Unable to reproduce the issue on windows-7, Mac-10.11.6 and linux Ubuntu 14.04 using chrome stable version 54.0.2840.99 and latest canary 56.0.2919.0 and reported version 54.0.2840.71.
Please find the attached screen-cast and could you please let know anything missed here to reproduce
the issue.

Thanks..

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Most inputs are stable, but not all.
c -> calendar.google.com
ch -> chromiumbugs.appspot.com
chr -> chrome-extension://abcdef
chrom -> chromecast
chrome -> chrome

I expect there to be the same suggestions for "ch", "chr", "chro" and "chrom" if the suggestion is chromiumbugs.appspot.com since all of those are prefixes, typing the next suggested character.

Version 54.0.2840.71 m (64-bit) Windows 10

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Here's what I get when I type "chromiumbugs", intending to go to chromiumbugs.appspot.com. Sometimes adding another character leaves no suggestion at all, even though it clearly knows about the site since it suggests it with both fewer and more characters. 

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Why "chromiu" gets no suggestion at all is beyond me. The other ones are common search terms (but the result should still be stable).

The reason you're not getting any suggestions is that you're running a fresh browser. Try visiting some of the links I mentioned, like http://chromiumbugs.appspot.com/ and search for the same terms I've searched for, then try again. 

I'd guess something like this would reproduce:
1. goto http://chromiumbugs.appspot.com/
2. search for "chromecast"
2.1 possibly install a chrome extension and visit it multiple times

3. repeat steps 1,2 until the browser learns that you frequently do these actions
4. type "chrome" and observe results

Is there some local database of previous searches used for suggestions that I could mine?

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Thanks for the reply.

Tested the issue as per Comment#2,3,4 & 5 on Windows 7 with chrome stable version#55.0.2883.87 and latest Canary-57.0.2963.0. Observed common search items for "ch", "chr", "chro" and "chrom" if the suggestion is chromiumbugs.appspot.com as per the expected behaviour in Comment#2.

Please find the attached screencast for reference & let us know your observations.

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Omnibox suggestions are based on the frequency of navigation from any given sequence of characters to the final URL (e.g. by direct selection from the dropdown list). So having different outcomes for "c", "ch", "chr", "chro" is expected.

fille@, the database can be viewed via chrome://predictors/

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