User blog comment:WaxPlanck/Busy Beaver Number Lower Bounds/@comment-5529393-20171117032831

It doesn't work like that. TM's act in a deterministic manner on a blank input, so Wythagoras's TM will always get between f_{w+1}(10) and f_{w+1}(11) ones.

There are two stages in Wythagoras's TM; the first stage is the set up the proper input, and the second stage is the run that input using an algorithm with an expandal growth rate. The first stage sets up 111__111111111111; it then runs that input on the second stage. If you ran it for 11,078 steps,  then it was already into the second stage.