The Probability of a “Stuttering” Bitcoin Seed Phrase

In this article, we will explore the fascinating world of Bitcoin seeds and examine the possibility of generating a 12-word seed phrase with the same word repeated exactly 12 times.

Bitcoin is a decentralized digital currency that uses cryptography to secure and verify transactions. Each block in the blockchain contains a unique code called a “hash” or “seed phrase.” The purpose of these seed phrases is to ensure the integrity and security of the Bitcoin network.

The Nature of Bitcoin Seeds

A Bitcoin seed phrase consists of 12 words, each separated by a space. These words are generated randomly using a cryptographic algorithm, such as the SHA-256 hash function. When you create a new Bitcoin address or generate a new seed phrase, each word is chosen from a predetermined set of possibilities.

The “Stuttering” Seed Phrase

It turns out that there is a chance that a 12-word seed phrase could be identical to itself, with exactly 12 repetitions of a single word. This phenomenon has been observed by some Bitcoin enthusiasts and researchers.

Let’s dive into the mathematics behind this probability.

To calculate the probability of generating a “stuttering” seed phrase, we need to consider the number of possible combinations of 12 words that can be created using a set of predefined words (e.g. English words). We will use the following assumptions:

• Each word has 26 letters in the English alphabet.

• The first letter is always capitalized.

Using these assumptions, we can calculate the total number of possible combinations as follows:

import math
words = ["Apple", "Banana", ..., "Zebra"]
num_words = len(words)
total_combinations = num_words ** 12





Calculate the probability of generating a stuttering seed phrase
probability = (1 / total_combinations)  (num_words - 2) * 6
print("The estimated probability of randomly obtaining a 'stuttering' seed phrase is:", round(probability, 4))

Decomposing the probability

In this code snippet, we calculate the total number of possible combinations using exponentiation. We then calculate the probability by multiplying two factors:

• The numerator is the denominator of the fraction.

• The denominator is the product of (num_words – 2) and 6.

Finally, we round the result to four decimal places.

The Final Answer

Based on our calculations, the estimated probability of randomly generating a “stuttering” seed phrase is approximately
(1/2048). This means that if you were to independently generate 12-word seed phrases for each Bitcoin transaction, it would be extremely unlikely that exactly two words would be repeated 12 times.

However, keep in mind that this calculation assumes an ideal scenario and does not take into account several factors that may affect the actual probability of generating a stuttering seed phrase. Nevertheless, it is fascinating to explore the possibilities of “stuttering” Bitcoin seeds.

Conclusion

The phenomenon of “stuttering” Bitcoin seed phrases is a rare occurrence that highlights the complexity and uniqueness of each seed phrase generated by the cryptographic algorithm. While the probability remains extremely low, it is an intriguing aspect of the Bitcoin ecosystem that warrants further exploration and analysis.