Quote from: jl777 on May 15, 2016, 03:41:06 AM

Quote from: hhanh00 on May 15, 2016, 02:38:28 AM

The first 1 comes from the address version and is always there for a normal bitcoin address. Every other 1 requires a byte equal to 0 is the pub key hash.
- 11: 1/2^8 = 1/256
- 111: 1/2^16 = 1/65536
- 1111: 1/2^24
etc

are you sure?
It seems base58 would have a 1/58th chance for a '1'

Base58 conversion always preserves leading 0 bytes by directly encoding them as a "1" at the start of an address. This is the reason all standard Bitcoin addresses start with 1, because of the hard-coded network ID byte of 00 for Bitcoin.

A byte can store a value 0-255; the chance that the next byte (the first digit of the hash) is also 0x00h is 1 in 256, and so on.

The Bitcoin address in it's native binary form (that you never see) is 25 bytes, it's parts are:
byte 0: Network ID Byte (0x00 for main bitcoin network)
byte 1-20: ripemd160 hash (20 bytes) of sha256 hash (32 bytes) of 0x04+public key (65 bytes)
byte 21-24: checksum: first four bytes of sha256 hash of sha256 hash of bytes 0-20 above

Only after the leading byte preservation is the address then put through Base58-encoding.

The other non-related "answers" seen in this thread are also wrong: because the largest Bitcoin address (all FFFFs for the hash plus checksum) is 1QLbz7JHiBTspS962RLKV8GndWFwi5j6Qr, there are strange address probabilities. The chance of an address starting with characters 12 - 1P is about 1-in-23; an address starting 1R-1z must be a 33 character or less address, and chances are 1-in-1353. As we now know, starting in 11 is 1-in-256.