Wordle thread

Tunadog

All-Conference
Nov 30, 2015
299
3,422
93
Sorry, I can't help that I'm so lucky at picking first words.
Wordle 1,898 2/6

🟩⬜🟨🟩🟨
🟩🟩🟩🟩🟩
 

hawkeyetraveler

Heisman
Aug 10, 2010
6,538
25,907
108
Awfully defensive. And tl;dr I am directly saying you almost certainly cheated to get 14 hole in one’s over 1,150 games - Gemini says the odds of getting 14 of them is twice as lucky as winning the powerball. So while I can’t say for certain you have cheated in our tourney…it is awfully suspicious.

Below is the detailed AI analysis of your statistics…
_______

Me to Gemini: “what are the odds someone gets 14 hole in one’s over 1,150 games played”

Gemini:

To calculate the probability of getting 14 "hole-in-ones" (solving the puzzle on Guess 1) out of 1,150 Wordle games, we look at how Wordle's answer selection works.

The Underlying Probability​

Wordle uses a curated list of non-obscure 5-letter words as solutions. While the original set contained 2,309 solution words, The New York Times currently curates an updated list of roughly 2,300 potential solutions.

  • Probability per random guess (p): 23001≈0.00043478 (or roughly 0.0435% chance per game if picking a random eligible word as an initial guess).
  • Number of trials (n): 1,150 games.
  • Number of successes (k): 14.

Method 1: Statistically Fixed Starting Word​

If a player uses the exact same valid starting word every single day without changing it, each daily solution is selected without replacement from the remaining set (or uniformly at random across the valid list). Over 1,150 games, the probability of hitting the target word on Guess 1 exactly 14 times follows a Binomial Distribution:

P(X=k)=(kn)pk(1−p)n−k
Plugging in the parameters:

  • (141150)≈6.476×1030
  • (0.00043478)14≈1.258×10−47
  • (0.99956522)1136≈0.6101
P(X=14)≈4.97×10−17
Odds of hitting exactly 14 hole-in-ones with a fixed word:

  • 1 in 20.1 quadrillion (or about 0.00000000000000497%).
If calculating the odds of getting 14 or more hole-in-ones (P(X≥14)):

  • 1 in 19.8 quadrillion.

Method 2: Random / Varying Starting Words​

If a player changes their starting word every day at random without keeping track of previously used solutions, the trials remain independent with p≈23001, yielding virtually identical odds (~1 in 20 quadrillion).

Method 3: Using Previous Knowledge / Historical Tracking​

If a player deliberately avoids starting words that have already appeared as answers in past Wordle games, the pool of potential solutions shrinks by 1 each day:

  • Game 1: p1=23001
  • Game 1,150: p1150=11501
Across 1,150 games using perfect historical elimination:

  • Average probability per trial (pˉ): ≈17251≈0.0005797
  • Binomial calculation with pˉ=0.0005797:
P(X=14)≈6.42×10−15
Odds using optimal historical elimination:

  • 1 in 156 trillion.

Contextual Context​

  • Pure luck (fixed word): 1 in 20,100,000,000,000,000 (20.1 quadrillion).
  • Optimal strategy (tracking past answers): 1 in 156,000,000,000,000 (156 trillion).
For perspective, the odds of winning the Powerball jackpot twice in your lifetime are about 1 in 85 trillion. Getting 14 Wordle hole-in-ones out of 1,150 games purely by chance is roughly twice as rare as winning the Powerball jackpot twice.

Unless the player has access to future answer lists, external spoilers, or site source code, achieving 14 hole-in-ones in 1,150 games is statistically improbable to the point of being practically impossible by random chance.
 

FLaw47

All-American
Dec 23, 2010
3,866
5,466
113
Awfully defensive. And tl;dr I am directly saying you almost certainly cheated to get 14 hole in one’s over 1,150 games - Gemini says the odds of getting 14 of them is twice as lucky as winning the powerball. So while I can’t say for certain you have cheated in our tourney…it is awfully suspicious.

Below is the detailed AI analysis of your statistics…
_______

Me to Gemini: “what are the odds someone gets 14 hole in one’s over 1,150 games played”

Gemini:

To calculate the probability of getting 14 "hole-in-ones" (solving the puzzle on Guess 1) out of 1,150 Wordle games, we look at how Wordle's answer selection works.

The Underlying Probability​

Wordle uses a curated list of non-obscure 5-letter words as solutions. While the original set contained 2,309 solution words, The New York Times currently curates an updated list of roughly 2,300 potential solutions.

