Question about uniqueness of keys/addresses in different derivation paths

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Question about uniqueness of keys/addresses in different derivation paths

I've been trying for the past few weeks to recover some ethereum that I forgot I had. It's a pretty significant amount (5 figures USD). Trouble is I only know the addresses right now. I don't remember what wallet/service they were associated with. I do have a bunch of mnemonic recovery phrases for various coins (most of which are poorly labeled or not labeled at all because I am great at keeping records, obviously).

Recently I was using Ian Coleman's Bip39 tool to check some recovery seed phrases with various derivation paths, and for a second I thought I had found one of the relevant addresses/Private keys, but it turned out to just be a close match. For example if my target address started with 0x12345abXXXXXXX… the address I found was 0x12345baXXXXXXX (XXX characters are where the similarities end)

So my question is, is that just bad luck/crazy coincidence? Or could it be that addresses generated by the same seed can be similar to others at different derivation paths for some mathematical reason I don't understand? Also, if the answer is the former, what is the probability of that happening (roughly)?

I have tried researching this but haven't been able to find any info related to this specific type of thing (none that I have been able to understand or recognize, at least).

If anyone here can shed some light on this for me I would very much appreciate it.

Thank you for your time.

submitted by /u/ibearbadnews
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