The findings in the article below have been superseded by a better analysis in this article.
You probably discovered when playing basic Wordle that it was easy. My previous article explained that a niaive strategy [search broadly three times and you’re almost inevitably there] suffices. So you started to play in Hard Mode. On the face of it, this narrows the scope of your search so it may get harder. I decided to test this. My advanced program makes its first guess randomly, taking care to use a word with five different letters. The second guess chooses a word from the database after it has been filtered using anything learned from the first guess. Again, if it can, it selects a word with five different letters. The third guess takes the same approach, updating the database as information about letters and their positions is gained. I ran it first on the same 16 words we looked at using GREAT, NOISY and CHUMP. Actually, very little has changed. We started with a random word. We followed with a second random word but we possibly don’t get a full five new letters but in compensation we do start trying to place discovered letters in their good position. Likewise for the third word. Here’s the first absolutely random run of the program:
Wordle: 'POINT'
Guess # remaining words including:
FAKES 289: BIDDY, BIGHT, BIGOT, BIJOU, BILLY, BIMBO, BINDI, ...
TOUGH 7: BOOTY, COOPT, DOTTY, JOINT, MOTOR, POINT, ROBOT, ...
JOINT 1: POINT, ...
finished with 4 guesses
Wordle: 'ROBOT'
Guess # remaining words including:
TILES 72: ABBOT, ABORT, ABOUT, ACTOR, ADAPT, ADOPT, AFOOT, ...
ABBOT 1: ROBOT, ...
finished with 3 guesses
Wordle: 'CRIMP'
Guess # remaining words including:
TUMOR 30: ALARM, BARMY, BERMS, BREAM, BRIMS, CHARM, CRAMP, ...
CHARM 3: CREME, CRIME, CRIMP, ...
CRIME 1: CRIMP, ...
finished with 4 guesses
Wordle: 'KNOLL'
Guess # remaining words including:
DUSKY 58: ABACK, ACKEE, ANKLE, BAKER, BATIK, BIKER, BLACK, ...
CRANK 4: KNIFE, KNOLL, KNOWN, TOKEN, ...
KNOLL 1: KNOLL, ...
finished with 4 guesses
Wordle: 'SUGAR'
Guess # remaining words including:
AUDIO 11: BUBBA, BULLA, BURKA, BURQA, BURSA, CULPA, CUPPA, ...
LUNAR 1: SUGAR, ...
finished with 3 guesses
Wordle: 'WHACK'
Guess # remaining words including:
DECRY 194: ABACK, ACING, ACTIN, ANTIC, ASPIC, ATTIC, BASIC, ...
POUCH 4: CHICA, CHICK, THICK, WHACK, ...
THICK 1: WHACK, ...
finished with 4 guesses
Wordle: 'MOUNT'
Guess # remaining words including:
AMEND 1: MOUNT, ...
finished with 2 guesses
Wordle: 'PERKY'
Guess # remaining words including:
BRUIN 266: ACRES, ACTOR, ADDER, ADORE, AFORE, AFTER, AGGRO, ...
FARTS 11: CORED, CORER, CORKY, DORKY, MERCY, MERGE, MERRY, ...
CORKY 1: PERKY, ...
finished with 4 guesses
Wordle: 'COULD'
Guess # remaining words including:
COINS 37: COACH, COBRA, COCKY, COCOA, CODEC, CODED, CODER, ...
COMER 9: COACH, COCKY, COCOA, COOPT, COTTA, COUCH, COUGH, ...
COTTA 5: COCKY, COUCH, COUGH, COULD, COYLY, ...
COYLY 1: COULD, ...
finished with 5 guesses
Wordle: 'THOSE'
Guess # remaining words including:
BOWED 62: AEONS, AFORE, ALONE, ANOLE, AROSE, ATONE, AZOLE, ...
EXTOL 7: ATONE, QUOTE, STONE, STORE, STOVE, TEMPO, THOSE, ...
THOSE 1: THOSE, ...
finished with 4 guesses
Wordle: 'EXIST'
Guess # remaining words including:
BLOCK 694: ADAGE, ADAPT, ADDED, ADDER, ADEPT, ADIEU, ADITS, ...
