More fun with Wordle – Second guess analysis

Update March 26, 2022: Added some runts-to-win analysis and updated the “top-25” words again based on that data, see the update section below for details.

Recently I published some analysis for that holy grail of Wordle, the best starting words: Fun with Wordle.

That analysis looked at thousands of guesses for how many words those guesses eliminate on average for all the Wordle answers, as well as millions of simulations using those starting words to get the average turns-to-win playing hard-mode and easy-mode. It used those results to suggest the top starting words.

Since doing that analysis, and even while doing that analysis, I was thinking about taking things to the next step, looking beyond the first guess, to see how things look when considering also the second guess. I noticed in the data, that sometimes a guess that measures as a worse first-guess by that analysis might actually come out better when considering the results after a second guess. This got me thinking about doing some deeper analysis.

Doing the same kind of brute-force simulation analysis on first+second guesses for all the possible guesses would be over 160 million simulations, which I estimated to be about 18 months of compute time on my available hardware. So instead of looking at all the possible guess words, I took the top 100 from the previous first guess analysis and ran those. That took about five days of compute time to run all those simulations. Due to these compute requirements, I didn’t run simulations for both hard-mode and easy-mode. All the results here were run in easy-mode.

Based on the previous analysis, I expected the difference between the best and worst starting words to be minimal, and that certainly turned out to be the case. The best first+second simulation gives an average of 1.017237 possible guesses remaining, while the 100th rated result gives an average of 1.06955 possible guesses remaining. It’s important to keep that in mind when reviewing this data – any of these starting words are good and will give you a good chance to solve the Wordle puzzles. The point being, as noted in the previous report: don’t get fixated on “the best” starting word. Nevertheless, the data is still interesting (at least to me).

Here’s a table of the raw results:


