Wordle Start Words

I have analysed commonly used start words for the game Wordle which can be played here. A prime concept in this analysis is that there are a certain number of possible solutions (at the time of writing this is 1,735 and it reduces by 1 each day). Each guess that you make will reduce the number of possible solutions and once they reach 1 you have the answer.

The Criteria

For each chosen start word this analysis looks at the number of Remaining Solutions for each possible colour pattern and records 5 criteria:

• Max – The worst case number of Remaining Solutions.
• Entropy – The higher the number, the higher the probability that the guess will bring you closer to the correct answer than one with a lower value. This isn’t a concept that can be described easily in a few words, but essentially it adds up the probability of getting each colour pattern (eg bbbbb, bbbbg, bbbby,… where b is black, g green and y yellow) in such a way that the flattest distribution gives the highest value. Mathematicians call it the amount of information the guess will provide. Watch this video if you would like to know more about information theory entropy and how it is calculated.
• One – The number of colour patterns that will uniquely identify the solution (Remaining Solutions of 1). ie There will be times when given the chosen guess and the pattern that comes back, there will only be 1 possible solution remaining.
• Two – The number of solution words, out of the 1,735 (at time of writing) available, that will have two or less Remaining Solutions after using the starting word.
• Three – The number of solution words, out of the 1,735 (at time of writing) available, that will lead to three or less Remaining Solutions.
• I have also indicated whether or not the potential best starting word can be the answer. There are 2 reasons that the answer can be No. Firstly, Wordle has a much longer list of words that will be accepted as guesses, but which will not solve the puzzle. Secondly, Wordle does not reuse answers, so once a word has already been a solution it can no longer be a solution.

Results

Word	Max	Entropy	One	Two	Three	Answer?
about	284	751	25	51	66	y
adept	234	739	22	46	61	y
adieu	218	600	16	30	45	n
aisle	147	929	21	43	79	y
arise	116	939	23	43	61	y
arose	143	936	22	44	71	y
audio	331	694	21	41	59	y
clamp	449	803	28	54	72	y
clasp	347	911	34	48	81	y
close	190	938	20	60	102	y
cones	206	919	28	66	84	n
depot	284	769	24	46	79	n
hates	212	864	28	46	61	n
heart	208	1, 094	30	64	103	y
lance	213	1, 039	31	61	91	y
leant	164	1, 047	29	53	110	y
meaty	252	787	21	53	68	y
ocean	182	870	34	56	70	y
opera	180	816	29	53	62	y
ouija	395	448	16	30	42	n
parse	206	1,166	32	76	118	y
pious	354	685	18	38	68	n
plaid	343	874	26	54	90	y
print	311	865	22	52	79	n
recap	243	861	23	53	86	n
roate	156	936	21	47	65	n
salet	165	1,147	31	69	96	n
scalp	347	823	27	47	71	y
serai	130	847	22	40	63	n
slate	165	1,146	32	66	93	n
slice	221	998	25	53	83	y
soare	143	981	21	41	68	n
stale	165	1,094	30	64	106	n
stare	173	994	18	44	80	y
steal	166	936	25	45	72	y
store	187	938	22	52	82	n
strap	271	896	28	58	88	y
tales	165	917	23	51	63	n
trace	203	1,169	32	76	100	n
train	204	1,060	33	55	94	n
tramp	330	788	27	47	74	y
trice	217	1,051	29	59	95	n
tried	243	1,044	32	64	79	n

Interpretation

Potential Answer

Theoretically, a guess that can’t be an answer could still be a good guess, but this is not supported by the evidence above. Words with “n” in the Answer? column aren’t standing out in this list enough to warrant an unwinnable step. Thus, whilst the unwinnable TRACE has the highest Entropy and Two scores it is only slightly better than the winnable PARSE, so I consider PARSE to be a better option.

Criteria Usefulness

None of these criteria are direct measures of the aim in playing the game. I play to find the word with as few guesses as I can. The best measure would therefore be about the number of guesses needed, which you would want to be less than 7. These criteria give numbers that can be much bigger than 7, meaning that small differences might make no or infrequent differences.

Number of guesses criteria are not provided because such measures require dealing with very large numbers and on using calculation techniques that are not easily emulated with spreadsheets.

The Max (Worst Case) criteria can be useful, however, it is the distribution of Remaining Solution sizes that is the key issue. Two (not real) extremes that illustrate the issue would be a word that provides potential answers in 17 groups of 100 and 1 of 35, versus another that provides 1 of 400 and 1335 groups of 1. The second distribution provides a better than 3 in 4 chance of finding the answer with one more guess, but its Worst Case is 4 times greater.

The Entropy criteria is a mathematically rigorous effort to evaluate which are the best distributions. However, depending on your strategy, it could be rational to put an even greater weight on small Remaining Solutions to improve the chances of quick answers at the cost of occasional slow answers, hence the One, Two and Three criteria.

Here is a table showing the number of words in categories of Remaining Solution sizes for a selection of the words in the table above.

	trace	parse	salet	heart	train	raise	irate	arise	meaty
Entropy	1,169	1,166	1,147	1,094	1,060	997	969	939	787
Answer?	n	y	n	y	y	y	y	y	y
>160	203	206	165	208	204	0	0	0	447
81-160	278	397	197	452	315	298	341	408	480
41-80	288	323	472	282	483	554	404	561	229
21-40	408	240	305	263	227	262	504	200	145
11-20	221	244	255	197	197	350	203	286	233
5-10	201	171	205	202	167	156	190	183	109
3-4	60	78	67	67	87	63	39	54	39
0-2	76	76	69	64	55	52	54	43	53
TOTAL	1735	1735	1735	1735	1735	1735	1735	1735	1735
0-10	337	325	341	333	309	271	283	280	201

Conclusions

• There doesn’t appear to be a reason to used the allowed words that aren’t answers
• Entropy is the most reliable criteria that is easily calculated
• PARSE appears to be the best choice at the moment
• The vast majority of high Entropy words have only two vowels and they are usually A and E
• Three vowel higher Entropy words usually have A, E and I
• Four vowel words are universally poor choices
• Some 3 vowel words have reasonably high Entropy and significantly lower Max (good) but they also tend to have fewer small Remaining Solutions. The lower Entropy suggests that the low Max doesn’t make up for the poorer distribution.

Exit

Please leave comments if you feel there are ways that this analysis can be improved or corrected. Also, if you have start words that you would like me to analyse, let me know in the comments.