Tonight’s Final Jeopardy had another excellent example of how the wording of the clue sometimes gives a hint of the answer. The category was The Bible. And the clue:
The first conversation recounted in the Bible is in Genesis 3, between these 2; it leads to trouble.
Given that conversation takes place early on in Genesis, you should be able to narrow it down to two possibilities. The players did; they were split between “Who are Adam and Eve?” and “Who are Eve and the serpent?” If you aren’t sure which is the correct response, go back and reread the clue.
Do you see it?
Pretend you are the writer for a moment and the correct response is “Who are Adam and Eve?” How would you write the clue? Probably like this:
The first conversation recounted in the Bible is in Genesis 3, between these 2 people; it leads to trouble.
But the clue doesn’t say people! It leaves it vague, and deliberately so. Jeopardy writers don’t like to be unnecessarily vague when they don’t have to. Here, however, they most certainly need to be. The correct response is “Who are Eve and the serpent?” But if they phrased the clue as:
The first conversation recounted in the Bible is in Genesis 3, between this person and this creature; it leads to trouble.
They can’t do that, though—it makes the clue painfully obvious. So they make it vague. But the fact that it is vague when it wouldn’t have to be otherwise actually makes it perfectly clear!
I’ve actually opined on this once before. About a year and a half ago, the clue was:
The circulation of the Times of New York & London totals about half the “Times of” this place, the largest of any English daily.
The High
For most of the game, challenger Matthew LaMagna held a large lead. During Double Jeopardy, other challenger Angela Chuang hit a Daily Double in the “I Have a Theory” category. At only ~$4000 and facing Matthew at ~$18,000, Angela had only one option: make it a true Daily Double. She did. That part was sweet.
So was the clue (paraphrasing):
Beautiful Mind John Nash is credited with launching this field in economics.
Obviously, the correct response was “What is game theory?” Angela nailed it. Again, sweet. Maybe she knows game theory!
The Low
Now the sour part. Despite her best efforts, Matthew pulled away. The scores entering Final Jeopardy were $20,800 for Matthew, $8400 for Angela, and $1200 for the returning champion. Wagers are trivial at this point. Matthew has first place locked. Angela has second place locked as well because she doubles up the third place’s dollar figure. It does not take a game theorist to see this, but it helps.
(Critically, the end dollar figures are irrelevant for second and third place. Second receives a fixed $2000; third place, $1000.)
However, despite Angela’s familiarity with game theory, she wagers $8300. The returning champion wagers nothing. Final Jeopardy’s clue is triple stumper. Angela drops to $100 and third place, when all she had to do was write $0 and guarantee herself $2000. Instead, she went home with a check for $1000.
To be fair, there might be reason to not wager $0 here even though you can guarantee second place by doing so. Everyone’s favorite love-to-hate champion Arthur Chu famously wagered enough so that he would draw with second place if second place wagered everything. But Angela wasn’t even going for that. The $8300 wager could do nothing but harm her. That was sour.
I have been watching Wheel of Fortune for more than 20 years now–my parents even tell me that the game taught me how to read. And all the while I have unquestionably thought that the best letters to call during the bonus round are C M D and A. But watching the program last night, I realized I had no factual basis for that. It was a belief. It was not science.
So I figured I would do some quick Googling and find out what the best letters actually were. Turns out, it seems no one has figured this out yet. (The best result was some dude on Yahoo! Answers, which wasn’t exactly reassuring.)
No problem. I found this website, which archives Wheel of Fortune bonus round puzzles and other associated information. It has a complete record from 2007-2012, or 1166 total puzzles. I scraped the data and began my analysis. Here are some of the important findings:
1) I am not a lone in my belief: C M D A are the four most frequently called letters at 64.6%, 59.9%, 57.9%, and 48.3%, respectively.
2) P H O G are the next four in order at 38.2%, 34.5%, 31.1%, and 21.0%.
3) O is the most common letter to appear in puzzles, consuming 9.5% of all letters. This just goes to show you that the bonus round puzzles are not a random sample of words from the English language–in real life, O is the fourth most common letter after E, T, and A.
4) Despite being the most common letter in English, E is the fourth most common letter in the puzzles after O, I, and A. Ostensibly, they give you R S T L N E for free because they are common letters. However, the producers intentionally pick puzzles where those letters don’t show up. Like cake, the value of R S T L N E is a lie.
5) M is an awful pick, ranking 21st on the list. It only accounts for 2.1% of the letters. Only V, J, Q, Z, and X are less frequent. No one ever calls V, J, Q, Z, or X unless they already know the answer to the puzzle and want to show off. Yet 57.9% of players pick M. Go figure.
6) H is a great selection. It has a frequency of 4.6%, placing the highest among non-R S T L N consonants. It ranks just slightly below the least frequent vowel (U, 4.7%) but higher than N (4.5%), S (3.8%) and L (3.7%).
7) If you solely want to maximize the number of letters that are revealed, H G D O is the best selection. D (3.5%) is very close to P and B (both 3.4%), so there is some wiggle room here.
To hammer home the point, the plot below shows the frequency of called letters versus what appears on the board (click to enlarge):
The mess on the bottom left corner is the V, J, Q, Z, X trash.
A couple of notes before I wrap this up. First, I want to emphasize the distinction between “most frequent letters” versus “best letters.” What shows up most frequently might not be the most useful in terms of actually solving the puzzle. G’s frequency might be overrated since a lot of those come from -ING suffixes, which you could reasonably guess if you see a word like _ _ _ _ _ N _.[1] Letters like C, B, or P might have an advantage in that they could appear at the beginning of words more frequently and are thus more valuable. This is something I could check on later.
This segues to the second point nicely. There are a bunch of interesting questions we can now answer now that I have this dataset. Expect more investigative posts like this in the future.
[1] The category What Are You Doing? only appears 9 out of 1166 times. Since this category always begins with a word ending in -ING, having the G be revealed in that slot is worthless to a contestant. But even if you remove those puzzles from the sample, G ranks much higher than the nearest alternatives.
William Spaniel 