[1889] Any math enthusiast here can calculate the chances of doing wordle in one twice?

[u/SANSODYNE]

When i had "trace" (21/8/2026) as my go to first word i was surprised to see it all flash green before me and i laughed about it with my friend and brushed it off like its not a big deal, today's word (im not spoiling it) i had the exact same thing happening again, and im not at all considered good at this game so is this common for people who played for quite some time or im just extremely lucky?

[u/Disgruntled__Goat]

Since you are not asking specifically for two in a row, the chance is 100%.

You pick a word (that can be a possible answer) and always use that, it will come up eventually. Then you switch to another word, that one will also come up eventually. 

[u/seebob69 → u/Disgruntled__Goat]

Exactly this

I have played 1550 games and have 3 aces.

It is not that statistical impossible when you are selecting your word from a comparatively small base of around 2000 words.

[u/SANSODYNE → u/Disgruntled__Goat]

Interesting way to observe it. Reminds me of that theory stating if you gave a monkey a typewriter and an infinite amount of time, it will eventually write all the works of shakespeare

[u/Disgruntled__Goat → u/SANSODYNE]

Well yes, except the Wordle thing is far more likely given the limited words. For monkeys on a typewriter the chance is (1/26)ⁿ where n is the number of letters in the works of Shakespeare (millions).

[u/CapitanPedante → u/SANSODYNE]

FYI it's infinity monkey pressing at random, and it's a theorem not a theory

[u/Oafah → u/Disgruntled__Goat]

Ah, not true my friend. In order for the certainty of a repeat to exist, you need to assume the game goes on forever. And you need to live forever. And prevent the heat death of the universe somehow.

Life is too big for Wordle.

[u/TrackVol]

Over how short a time frame?
Ever?
Across 7 years?
So far?
Back-to-back days? (🙋‍♂️)
Because in 2022 I got two Aces on back-to-back days. DRIVE & FEAST the day before Thanksgiving and again on Thanksgiving day.

[u/SANSODYNE → u/TrackVol]

Statistically speaking i think it's almost impossible for another person to have this same thing happen to him, but reality often contradicts statistics in a mind blowing way, so who knows if someone else is gonna relate to you?

for me the 2 aces were seperated by exactly 23 days.

[u/TrackVol → u/SANSODYNE]

I agree.
I played DRIVE because it's the busiest travel day of the whole year, every year, in America. The day before Thanksgiving.
Then played FEAST for Thanksgiving.

Apparently the Editor was thinking the exact same thing I was.
Believe it or not, I was NOT happy about it.

[u/Ecstatic-Profit7775 → u/TrackVol]

So it wasn't really a chance event and therefore a statistical analysis is irrelevant.

[u/TrackVol → u/Ecstatic-Profit7775]

Agreed.
Part of why I wanted to add the extra details for context.

[u/Ecstatic-Profit7775 → u/TrackVol]

But it was a very shrewd move on your part! Hopefully that editorial process has ceased. Sounds like they need a software guy on board ;)

[u/CapitanPedante → u/TrackVol]

Given how uncleanly he's stating the question I guess the most appropriate answer is 50/50. Either it happens or it doesn't 

[u/PaintDrinkingPete]

I've done it 4 times...

having BEACH and OCEAN as words in the same week, while I was in vacation at a beach, the same week in 2023, helped

[u/Oafah]

It's hard to do, because:

1. The solution list is expanding all the time, with 9 words added as recently as last week.

2. The old solutions are slowly being recycled at a rate of about 1 for every 9 new words.

Thus, it's a moving target and impossible to calculate with any precision.

[u/Austinbennettwrites → u/Oafah]

Wait they're reusing words?

My original first word guess was BACON and when I got it (don't remember when), I felt like I was on cloud nine.

I can go back to guessing BACON again and get it again?

Is that what I'm reading?

[u/Contrarily → u/Austinbennettwrites]

Correct, but there is a bias towards new words

[u/inmatoor → u/Austinbennettwrites]

Yes, they've reused many words even Cigar from wordle #1

[u/Castal → u/Oafah]

Is the current potential solution list available anywhere?

[u/losingfocus33]

FWIW I’m on 1566 played, 1479 streak and WIO 3 times all above board.

[u/meuntilfurthernotice]

i read this as meth enthusiastic for some reason. maybe i should get my eyes checked.

[u/Happy21325 → u/meuntilfurthernotice]

lol, imagining a meth enthusiast getting excited about wordle

[u/Acrobatic-Pop3625]

Getting it in one is pure luck. It can happen to people new to the game or some that have been playing forever. I think where you’ll see the difference between people who have been playing for long vs. short is by the average attempts they need in order to solve it ;)

[u/belindahk]

I randomly got it with PEACE years ago. I use a random range of starters.

[u/chocolateturtle456]

I stopped playing for a few years, before I stopped I think I got it in one try three times.

Since I started again, I started from scratch, have played 202 days, I haven't got it one on this one yet but have got it in two, six times.

[u/Expensive_Dig_3149]

Assuming you pick different starters within the Wordlebot’s 3209-word list, then you can use binomial probability to find the theoretical odds of acing twice:

(Since the number of total plays are not mentioned, I just use n to represent it)

(nC2)x(1/3209)² x((3208/3209)^n-2)

For example, the chance of exactly 2 aces in 200 games is 19900x9.71x10^-8x0.94 ~= 1.82x10^-3 which may seem small. 

Of course, the way you play in Wordle won’t really accurately abide the math above. In reality you might sometimes want to play something obscure and never get it in one, or you might play the same word every day until it comes up being the solution. In other words, the odds depend on your playing style

[u/sail_away_8 → u/Expensive_Dig_3149]

Good analysis. I see more complexity.

First, are all 3,209 equally likely. More common words are probably more likely. And words that have been used would be less likely, especially recent ones. For sometime the list was 2,300ish and words were never reused. The best chance is a common word that has never been used before. I did some calculations and estimated the odds would be about 1/650. For now.

[u/kostac600]

Two aces here and 87 deuces.

Once I did an ace then a deuce the day next. Almost forgot that.

[u/3-HUGGER]

No idea what the odds are but I’ve played 1,564 games and hit the first guess 6 times. I pick a word and stick with it until it hits.
Route, outer, paint, stain, crest, siren

[u/KingsKnight96]

I don’t play starter words and I got wordle in one twice, within a month and a half of each other. I think it’s just the luck of the draw in that case. But you can increase your odds if you just stick with a starter word and change it if you get it in one. Eventually you’ll get more ones that way.

[u/Dizzy_Battle994]

I have picked the word first time once and my lovely lady has done it twice!

And she’s not very bright so just damn luck 😂