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…
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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
: 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)):
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:
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.