The state diagrams show that  sequence detectors do not necessary fall back to the initial (reset) state whenever wrong symbol is recepted. 110 stays at stage 11 and, thus, detects the pattern as soon as 0 arrives whereas detector of 111 must start over if any 0 arrives. This makes 110 to appear more likely in the stream. The diagram was created intentionally for illustrating the w:Gambler's fallacy, after https://jliszka.github.io/2013/08/12/a-frequentist-approach-to-probability.html using Finite State Machine Designer.
Own work
Javalenok