never necessary - they are our country’s DNA, our common tongue, the meritocratic myth that feels axiomatically natural to us.

Obviously, the game I’m talking about is Jeopardy!, the undisputed champion of game shows, and as it capitalizes on this ubiquity and sustained popularity, the game that is bigger business than ever announced on Monday its biggest game ever. Riding the historic success, record-shattering wins and smash hit ratings of James Holzhauer’s 2019 run on the show, a 32-game win streak many considered the most dominant in the show’s 35 seasons (contestants were limited to 5 straight wins before a 2003 rule change), the show called up the other two of the three players considered the best ever, Brad Rutter and Ken Jennings, and announced a championship series beginning January 7 to determine once and for all the best to ever do it. In light of widespread concern among fans over beloved host Alex Trebek’s health and his ability to have all the right answers to their favorite players’ questions, the move has thrilled fans and stirred hype and dollars across the country in anticipation.

Given the scale of this event (billed ‘Jeopardy! The Greatest of All Time’), the oddsmakers, too, have been quick to make their estimations and eager to take our bets (with an extra cut for themselves), but because of the unique nature of this competition, careful analysis of each player’s style and the nuts and bolts of the competition may give a savvy analyst a real edge over Vegas, which has little history offering bets on Jeopardy!. This opportunity for handicapping is unprecedented in itself - not only in the sense that betting has only recently become a topic acceptable in mainstream discussion, but that Jeopardy! rarely sees games with enough star power to announce the competitors this far in advance. The last time Jeopardy! held such an event, when IBM’s Watson language processing engine handily defeated Rutter and Jennings in 2011’s highly-promoted rehashing of man vs. machine, audience ratings hit a 6-year high, beating every show on television save for “American Idol”. This 6-year high was the best the show had done since 2005’s Rutter-Jennings clash in the Ultimate Tournament of Champions, which followed Jennings’ 2004 ratings sensation of a winning streak, and was eclipsed later only by Holzhauer’s June 2019 defeat.

Headlined by the three names responsible for Jeopardy!’s biggest ratings bonanzas in the last 20 years, then, there is every reason to expect that a game featuring the trio, to say nothing of the context of Trebek’s health, is as close to a layup as it gets in generating fan interest, and Las Vegas seems to agree. Because Jeopardy! episodes are taped within a month or two of airing, sportsbooks have generally not offered odds on Jeopardy! episodes near their airdate out of fear that audience members, who are nominally sworn to secrecy, will break their promise and decide to bet on a show they know the outcome of, or tell someone who will. The massive fanbase this matchup offers, though, combined with the very unfavorable odds for bettors (more on that in a second), means books willing to take bets on the event will be swimming in profit no matter what happens, provided they do their due diligence to monitor betting activity and lock things down if the winner becomes obvious.

To this end, according to the tweet above, odds at Bovada, a popular offshore bookmaker, listed Holzhauer at +110, Jennings at +115, and Rutter at +280, implying win probabilities of 47.6%, 46.5%, and 26.3% respectively. Clearly, one or more of those win probabilities is too high, and it’s possible all three are too high - they sum to 120.4%, whereas the sum of win+lose+draw on a given soccer game tends to be around 105%. This unusually high cut for the casino is essentially insurance against inside knowledge, and you won’t see many better menus of odds from sane sportsbooks. But for those of us with a gambling streak, this is a rare occurrence where history and careful thought about the styles of players whose interactions might be more predictable than we think¹ can let us convince ourselves that we, too, have inside knowledge, and are the big fish the casino insures against. Realistically, you should only make a bet on entertainment if you do have inside knowledge, but unfortunately this is wildly illegal, and the only Jeopardy! analysts savvy enough to have real confidence in, inconveniently for us, are all playing in the game. However, as someone who has played and logged my scores in 1000+ different games of Jeopardy!² (not a story for this article) over a much longer length of time than I feel comfortable admitting to people, I believe the odds above, pending further movement, present with them an opportunity for a genuine edge that confident-feeling adults of legal gambling age could feel good about betting on³ (disclosure: this will not include me).

The Analysts

Above I said that the best analysts were all playing in the game, but within that group, James Holzhauer is likely the best, and it may not be close. Trained and experienced in sports gambling, Holzhauer unequivocally understood better than any other human in Jeopardy! history how to maximize the expected value of the money he took home, and during his superhuman run leaned on his encyclopedic knowledge to make huge bets on every Daily Double (DD) and Final Jeopardy! (FJ) he could, effectively parlaying his money from one bet to the next and racking up massive payouts. If we imagine the probability of getting any of these questions right as roughly equal (let’s call it p) for any given player, that is not depending on the dollar value of the clue, the probability of getting three correct⁴ in a game is p^3, multiplying your original money by 2^3, or 8, if you bet it all and get them all right. For the average Jeopardy! player, this strategy is laughably risky - a decent player that can expect to get roughly 60% of these questions right has an expected return of 8*(.6^3), or $1.728, for every dollar they start with, but only a .6^3, or 21.6%, chance of actually getting everything right and winning the game, which is the only way to keep the money you win.

