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I recently picked up Dungeon Wordle from the Wordle Jam on itch.io, and I was really impressed...

But the way the game 'randomises' what item you get for a given day, is based on the answer to the Wordle puzzle for that day.

Given the table in the Dungeon Wordle pdf (which I won't reproduce here, it's available with the game and is 'pay what you want'), and assuming the words 'randomly generated' are from this shuffled word list, are all combinations of items possible, and if so are some more likely than others?

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    \$\begingroup\$ This question is about a solo journalling RPG that uses Wordle as a source of 'randomness'. It is therefore inherently about Wordle, which you might describe as a videogame, but within the context of this RPG. \$\endgroup\$
    – Carcer
    Commented Jan 21, 2022 at 18:36
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    \$\begingroup\$ Do you have any sort of relationship with the author of this game? I ask because it feels like you're trying to persuade people to buy the product. \$\endgroup\$
    – Dan B
    Commented Jan 21, 2022 at 19:55
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    \$\begingroup\$ @AncientSwordRage you have opened both your questions anout the game by indicating where one can get it and that you were "very impressed" by it. (I'm not intending to infer anything deliberate in your behaviour here, but I can see why someone might think that you're advertising.) \$\endgroup\$
    – Carcer
    Commented Jan 21, 2022 at 20:20
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    \$\begingroup\$ @AncientSwordRage Like I said, I'm not personally rushing to assume any ulterior motive - I can just see why someone more suspicious might. \$\endgroup\$
    – Carcer
    Commented Jan 21, 2022 at 20:31
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    \$\begingroup\$ As a new indie game, linking to the product page is the most natural way I can think of to provide meaningful context to the question about what the game is, and hyping up games that you enjoy on the stack seems like the most natural way to encourage readers of the stack to enjoy those games too. Also this: How to improve/maintain the quality-of-life of small fandoms in the face of a dominant big fandom on an open Stack Exchange? \$\endgroup\$ Commented Jan 21, 2022 at 20:33

2 Answers 2

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Not all combinations are possible using the given word list

A simple proof that not all combinations are possible arises from the length of the word list. There are 17,576 possible combinations of segments from the table (26^3, as we're selecting 3 segments each from a separate list of 26 possibilities), but the word list is only 2,315 entries long, so it is clearly impossible to create every potential item from that word list alone.

Even if you were to assume that every word from the list does correspond to a different item, working your way through the entire word list would only explore slightly over 13% of the possible combinations. In actuality, because of the number of words which are equivalent - in the sense that they have the same 1st, 3rd, and 5th characters and thus map to the same item - that wordlist only actually produces 1,434 unique items (about 8.2% of the possible items).

Stats

Of the occurring character combinations, the majority of them - 994 of the 1434 unique combinations - occur only once, but some are much more frequent. The top 5 character combinations, each occurring ten or more times, are:

Letter Combination Number of Occurrences Relative Frequency
SAE 24 1.04%
SOE 18 0.78%
SIE 17 0.73%
SAK 12 0.52%
SET 10 0.43%

So as we can see the single most common combination is SAE, and thus the game's most commonly encountered item will be a Stinky Artefact of Ecstasy, closely followed by the Stinky Ocarina of Ecstasy and the Stinky Ink of Ecstasy. I will refrain from speculating on the nature of such items, but the intrepid adventurer in the world of Dungeon Wordle would probably benefit from some nose plugs.

Moving on, here's a breakdown of letter frequency in each individual character position:

Letter 1st Freq 1st % 3rd Freq 3rd % 5th Freq 5th %
A 141 6.09% 307 13.26% 64 2.76%
B 173 7.47% 57 2.46% 11 0.48%
C 198 8.55% 56 2.42% 31 1.34%
D 111 4.79% 75 3.24% 118 5.10%
E 72 3.11% 177 7.65% 424 18.32%
F 136 5.87% 25 1.08% 26 1.12%
G 115 4.97% 67 2.89% 41 1.77%
H 69 2.98% 9 0.39% 139 6.00%
I 34 1.47% 266 11.49% 11 0.48%
J 20 0.86% 3 0.13% 0 0.00%
K 20 0.86% 12 0.52% 113 4.88%
L 88 3.80% 112 4.84% 156 6.74%
M 107 4.62% 61 2.63% 42 1.81%
N 37 1.60% 139 6.00% 130 5.62%
O 41 1.77% 244 10.54% 58 2.51%
P 142 6.13% 58 2.51% 56 2.42%
Q 23 0.99% 1 0.04% 0 0.00%
R 105 4.54% 163 7.04% 212 9.16%
S 366 15.81% 80 3.46% 36 1.56%
T 149 6.44% 111 4.79% 253 10.93%
U 33 1.43% 165 7.13% 1 0.04%
V 43 1.86% 49 2.12% 0 0.00%
W 83 3.59% 26 1.12% 17 0.73%
X 0 0.00% 12 0.52% 8 0.35%
Y 6 0.26% 29 1.25% 364 15.72%
Z 3 0.13% 11 0.48% 4 0.17%

As we can see it is no surprise that the combination SAE occurs most frequently - S, A, and E are far and away the most common characters in the 1st, 3rd, and 5th positions, respectively, so the game is strongly biased towards producing items that are Stinky, items that are Artefacts, and items that are Of Ecstasy.

As Chemus observed it is unfortunately impossible to produce any Xeric items from the given wordlist, nor any items Of Justice, Of Questioning or Of Villainy; but of the letters that do actually occur, the least common adjective is Zany (3), the least common noun is Quill (1), and the least common descriptor is Of Utopia (1).

But what if we had a bigger word list?

Since Wordle has been bought by the NYT, and they've been making various changes to the wordlist their version uses, it's possible that Wordle could end up using a significantly larger wordlist than was generated for the original version. With that in mind, how much of a difference does a larger wordlist make?

As an example, let's look at the wordlist available from https://github.com/dwyl/english-words. At the time of writing, the "words_alpha.txt" list (consisting only of the 'words' that only use alphabet characters and not numbers or symbols) comprises a mighty 370,105 words. Filtering that down to just the words that are 5 characters, we find 15,920 five-letter-words.

That's many more than used in the original wordlist, but even this isn't enough to pass the brute force check; 15,920 is still 1,656 words shy of the 17,576 possible combinations of the table. After filtering out for table-equivalent words, this list shrinks to 5,342 unique combinations, so still less than a third of the possible items. And that's using a pretty huge wordlist which - by my casual inspection of random sections of the list - is pretty inclusive about what it considers an allowable "English" word!

Further confounding this, the only confirmed information about NYT's changes to the wordlist that I could find suggested that it was removing words, either for being potentially offensive or for being too obscure. So, even if they add new words they are restricting the selection in ways which make it very likely that some letter combinations won't appear as a result.

Altogether, I would be confident to claim that Wordle currently does not and will most likely never have an English-language wordlist that permits all 17,576 letter combinations from Dungeon Wordle.

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No

Doing a brute force approach of separating the letters and sorting them in a spreadsheet, and then looking through the sort, I've determined that sadly, there can be no Xeric items of anything, nor any items of Villainy, of Questioning, or of Justice.

All 26 item types are available, but their descriptors and what they're "of" are slightly limited, though only slightly.

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    \$\begingroup\$ Ironic considering that "xeric" itself would have been a valid Wordle. \$\endgroup\$ Commented Jan 22, 2022 at 0:01

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