DREGS 28: AMUSE, ANISE, ASHEN, ASPEN, ASSET, ENSUE, ESSAY, ...
ASHEN 5: EXIST, MESSY, SETUP, SPITE, SUITE, ...
SETUP 1: EXIST, ...
finished with 5 guesses
Wordle: 'SHARD'
Guess # remaining words including:
EXPOS 96: ANGST, ANTSY, ARTSY, ASANA, ASSAY, ASTIR, ASURA, ...
SHIFT 3: SHALL, SHARD, SHARK, ...
SHARD 1: SHARD, ...
finished with 4 guesses
Wordle: 'PLEAT'
Guess # remaining words including:
BEAKS 139: ACHED, ACTED, ACUTE, ADDED, ADDER, ADDLE, ADEPT, ...
AMEND 10: CHEAP, CHEAT, CLEAR, CLEAT, FAERY, GREAT, OPERA, ...
TREAT 4: CHEAT, CLEAT, PLEAT, WHEAT, ...
WHEAT 2: CLEAT, PLEAT, ...
PLEAT 1: PLEAT, ...
finished with 6 guesses
Wordle: 'SKILL'
Guess # remaining words including:
DOYEN 380: ABACK, ABUTS, AFFIX, ALARM, ALBUM, ALGAL, ALIAS, ...
BRUSH 60: ALIAS, ASPIC, ATLAS, AXILS, CALFS, CALLS, CALMS, ...
FLATS 1: SKILL, ...
finished with 4 guesses
Wordle: 'CYNIC'
Guess # remaining words including:
TOPIC 6: BASIC, CIVIC, CUBIC, CYNIC, MAGIC, MUSIC, ...
CYNIC 1: CYNIC, ...
finished with 3 guesses
Wordle: 'AROMA'
Guess # remaining words including:
CHEAT 232: ABAYA, ABYSS, ADIOS, ADMIN, ADOBO, ADORN, AFFIX, ...
FLAWS 58: ADMIN, ADOBO, ADORN, AGGRO, AGING, AGONY, AGORA, ...
AUDIO 9: AGONY, AGORA, AMONG, ANNOY, APRON, ARBOR, ARGON, ...
ARBOR 1: AROMA, ...
finished with 5 guessesIt’s pretty impressive! Only 4 of the 16 words required more than 4 guesses. Maybe this was a fluke so let’s do it 1000 times and average the result. The table below shows the average number of guesses required and the distribution of scores for each wordle. I think it clearly illustrates that Hard Mode Wordle is very easy too with only 42 of the 16000 games played resulting in failure against random play. When run against 250 randomly chosen words, failure rate is about 6%
Guesses
Wordle Avg 1 2 3 4 5 6 >6
------------------------------------------------------
'POINT' 4.5 0 3 119 381 386 108 3
'ROBOT' 3.9 0 11 252 576 159 2 0
'CRIMP' 4.1 0 3 168 539 260 30 0
'KNOLL' 4.1 0 7 200 534 241 18 0
'SUGAR' 3.9 0 26 253 554 162 5 0
'WHACK' 4.0 0 27 230 458 253 30 2
'MOUNT' 4.1 0 12 166 523 277 22 0
'PERKY' 4.4 0 16 154 330 392 102 6
'COULD' 4.2 0 5 173 494 287 37 4
'THOSE' 4.2 0 13 205 464 251 65 2
'EXIST' 4.1 0 15 165 523 257 39 1
'SHARD' 4.5 0 26 140 280 394 146 14
'PLEAT' 4.4 0 6 142 372 375 98 7
'SKILL' 4.2 0 4 123 594 263 16 0
'CYNIC' 4.1 0 5 199 543 231 22 0
'AROMA' 4.3 0 6 173 432 312 74 3
' 250 ' 4.5 0 10 146 366 286 128 64Conclusion
If we assume the words in their database are recognisable to the average player, Wordle can be played with a fairly ‘blind’ strategy and in that sense it is easy to play, even in Hard Mode. If NYT wants to make it harder, they should stop signalling that letters are in their correct position; i.e. use only yellow flags. I estimate that the effect of that is to increase the failure rate from 6% to about 38%.
Asynchronists 