1	rank	word	mean result	first rank	first mean result	first worst case	difference	top 25
2	1	LEAST	1.017237	20	81.07	228	-19	STAY
3	2	DEALT	1.018016	64	94.17	266	-62	IN
4	3	STOLE	1.019342	39	87.7	232	-36	IN
5	4	LEANT	1.020182	19	80.68	220	-15	STAY
6	5	TRAIL	1.020572	23	82.63	232	-18	STAY
7	6	ROAST	1.020754	32	85.84	272	-26	IN
8	7	SLATE	1.021823	10	74.06	228	-3	STAY
9	8	SOLAR	1.022425	33	85.84	242	-25	IN
10	9	STONE	1.022694	80	97.65	263	-71	IN
11	10	RAISE	1.023222	1	62.54	173	9	STAY
12	11	STALE	1.023447	15	78.18	228	-4	STAY
13	12	STAIR	1.023595	46	89.81	268	-34	IN
14	13	TRIAL	1.023599	34	86.18	232	-21	IN
15	14	SONAR	1.024435	53	91.09	270	-39	IN
16	15	IRATE	1.025149	3	65.98	200	12	STAY
17	16	LEAPT	1.025409	99	100.36	265	-83	IN
18	17	TRAIN	1.025626	57	92.27	277	-40	IN
19	18	AROSE	1.025834	4	68.15	187	14	STAY
20	19	ALONE	1.025873	18	80.39	193	1	STAY
21	20	ATONE	1.026401	21	81.72	196	-1	STAY
22	21	CLOSE	1.026405	90	99.34	256	-69	IN
23	22	YEAST	1.027605	84	98.16	266	-62	IN
24	23	SCALE	1.028068	51	90.71	262	-28	IN
25	24	REACT	1.028363	24	82.83	257	0	STAY
26	25	ALIEN	1.028783	35	86.56	229	-10	IN
27	26	SLICE	1.029207	94	99.76	301	-68
28	27	STEAL	1.029861	79	95.91	246	-52
29	28	RENAL	1.030377	29	84.34	224	-1
30	29	ALERT	1.030433	12	74.77	207	17	OUT
31	30	STARE	1.030494	8	73.51	234	22	OUT
32	31	ARSON	1.031334	100	100.5	270	-69
33	32	AISLE	1.031438	16	78.86	202	16	OUT
34	33	SNARL	1.032404	82	97.97	249	-49
35	34	TRADE	1.032564	25	83.3	276	9	OUT
36	35	CANOE	1.03275	49	90.05	223	-14
37	36	TREAD	1.032845	81	97.8	276	-45
38	37	SAUTE	1.033058	37	86.7	228	0
39	38	TRICE	1.033153	44	89.08	286	-6
40	39	ARISE	1.033222	2	65.62	173	37	OUT
41	40	ISLET	1.033317	95	99.91	280	-55
42	41	NOISE	1.034127	65	94.21	268	-24
43	42	STORE	1.034322	28	83.77	251	14
44	43	PLATE	1.034435	60	92.73	265	-17
45	44	CRANE	1.034708	22	82.2	276	22	OUT
46	45	TRACE	1.034799	14	77.05	257	31	OUT
47	46	CRATE	1.034881	13	75.91	257	33	OUT
48	47	TENOR	1.036223	47	89.84	269	0
49	48	ROUTE	1.036691	48	89.88	260	0
50	49	CASTE	1.03738	42	88.05	255	7
51	50	RATIO	1.037731	69	94.61	197	-19
52	51	ALTER	1.037765	6	72.66	207	45	OUT
53	52	LATER	1.038341	7	72.72	207	45	OUT
54	53	LANCE	1.038367	68	94.55	284	-15
55	54	PARSE	1.038428	45	89.45	277	9
56	55	SCARE	1.038722	26	83.44	245	29
57	56	SANER	1.038748	5	72.32	228	51	OUT
58	57	PEARL	1.038766	70	94.75	277	-13
59	58	PLANE	1.039402	89	99.29	297	-31
60	59	ADORE	1.039498	54	91.47	247	5
61	60	RESIN	1.03977	87	98.74	252	-27
62	61	SNARE	1.039918	9	73.65	228	52	OUT
63	62	SAUCE	1.040398	86	98.29	257	-24
64	63	RINSE	1.040411	40	87.73	252	23
65	64	CAUSE	1.041148	88	99.18	257	-24
66	65	RISEN	1.041152	73	95.24	252	-8
67	66	SCORE	1.041923	71	94.89	264	-5
68	67	LEARN	1.041958	17	79.94	224	50	OUT
69	68	CLEAR	1.042001	55	92	261	13
70	69	LATHE	1.042209	72	95.16	257	-3
71	70	CATER	1.042308	27	83.58	257	43
72	71	LASER	1.042425	11	74.39	213	60	OUT
73	72	CADRE	1.042642	91	99.55	317	-19
74	73	SNORE	1.042958	30	85.6	244	43
75	74	AIDER	1.043201	78	95.9	226	-4
76	75	GRATE	1.0433	41	87.74	286	34
77	76	TAPER	1.043387	56	92	277	20
78	77	SPARE	1.043621	67	94.35	277	10
79	78	SHALE	1.045201	66	94.33	249	12
80	79	CRONE	1.047202	83	98.07	297	-4
81	80	BLARE	1.04845	85	98.29	303	-5
82	81	SHEAR	1.048735	77	95.72	247	4
83	82	TEARY	1.049389	38	87.05	207	44
84	83	ROUSE	1.049433	61	93.23	254	22
85	84	HEART	1.049796	59	92.66	273	25
86	85	PALER	1.050359	63	93.76	277	22
87	86	LOSER	1.050494	31	85.8	224	55
88	87	GREAT	1.050697	96	100.06	286	-9
89	88	SIREN	1.050849	36	86.61	252	52
90	89	HATER	1.051429	52	91	273	37
91	90	TAMER	1.053833	75	95.37	282	15
92	91	SHARE	1.054114	43	88.28	247	48
93	92	LARGE	1.054673	62	93.52	282	30
94	93	SHIRE	1.055725	93	99.72	280	0
95	94	URINE	1.058298	92	99.58	263	2
96	95	GLARE	1.05874	58	92.37	282	37
97	96	YEARN	1.06016	76	95.66	225	20
98	97	LAGER	1.062014	98	100.23	282	-1
99	98	LINER	1.064933	74	95.35	236	24
100	99	EARLY	1.065825	97	100.17	223	2
101	100	LAYER	1.06955	50	90.7	222	50

In the previous analysis, we suggested the “best” starting words as LEAST or TRACE for hard-mode or SLATE for easy-mode. In this first+second analysis, our “best” starting word of LEAST holds up. It comes out on top here again. Here however, TRACE gets dropped from the top-25 entirely. SLATE holds on to a top-10 ranking but drops from “best” to number 7 (still very good).

Some big movers in this are LEAPT which moves from 99th in the first guess results, all the way to 16th in the first+second simulation results; STONE moving from 80th to 9th; CLOSE from 90th to 21st; DEALT moving from 64th all the way to number 2.

