SYNCHRONIZE

initial synchronize: [+100]

0                           100

"hey client, subtract 50 from your client tick"

0             50            100






success (no late inputs):

"hey client, subtract 25 from your client tick"

0      25     50

etc.





failure (late inputs ):

"hey client. whoops. add 25/2 to your client tick"

25    37.5    50

failure again:

"hey client. whoops #2. add 25/2/2 to your client tick"

37.5    43.75    50

etc...



So it seems that just working out the interval, and then either adding or subtracting half does the job.

Of course if network conditions change during the synchronization all bets are off.

Ideally synchronization would detect that it couldn't find a good bracket and fail the client (sync failure)

The client could interpret this as trying to synchronize again from scratch n times, or just as a failure.