WORDL, anyone?

[Brooothru]

Obviously I have too much time on my hands. Somehow SWMBO'd got me hooked on WORDL, which (besides strong coffee) daily gives me a purpose to wake up.

Following a recent frustrating string of "fives" (taking 5 tries to solve the daily puzzle) I tried to calculate the odds of randomly entering 5 letters to guess the correct answer. I came up with 5^26, but that doesn't seem right, especially considering double consonants and double vowels.

It's been 55 years since I took Probabilities and Matrices (back then known as "Probabilities on Mattresses"), and I never was much of a 'mathalete' to begin with.

The elusive answer has become an irrational obsession (pun intended), almost as much as solving the daily puzzle. Can someone show me the math?

 

[marc1]

This guy goes through a lot of simulations talking about the probabilities and information gained from different guesses.

 

[bracconiere]

i just clicked this thread thinking it was going to be new version of pig latin....

 

[Deadalus]

Sorry I don't want to watch the video as I just like to play on my own.

26^5 is the number of possible ways to arrange five letters, so you were just a little backwards on the equation. Simple example for that, there are 100 ways to arrange ten digits as a two digit combination (10^2). This assumes the letters and digits are replaced, which they are. Next, you would need to know the number of five digit words in the accepted Wordle list. That number is 2,315. So you have a 2,315/26^5 chance of randomly selecting the correct answer when you randomly select a letter for each of the five letters. ~1 in 5,132.

Now, you can't enter a word not on the list during the game. So a random five letter word from the list would give you a 1 in 2,315 chance to win on the first try. If you have the list of words already used, you could increase your chance of success by substracting the number of the wordle from 2315. The wordles are numbered from the beginning and it's been said that the words don't repeat (sampled without replacement).

 

[Brooothru]

Sorry I don't want to watch the video as I just like to play on my own.

26^5 is the number of possible ways to arrange five letters, so you were just a little backwards on the equation. Simple example for that, there are 100 ways to arrange ten digits as a two digit combination (10^2). This assumes the letters and digits are replaced, which they are. Next, you would need to know the number of five digit words in the accepted Wordle list. That number is 2,315. So you have a 2,315/26^5 chance of randomly selecting the correct answer when you randomly select a letter for each of the five letters. ~1 in 5,132.

Now, you can't enter a word not on the list during the game. So a random five letter word from the list would give you a 1 in 2,315 chance to win on the first try. If you have the list of words already used, you could increase your chance of success by substracting the number of the wordle from 2315. The wordles are numbered from the beginning and it's been said that the words don't repeat (sampled without replacement).

Excellent. Exactly the explanation I was looking for. Many thanks!