TLDR; According to GPT O1, assuming a Gaussian distribution, you need 0.0105 BTC to be in the top 0.1%. However, if we add other "more realistic" assumptions on distribution, you need 10 BTC to be in the top 0.1%

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To determine how much Bitcoin you need to hold to be in the top 0.1%, 1%, and 10% of Bitcoin holders globally, we can model the distribution of Bitcoin holdings using a Gaussian (normal) distribution. Here's a comprehensive analysis based on the given assumptions:

Assumptions

• Total Bitcoin Supply: 21,000,000 BTC
• World Population: 8,000,000,000 people
• Distribution Model: Gaussian (Normal) Distribution

Calculating the Mean Holding

First, calculate the average (mean) Bitcoin holding per person:

Mean(μ)=Total Bitcoin/World Population=0.002625 BTC per person

Determining the Standard Deviation

In a Gaussian distribution, the mean and standard deviation (σ) define the spread of the data. However, the total Bitcoin supply constrains the distribution. For simplicity, we'll assume that the standard deviation is equal to the mean:σ=μ=0.002625 BTCσ=μ=0.002625 BTC Note: This is a simplification. In reality, Bitcoin holdings are likely more skewed, but for the purpose of this calculation, we proceed with this assumption.

Calculating Bitcoin Holdings for Top Percentiles

Using the properties of the normal distribution, we can determine the Bitcoin holdings required to be in the top 0.1%, 1%, and 10%.

Top 0.1%

• Z-score for 99.9th Percentile: ≈ 3.09
• Required Holdings:

x=μ+zσ=0.002625+(3.09×0.002625)≈0.0105 BTC x=μ+zσ=0.002625+(3.09×0.002625)≈0.0105 BTC

Top 1%

• Z-score for 99th Percentile: ≈ 2.326
• Required Holdings:

x=μ+zσ=0.002625+(2.326×0.002625)≈0.0087 BTC x=μ+zσ=0.002625+(2.326×0.002625)≈0.0087 BTC

Top 10%

• Z-score for 90th Percentile: ≈ 1.282
• Required Holdings:

x=μ+zσ=0.002625+(1.282×0.002625)≈0.00599 BTC x=μ+zσ=0.002625+(1.282×0.002625)≈0.00599 BTC

Summary of Required Bitcoin Holdings

Conclusion

Under the assumption of a Gaussian distribution of Bitcoin holdings across the global population:

• To be in the top 0.1%, you need to hold approximately 0.0105 BTC.
• To be in the top 1%, you need to hold approximately 0.0087 BTC.
• To be in the top 10%, you need to hold approximately 0.0060 BTC.

A more realistic model:

Given the skewed distribution, the Bitcoin needed to be in specific percentiles increases significantly compared to the Gaussian model.

• Top 0.1%:
  • Estimated Holdings: ≈ 10 BTC
• Top 1%:
  • Estimated Holdings: ≈ 1.133 BTC
• Top 10%:
  • Estimated Holdings: ≈ 0.1 BTC