While a game is still winnable theoretically if the player bets it all and loses at least once, winning from there requires a lot of good luck, and our generic player is better off with the more or less 33.3% chance they have playing normally. For James Holzhauer, though, who got about 95% of these clues correct, the chance of getting all 3 is 85% with a massive $6.86:1 expected return, and his skill was enough against regular competition during his run that a rare miss was never enough to sink him anyway - in his loss to Emma Boettcher, he did not answer a single question incorrectly (it was instead Boettcher who found and took advantage of the coveted opportunities to multiply her money). For Holzhauer, or anyone else who completes step 1 of assembling and remembering nearly every bit of trivia that could possibly be worth knowing, the bet-big strategy is an easy call, but for Joe Jeopardy! this will more often than not lead to a quick run on the show. Though the strategy had been tried before, Holzhauer was still portrayed in the media as a strategic innovator due to the record-breaking success he and his inhumanly impressive recall displayed during the run, and it was hard not to be floored. Before Holzhauer, the single-game record stood at $77,000 and was held by Roger Craig; Holzhauer’s new record currently stands at $131,127. Holzhauer also holds the new second-best single-game score of $130,022, and in fact holds #3-#16 on the list as well, along with #18-#21, #25-#26 and many other entries farther down the leaderboard. His run was so historically dominant, so strategically sound and so fresh in our minds, that it is easy to see why he is the co-favorite for next January.

Right there next to him, with odds a pinch lower, is the first Jeopardy! superstar, Ken Jennings, whose 74-game winning streak that spanned two seasons of the show in 2004 looks destined to join Joe DiMaggio, the 1972 Lakers and Cal Ripken, Jr. in the annals of unbreakable sports streaks, and launched him to prominence as the world’s preeminent trivia emperor. Throughout his run, which took advantage of the change a year earlier in the rule that would have forced Ken to cede the leftmost podium after 5 wins, Jennings repeatedly demonstrated mastery of the most difficult and obscure reoccurring topics in the show alongside an uncanny ability to win the race to the buzzer on a question. Where it could be said that Holzhauer was playing to maximize expected winnings, Jennings seemed more clearly to be playing to maximize win probability, making much more conservative DD/FJ wagers that ensured the large leads he built elsewhere on the board remained intact. After all, one way to guarantee more money is to come back tomorrow, and Jennings made a habit of doing so for weeks, which dragged into months as Americans gazed slack-jawed at our TVs throughout the spring, summer, fall and nearly the winter of 2004. By the time he finally lost to Nancy Zerg in his 75th consecutive appearance, Jennings had set the regular-play cumulative winnings record of $2,522,700, a number Holzhauer fell about $56,000 short of, but that no other contender has matched even a third of. Jennings has understandably been a frequent participant in Jeopardy! tournaments since his original run, amassing another $1,000,000 in combined prize money since, including a distant second-place finish in the IBM Challenge at the hands of Watson, and on the strength of this resume was regarded as the consensus Jeopardy! GOAT before Holzhauer’s electrifying run finally signalled a true challenger to the title.

At one point, though, the best Jeopardy! player to ever grace the podium was permanently settled on national television, and the winner was neither Jennings nor Holzhauer. The third participant in ‘Jeopardy! The Greatest of All Time’, Brad Rutter, is somewhat less of a celebrity than the other two. Rutter, who competed in 2000 and was a victim of the 5-win rule, made his return in Jeopardy!’s 2005 Ultimate Tournament of Champions, which allowed every past 5-game winner (among other champions) a shot in a mega-tournament premised on determining whether newly-minted rock star Jennings was truly the best player ever, and advanced cleanly through the field before upsetting Jennings in the highly-publicized championship. Rutter returned for the IBM Challenge in 2011, finishing behind Watson and Jennings, but bounced back by winning 2014’s Battle of the Decades tournament and leading his team to victory in 2019’s Jeopardy! All-Star Games. Rutter, who like his competitors knows to a stunning level of detail nearly every salient story of our culture, played as conventionally as Jennings, but has never lost a game of Jeopardy! to a human (in his only loss, he placed behind both Watson and Jennings, so it might be more precise to say he has never lost a match won by a human), and is a Jeopardy! machine in his own right. Like his counterparts, Rutter has left no stone unturned in pursuit of the truly esoteric knowledge of our universe, and all three are highly skilled at ringing in as instantly as possible. In terms of pure talent, it is extremely difficult to speculate on the advantage any of them may have, or even to be confident in one’s hunch.

