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Isn't the probability of generating all types of wallet addresses the same? What makes this pattern different or even “impossible” if the function is the same for everyone?

Ps: Don’t worry, the link here helped.

It’s not impossible, it’s just that the number space is so enormous that it’s exceedingly unlikely that it will ever be found: every random private key you generate will map to one of 2160 possible P2PKH addresses.

Also see, Bitcoin Stack Exchange Is each Bitcoin address unique?

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