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Probability of typing a wrong Bitcoin address

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I heard someone say that Bitcoin is dangerous because you could easily make a typo when entering an address, sending money to the wrong person, and have no recourse. There are dangers associated with Bitcoin, such as losing a private key, but address typos are not a major concern.

Checksums

There are several kinds of Bitcoin addresses. Each is at least 20 bytes (160 bits) long, with at least 4 bytes (32 bits) of checksum. The chances of a typo resulting in a valid checksum are about 1 in 232.

Used addresses

Let’s ignore the checksum for this section.

Because addresses are formed by cryptographic hash functions, we can assume the values are essentially randomly distributed in the space of possible addresses. The addresses are deterministic, but for modeling purposes, random is as random does.

This means a typo of an actual address is no more or less likely to be another actual address than an address typed at random. This is unlike, say, English words: a mistyped English word is more likely to be another English word than random keystrokes would be.

There have been on the order of a billion Bitcoin addresses used, in a space of 2160 possibilities. (Actually more since some addresses have more than 160 bits.) There’s about a 1 in 1039 chance that a random 160-bit sequence corresponds to an address somewhere on the Bitcoin blockchain.

Addresses close in edit distance

Someone with the Caesarean handle Veni Vidi Vici on X asked

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