Bonus Round Letter Selection

As I said in many interviews and told many future contestants, it's always a good idea to have a set 3 consonants and a vowel (add a back-up letter in case of Wild Card), that way you know exactly what you're working with on the used letter board. In my case, my letters are HMDO (with B as a back-up [that would've helped during my puzzle ]). Even though I know part of the solution, I always go with my 'go-to' letters and it seemed to have helped! As for the seeing certain letters pop up during my fellow contestants' bonus rounds on tape date, I wouldn't change any letters either way. It seems like Wheel has been unpredictable with their BR puzzles especially during 'budget-fitting-BR-time.'

If I were to do anything different, however, I would've studied up on smaller 4-5 letter words that do not have any RSTLNE or my go-to letters, but I didn't need that I guess

And that's why the show avoids using too many of those letters more than half the time these days.

Also, H is actually next in line in terms of popularity. It's actually in the same league as R and L.

Indeed! I'll have to think about that one... thanks to all for the responses!

Let's say you have the answer with RSTLNE. You pick the three and a vowel, but it turns out your intended guess was incorrect. What then?

The previous puzzle was A HUGE GAMBLE. Maybe that was the one.

I haven't been a contestant either, but I've always got a spare $0.02 to throw in on this subject...

Actually, about a cent and a half of that two cents will be borrowed from somebody else, specifically Wayoshi. Referring to data he's collected as part of his WOFTracker project, we have a breakdown of the percentage of the time each letter appeared in puzzles from Seasons 29 to 31, a sample size of 585 Bonus Rounds. I'm going to paraphrase them a bit, but if you want to see the data in full, just check out our Links page.

O - in 414 puzzles (71% of sample)
I - 372 (64%)
A - 369 (63%)
U - 263 (45%)
---------------------------------------
H - 251 (43%)
G - 241 (41%)
P - 222 (38%)
C - 199 (34%)
B/D (tied) - 194 (33%)
Y - 179 (31%)
W - 171 (29%)
F - 151 (26%)
K - 139 (24%)
M - 127 (22%)
V - 113 (19%)
J - 37 (6%)
Q - 30 (5%)
X - 24 (4%)
Z - 18 (3%)

So it's clear that there's statistical support for BGHO - you get the best vowel and three of the six top consonants. CDMA, on the other hand, is merely okay - third-best vowel, two of the six best consonants, and M is well down the list. In fact, WKYI, which I sometimes employ when I feel the writers have employed a tricky adjective-noun combo, is nearly as good as CDMA - W/Y are just below C/D, almost anything (including K) is better than M, and I just edges out A in the vowel department.

Honestly though, I don't endorse using one set package of picks to always plug in no matter the puzzle. As far as I know (and someone can correct me on this), you're not on the clock when picking, so you can take that couple extra seconds to decide what fits best in the unfilled blanks. Sometimes CDMA might be a winner after all, or maybe WKYI will fill in everything. You have to use your best judgment and your letter sense to see you through.

Well I couldn't quite let this go, and now I've spent far too much on it.

Picking a letter that's a non-dud is a start, but you also want to consider how much the letter will help you solve the puzzle. I used WayoshiM's s29-31 tables to create scores for each letter: duds are worth 0, singles worth 1, doubles worth 2, ...

Here are the results over all vowels:

So O is the undisputed queen of the vowels, even ahead of E (which is unsurprising, given that they want to give puzzles with few Es).

Consonants are basically exactly in line with the frequency analysis: H = 314, G = 281, P = 265, D = 233, B = 231, C = 223; all the rest are under 200.

Now the more interesting analysis for me is in the "bang for your buck" metric. If your letter is in the puzzle, how much does it help you? Or, more concretely, how many spaces do you get if your letter is in the puzzle? X and Q are big losers: if they are in the puzzle, you'll only get one space. The big winner turns out to be Z: it's only in 18/585 puzzles, but 7/18 times it exists as a double, making the expected number of spaces revealed 1.389. The order is a bit different looking at consonants this way: H = 1.251, D = 1.201, P = 1.194, F = 1.192, B = 1.191, G = 1.166, C = 1.121; all the rest are 1.10 or under. (O wins here too with a whopping 1.592, far ahead of the next closest, A, with 1.450)

So this speaks to 2 slightly different strategies. First, we have "Maximize Non-Duds," or MAD. With MAD, the goal is to get as many correct letters as possible. Second, we have "Get Letters And Destroy," or GLAD. (I admit to backronyming the second strategy) With GLAD, the goal is to fill up as many spaces as possible given that you can only select 4 letters.

MAD strategy: HGPO(D)
strict GLAD strategy: ZHDO(P)
realistic GLAD strategy: HDPO(F)

I say that because clearly Z is high risk/high reward. If it's in the puzzle, it's nearly a 50-50 shot there'll be 2, but you know, then you're the person who picked Z in the bonus round. Parentheses signify wild card selections.

While I thought these strategies might yield different results, they turn out to be shockingly similar. The MAD strategy filled 32.6% of the non-RSTLNE spaces (37.6% with the WC), and GLAD filled 31.5% (35.4% with WC). That comes from the fact that F is far more likely to occur multiple times if it appears, relative to its frequency in the puzzles.

So my conclusion is that at least based on the past 3 seasons, H, P, and O are must select letters. The choice of G, D, or F as your final selection would all be reasonable depending on how much risk you're willing to subject yourself to.

(Of course there are MASSIVE caveats to this analysis. I don't have the actual puzzle data, so the "% filled in" numbers are on average, and would assuredly change if I looked at the success of each strategy puzzle-by-puzzle. Similarly, I'd love to look at which letters are likely to co-occur, which might change what the best strategy is. As in, maybe H and G are unlikely to appear separately. In which case, it might make more sense to hedge your bets by not selecting both.)

I'll be perfectly honest. When I found myself faced with picking my 3 and a vowel, I honestly had no idea what to pick. The Wild Card was never in play so I didn't have to worry about a fourth.

For the uninitiated, this is what RSTLNE gave me:

_ / S _ _ _ _ _ _ R E
PERSON
RSTLNE

Not exactly indicative of any obvious letter patterns. The only thing I had to go on was that initial letter at the beginning and the -RE at the end. Here's what was going through my head...

"Well, what's that first letter likely going to be? A. Are there going to be any more in the other word? Probably not. So don't call A.

What ending makes the most sense: -IRE, -ORE, or -URE? If they were feeling really dickish I suppose they could've had -GRE or even -YRE, but there are only so many words that end like that and start with S. Frankly, while -URE could be plausible, -ORE sounds like the biggest possibility. So I have my vowel.

"Now what about the three consonants?"

I'd like to think my internal monologue went something like this:

"Well, if it ends in -ORE, maybe there's an M right before it (-MORE). Not sure what the full word could be, but hey, it's either that or SM- something. Better cover my bases with SP- as well and hope it's enough to set off a lightbulb somewhere. As for the last one...D is relatively common in PERSON puzzles, let's throw that in there too."

In reality, it was something like this:

"I have no blinking clue what to call here. Let's just pick three plausible random consonants and hope for the best. And don't call A."

Luckily for me, I called the right stuff!

Interesting. Are there patterns that emerge throughout a day? Or were you more so looking to see others' strategies?