  • Probability per random guess (p): 23001≈0.00043478 (or roughly 0.0435% chance per game if picking a random eligible word as an initial guess).
  • Number of trials (n): 1,150 games.
  • Number of successes (k): 14.

Method 1: Statistically Fixed Starting Word​

If a player uses the exact same valid starting word every single day without changing it, each daily solution is selected without replacement from the remaining set (or uniformly at random across the valid list). Over 1,150 games, the probability of hitting the target word on Guess 1 exactly 14 times follows a Binomial Distribution:

P(X=k)=(kn)pk(1−p)n−k
Plugging in the parameters:

  • (141150)≈6.476×1030
  • (0.00043478)14≈1.258×10−47
  • (0.99956522)1136≈0.6101
P(X=14)≈4.97×10−17
Odds of hitting exactly 14 hole-in-ones with a fixed word:

  • 1 in 20.1 quadrillion (or about 0.00000000000000497%).
If calculating the odds of getting 14 or more hole-in-ones (P(X≥14)):

  • 1 in 19.8 quadrillion.

Method 2: Random / Varying Starting Words​

If a player changes their starting word every day at random without keeping track of previously used solutions, the trials remain independent with p≈23001, yielding virtually identical odds (~1 in 20 quadrillion).

Method 3: Using Previous Knowledge / Historical Tracking​

If a player deliberately avoids starting words that have already appeared as answers in past Wordle games, the pool of potential solutions shrinks by 1 each day:

  • Game 1: p1=23001
  • Game 1,150: p1150=11501
Across 1,150 games using perfect historical elimination:

  • Average probability per trial (pˉ): ≈17251≈0.0005797
  • Binomial calculation with pˉ=0.0005797:
P(X=14)≈6.42×10−15
Odds using optimal historical elimination:

  • 1 in 156 trillion.

Contextual Context​

  • Pure luck (fixed word): 1 in 20,100,000,000,000,000 (20.1 quadrillion).
  • Optimal strategy (tracking past answers): 1 in 156,000,000,000,000 (156 trillion).
For perspective, the odds of winning the Powerball jackpot twice in your lifetime are about 1 in 85 trillion. Getting 14 Wordle hole-in-ones out of 1,150 games purely by chance is roughly twice as rare as winning the Powerball jackpot twice.

Unless the player has access to future answer lists, external spoilers, or site source code, achieving 14 hole-in-ones in 1,150 games is statistically improbable to the point of being practically impossible by random chance.

I think that his long-term statistics are a lot more concerning, to be honest. I can't say that I've checked behind him to confirm that his 3.22 average is correct, but my understanding is that a 3.4 is about the mathematical floor for what optimal play will net you over a long horizon, so having a 3.22 over three years is incredibly suspicious.
 

scotchtiger

Heisman
Dec 15, 2005
135,270
23,494
113
I think that his long-term statistics are a lot more concerning, to be honest. I can't say that I've checked behind him to confirm that his 3.22 average is correct, but my understanding is that a 3.4 is about the mathematical floor for what optimal play will net you over a long horizon, so having a 3.22 over three years is incredibly suspicious.

I could see someone cheating for a tourney, but who the hell does it for personal stats over 3+ years? It’s just odd.

I haven’t played a fraction of you guys (just started this year and this thread), but I’ve never had an ace or close to it. Only one eagle. Hell I just got more thoughtful about my opening word at the turn in this tourney.
 
Dec 4, 2001
5,733
18,778
113
I think that his long-term statistics are a lot more concerning, to be honest. I can't say that I've checked behind him to confirm that his 3.22 average is correct, but my understanding is that a 3.4 is about the mathematical floor for what optimal play will net you over a long horizon, so having a 3.22 over three years is incredibly suspicious.
Optimal play indeed. If you count your total failures as a 7 and count them in, my long term average is 4.28. If you just count up the holes without total failures mine is 4.18. I like to think I’m pretty good, but recognize there are better players. With that being said, his stats are preposterous.
 

FLaw47

All-American
Dec 23, 2010
3,866
5,466
113
I could see someone cheating for a tourney, but who the hell does it for personal stats over 3+ years? It’s just odd.

I haven’t played a fraction of you guys (just started this year and this thread), but I’ve never had an ace or close to it. Only one eagle. Hell I just got more thoughtful about my opening word at the turn in this tourney.

My nice version of this is that he doesn't consider whatever he's doing to be cheating.
 
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