Solving puzzles

Wordle 240 2/6

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I have been playing this word game all this month.  So far I am 14/14. I kept seeing this headlines on the news websites about best starting word for Wordle. That made me think more about how this thing worked. I read some of the articles. 'They' say there are 2,315 common 5 letter words in the Wordle dictionary from which each word of the day is chosen.  As of today, 240 of those words have been used, and I am assuming there will not be repeats anytime soon.  So, how likely are we to get the exact word in the first guess, 1 in (2,315 - 240) = 1 in 2,075 chances. There are no words made by plural S, (words).  And the dictionary of acceptable guess is much greater than 2,315. However, NYT has bought the game, and are in the process of removing words some unknown at NYT deems socially offensive.  I am guessing NYT is judge and jury of acceptable words.  No democracy at NYT.

Those best start word stories made me wonder how one decides the best start word. In the world of probability, each of the 2,075 remaining on the list has an equal change of being tomorrows word.  The articles almost all said AI intelligence was used to summons the very best word.  So, I tried it myself.  Using my limited understanding of probability, and my understanding of Excel's capabilities, I did a few searches and made a few excel formulas, after searching the web for letter usage in our English language.

And the best starter word for today's puzzle was CHEAT cause that is what happened when I looked for the word list. I had not worked the puzzle yet, and saw how the word started.

Here is what I found about frequency of letters in English language words, for 1 to 26.

Letter	Frequency
E	1
T	2
A	3
O	4
I	5
N	6
S	7
R	8
H	9
D	10
L	11
U	12
C	13
M	14
F	15
Y	16
W	17
G	18
P	19
B	20
V	21
K	22
X	23
Q	24
J	25
Z	26

Since most 5 letter words contain only 2 vowels, the science of probability would support words containing 2 vowels from the first 7 to 10 letters from that list; ETAOINSRHDL. I personally prefer words using e a t and r. But, this frequency table is taken from hundreds of thousands words, not a limited 5 letter common usage list.

So, to waste a little more time, I found a list of the 240 words already used and ran that list through my excel frequency list formula.  Below is that 240 word list frequency table. The smaller list skews the above frequency list somewhat.  This makes ERAOTILSUCN top the list.  I still like a word with EA or OI with RTL or N.  My biggest problem with all word puzzles is my lack of spelling skills. Would anyone guess I did not have a very busy work day at work today?

LETTER	Frequency
E	109
R	108
A	91
O	76
T	73
I	66
L	63
S	54
U	50
C	50
N	47
D	40
Y	38
P	38
H	35
G	35
B	34
M	28
K	24
F	23
W	16
V	11
X	5
Q	4
Z	4
J	3