Words that would move into the top-25 after this analysis are:

word	new rank	old rank	spots moved
LEAPT	16	99	83
STONE	9	80	71
CLOSE	21	90	69
DEALT	2	64	62
YEAST	22	84	62
TRAIN	17	57	40
SONAR	14	53	39
STOLE	3	39	36
STAIR	12	46	34
SCALE	23	51	28
ROAST	6	32	25
SOLAR	8	33	25
TRAIL	13	34	21
ALIEN	25	35	10

words moving into the top-25 starting words

We also have some big movers moving out of the top-25, including SNARE which was ranked at 9 and is now 61st; ARISE was our number 2 word and is now 39th; SANER was 5th and is now 56th.

Words that move out of the top-25 are:

word	new rank	old rank	spots moved
LASER	71	11	60
SNARE	61	9	52
SANER	56	5	51
LEARN	67	17	50
LATER	52	7	45
ALTER	51	6	45
ARISE	39	2	37
CRATE	46	2	37
TRACE	45	14	31
STARE	30	8	22
CRANE	44	22	22
ALERT	29	12	17
AISLE	21	16	16
TRADE	34	25	9

words moving out of the top-25 starting words

These results suggest that there are likely guess-words outside the top-100 first-guess rankings that would be top-100 starting words, perhaps even better, perhaps even top-25. However, as noted, I don’t know how many more CPU resources I want to devote to this analysis. I did, however, try one of the favorite starting words, ADIEU, which is not in the top-100 first-guess rankings. It ranked 315th in the first guess simulation results. In running first+second simulations, ADIEU does move up significantly, all the way to 98th, but not into the top-25 starting words, at 1.061061 average remaining possibilities after two guesses.

I’ll be changing my guesser to pick from these new top-25 starting words. We’ll see if it has much impact on the overall turns-to-win of the guesser.

It takes about an hour to run all the simulations required for this first+second analysis for any given starting word. If you have one you’d like me to try, let me know and I can see how it does.

Update March 26, 2022:

I ran simulations on the new top-25 words shown above and made a new top-25 based on turns-to-win as well as failures (for hard-mode), including the popular favorite ADIEU. Here’s that data:


1	word	turns to win	failures	succcess
2	SLATE	3.228101	3	99.87%
3	LEAST	3.230069	1	99.96%
4	TRACE	3.233102	1	99.96%
5	REACT	3.247615	3	99.87%
6	CRATE	3.249674	6	99.74%
7	STALE	3.256288	3	99.87%
8	STARE	3.258568	4	99.83%
9	LEANT	3.258778	2	99.91%
10	TRAIL	3.259436	4	99.83%
11	TRIAL	3.260624	3	99.87%
12	RAISE	3.262587	5	99.78%
13	ALTER	3.264731	1	99.96%
14	LATER	3.272451	4	99.83%
15	SANER	3.272767	3	99.87%
16	CRANE	3.273397	1	99.96%
17	ROAST	3.273515	2	99.91%
18	TRAIN	3.27383	1	99.96%
19	IRATE	3.274935	3	99.87%
20	AROSE	3.275249	2	99.91%
21	DEALT	3.276116	2	99.91%
22	SNARE	3.277778	5	99.78%
23	LEARN	3.277971	3	99.87%
24	ALERT	3.280208	0	100.00%
25	SCALE	3.281629	1	99.96%
26	CLOSE	3.283362	1	99.96%
27	ARISE	3.284165	4	99.83%
28	ALIEN	3.284288	5	99.78%
29	TRADE	3.287695	1	99.96%
30	ALONE	3.288069	4	99.83%
31	STOLE	3.289303	0	100.00%
32	STAIR	3.297051	3	99.87%
33	STONE	3.297227	1	99.96%
34	LASER	3.298352	3	99.87%
35	AISLE	3.30052	3	99.87%
36	SONAR	3.301821	3	99.87%
37	SOARE	3.302255	3	99.87%
38	ATONE	3.303726	1	99.96%
39	YEAST	3.313666	4	99.83%
40	SOLAR	3.318162	2	99.91%
41	LEAPT	3.321057	1	99.96%
42	ADIEU	3.439809	8	99.65%

After this new adjustment, the words we added to the top-25 from our original top-25 are: CLOSE DEALT ROAST SCALE TRAIN TRIAL

And the words we removed from the top-25 are: AISLE ALONE ARISE ATONE LASER TRADE

In the end, LEAST holds up as, if not the best, certainly one of the best starting words. Likewise, ADIEU remains outside the top results.

Update March 26, 2022:

Post navigation

1 comment for “More fun with Wordle – Second guess analysis”