Strategy Talk: Seth Wilson’s Bet Tonight Wasn’t As Bad As You Think

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:
Seth $19,000
Margie $17,000
Eric $1,800

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:
Big ($15,001):
Win if:
Correct (52.63%)
or both wrong & 2nd overbets (29.05% * 47.91% = 13.92%)
Chances: 66.55%

Small ($2):
Win if:
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%)
Chances: 62.55%

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.

3 Comments on "Strategy Talk: Seth Wilson’s Bet Tonight Wasn’t As Bad As You Think"

  1. Go big or go home…

    I might react differently if the category had been “Opera” or “19th century French Lit”, but the “Economy” catagory hits my wheelhouse (future Jeopardy answer? lol)…

  2. Except that Seth doesn’t have an invariable propensity to make a small bet when he leads in a 2/3 situation. His wagers are all over the place in that scenario. Compare his cover wagers in games 2 and 8 of his run. I think he simply bets small when he doesn’t like the category — which he ADMITTED in an interview was the case for his game 13 wager. I also doubt that seeing one small wager from him in a given week would motivate many contestants to alter their betting strategy. And an astute opponent might well surmise that his small wager was based on the category and nothing more.

    Seth is a very good player and I think he ended up 9 out of 13 on his FJ’s; so I don’t think the aggregate stats for how ALL leaders fare on FJ’s are completely relevant, and your analysis may have understated the difference between his likelihood of winning under his two different wagering scenarios. Finally, I think he should have bet on himself instead of betting defensively like he did. Especially because a category name simply isn’t a reliable proxy for how difficult the clue will turn out to be. That’s not to say his wager was horrible, but I do think it reduced his chances of winning. And given that he was already a 12-day champion, it also cost him what was a reasonable chance at a few more victories.

    • Andy Saunders | October 6, 2016 at 3:51 pm |

      At 13 games, I don’t have enough data to determine with any sort of statistical certainty what sort of player Seth is in Final Jeopardy. For all we know, he could be an average player who went on a good run. The only player in the history of the show for whom we have that sort of data is Ken Jennings. Thus, I feel perfectly justified in using the average data in this case from a statistical perspective.

      If you think my analysis understated the difference, please explain how. (Your use of “and” tells me that this is a separate concern to you from my use of the average data.) The numbers are right there: My conclusion was similar to yours. Yes, his chances of winning this specific game were diminished. But from a purely numerical point of view, even if his winning percentage gets knocked down to 54%, if that wager ends up drawing out a suboptimal large wager later (meaning a 66% game like this becomes an 82-83% crush scenario), it is still worth it from a combined winning percentage point of view.

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