If you were watching tonight’s Jeopardy!, you saw the defeat of Seth Wilson to Margie Eulner Ott after Seth bet just $5 in Final Jeopardy.
In case you missed it, the scores were:
The conventional wisdom in this sort of situation is to make the “standard cover” wager, in this case, $15,001. But how does Seth’s bet of $5 stack up?
Thankfully, because of the exhaustiveness of the data sitting at J! Archive, it is actually possible to quantify the winning percentage of each bet.
The conventional bet of $15,001 wins in the following cases:
1) Seth gets Final Jeopardy! correct; or,
2) Both Seth and Margie miss Final Jeopardy, and Margie over-wagers.
(An “over-wager” is defined here as a bet that loses a double-stumper between the two leaders).
The $5 bet (or even a $2 bet wins in the following cases):
1) Margie misses Final Jeopardy; or,
2) Margie underbets (less than the difference between 1st and 2nd); or,
3) Margie bets to take the lead by $1, and Seth gets Final Jeopardy correct.
Here are the numbers:
From the start of Season 31 to this point of Season 33:
Leaders are 52.63% in Final;
2nd place is incorrect 54.73% of the time;
Dating back to 2001 in regular play, and in four-fifths games:
2nd place “over-wagers” 47.91% of the time (390/814);
2nd place bets to take the lead by $1 5.53% of the time (45/814);
2nd place underbets (less than the difference between 1st and 2nd) 4.91% of the time (40/814).
Doing the calculations:
or both wrong & 2nd overbets (29.05% * 47.91% = 13.92%)
2nd incorrect (54.73%)
or 2nd underbets (4.91%)
or right and second bets to take lead by $1 (5.53% * 52.63% = 2.91%)
So, this bet, on its surface, lowers Seth’s winning chances slightly in this specific game.
However, an astute opponent waiting in the audience may notice Seth’s propensity to make a small bet and may make a sub-optimal wager in the future in light of this information, leading to a greater chance of victory down the round.
Due to the possibility of a heightened victory chance of future game cancelling out any lessened chances in this game, it is my conclusion that Seth’s $5 bet is far from any sort of egregious blunder, but a simple gambit that in this specific case failed to work out. Unfortunately, it ended a great streak at 12 games, but I applaud Seth’s willingness to take this chance. We’ll see him again, I’m sure, in the Tournament of Champions.