I have no idea off hand how many online guesses to any one account google or the other services will allow however that is hardly the main danger to accounts security.
Once more fool or hacker online brute force attacks are not the only or the main danger that strong passwords guard against.
Hackers getting to the hash passwords databases and then running offline attacks on the whole database of passwords is the main risk,
Adobe for example just repeat just got at least 38 millions of it customers
password hashes taken for offline attacks where many billions of guesses a second brute force attacks can and are being done to them.
If you has used a four character random number password on the Adobe sites your password would had been crack in a millisecond or so at most.
There is no reason to think that google or yahoo or any of the others will not have or even have not had their passwords files hack in the same manner as others major websites had have over the years and that are only the cases we know about.