The Pick

Before we discuss which player might actually be worth betting on, it’s worth coming to an understanding of what it means to think intelligently about this kind of Jeopardy! competition, and its tactical implications. In ‘Jeopardy! The Greatest of All Time’, Holzhauer, Jennings and Rutter will play a best-of-7 series of Jeopardy! games, of which the first man to win 3 will be crowned the winner. Importantly, the total money accumulated appears to be irrelevant to the payouts for winning or participating - gone is any financial reason to selfishly bet more aggressively than if one were simply trying to maximize their chances of winning. Additionally, we can expect the questions to be meaningfully harder than in regular-play Jeopardy!, perhaps to an extent never seen, and most importantly given the talent parity we can expect the players’ strategies in-game and across games to adapt to those of one another. It is possible that all three will take this information and play Holzhauer’s high-variance strategy, knowing that at roughly equal levels of skill, playing conservatively against a gambler won’t do anything to help the fact that you already need to get lucky to win a game you have a ⅓ shot in. Conversely, they may all play conventional styles, as Holzhauer comes to terms with his mortality in the face of his peers and harder questions and finds himself left in the dust too often to continue his signature “all-in” strategy. However the series ends up playing out, it is likely that all three will play similarly, hedging their bets with moderate risk and a mix of the above until times get desperate, at which point any of them are equally capable of playing as high- or low-variance a strategy as necessary. All three have studied Holzhauer’s game as well as the games of one another, and are surely ready to change betting strategies on the fly. Outside of Holzhauer potentially possessing a marginally more developed gambler’s sense of a good wager or simply having a young man’s energy, it is unlikely that any of the players have a tactical advantage over one another either.

While Holzhauer has the potential advantage of having spent nearly a year practicing, preparing and performing on the big stage near-constantly (shortly after his run ended, he competed in and won the November 2019 Tournament of Champions before preparing to face Jennings and Rutter), all three are extremely seasoned and equally capable of performing to the best of their abilities when the time comes. All three were surely given adequate warning of this competition or had a reasonable expectation of it, and as we surmised above it is doubtful any will have a meaningful tactical advantage. All three are effectively machines at this game who have studied it and the knowledge required to a level beyond redundancy, and I am unsure that any one of them has a real talent advantage over the others, despite Jennings and Holzhauer’s more impressive Wikipedia pages. For this reason, consulting Vegas’ impression of the competition once more, Rutter seems to me to be the one to watch for. My own hunch, for whatever little it is worth, is that games like Jeopardy!, where the numbers we remember are streaks and winnings racked up against us pathetic earthlings, are much more random than we like to give them credit for when the competition is equally dominant, and comparing the relative dominances of Rutter, Jennings and Holzhauer strikes me as impossible out of context. I don’t see any convincing evidence that any of these players, given their massive knowledge bases, impressive buzzer skills and history of thrashing their competition, is meaningfully better or worse than the others, and at the odds above I am intrigued by the idea that Rutter is worse than a ⅓ proposition. Lord knows in comparison to those onscreen that us humble viewers are nothing but dumb money, but if I were to throw mine down, I’d like Brad Rutter’s odds.

Daniel Waldman is President of the Sports Analytics Group at Berkeley.

1. 1. By percentage, a random Jeopardy! question is substantially easier for any of them (95+%) than a free throw is for the all-time best free-throw shooter in NBA history.⁵

2. 2. I assume you clicked this article expecting someone who has an idea what they are talking about, so feel free to click away here if you’re unimpressed, but I’ve done the math and at about 8 minutes per game (shoutout to j-archive.com) this was 6 days straight of my life. At my peak I knew the question to about 68% of the answers in a given Jeopardy! game. It was all worth it for this article.

3. 3. While using a legal gambling platform and while in a jurisdiction where placing such a bet would be legal, and obviously while transacting with an appropriately licensed bookmaker. The Sports Analytics Group at Berkeley takes illegal gambling very seriously.

4. 4. James averaged 3.30 DD/FJ attempts per game, a number that goes up the better you are, because you get more DD opportunities the more regular clues you get right. Clearing 3 DD/FJ attempts per game is generous even for a good player, and the average is just under 2.

5. 5. Stephen Curry.