Commenter Barry Forer asks, "I've always wondered how well contestants can predict whether they will get a Daily Double correct or not [...] are contestants who are more confident more likely to be correct on a Daily Double than those who are less confident?"
For consistency's sake, let's limit our focus to episodes that have aired since 2002—the first year all episodes used the dollar-values still in place today—and to the first round, when wagers are presumable influenced more by confidence than accumulated score. The most popular first-round Daily Double wager is $1,000, accounting for more than one-third of wagers. (Even if you have $0, you're allowed to bid $1,000.) Contestants who made this baseline wager, guessed correctly 68 percent of the time. At lower wagers, players were right only 65 percent of the time; above $1,000, they were right 70 percent of the time. The most common sub-$1,000 wager is $800, after which contestants guessed correctly just 56.5 percent of the time.
The largest Daily Double wager in the J-Archive database came in the episode that aired on September 6, 2002. Jake Maeroff ("a law student from Plantation, Florida") landed on a second-round Daily Double in the "Saints on a Map" category, and wagered $14,000. His clue: "Jesse James was terminated in this city, once home to a terminus of the Pony Express." Maeroff answered correctly—James was killed in St. Joseph, Mo. Maeroff was playing against Myron Meyer, whose one-game winnings in the previous episode set a record (broken several times since) at $50,000. In that game, Meyer wagered a then-record $13,000 on a Daily Double—and also answered correctly.
Commenter Amanda Benjamin asks, "What is the most money a contestant could possibly win in one game?" A set of ambitious commenters chimed in: You'd have to answer all the questions correctly, find all the Daily Doubles—which would all have to be in the top row—last in each round, and bid all your cash in Final Jeopardy. Commenter Dunk, who solved this equation most convincingly, writes: "The contestant would have $35,600 after Jeopardy, $283,200 after Double Jeopardy, and $566,400 after Final Jeopardy."
But, as Amanda notes, even the most brilliant player could never hope to achieve this score, since Jeopardy's creators would never place so many of the Daily Doubles so close to the top of the board. What's a more realistic score? It's hard to say, but here's a piece of the puzzle: The highest placement of all the Daily Doubles in the J-Archive database was all three in the second row; this happened on Sept. 26, 1997, and Dec. 28, 2006. For these boards, the highest possible score is $556,800.
As a few readers pointed out, Watson's very first pick in his first televised match against Ken Jennings and Brad Rutter was the leftmost cell in the fourth row from the top—precisely the board position I had identified as the most likely place to find a Daily Double. Of course, Jeopardy taped the episode long before I wrote the piece, and IBM's programmers are orders of magnitude more skilled than I am, so I won't take any credit. But I did ask the Watson team about the coincidence.
Daily Double distribution was indeed a "significant factor" in Watson's selection, wrote team leader David Ferrucci, but so were "other factors such as its predicted accuracy in each category and using lower-value clues to learn with less risk how the category works."
In case you were curious, here's a chart showing the full distribution of Daily Doubles: