1RB1RA 1LC0RE 0LF1LD 1LA1LC 1RA1RB ---0LD

1RB1RA_1LC0RE_0LF1LD_1LA1LC_1RA1RB_---0LD (bbch) is a halting BB(6) TM which runs for around $10^{15713}$ steps and achieves a sigma score of around $10^{7857}$.

Analysis by Shawn Ligocki:

B(a, b) = $ 101^a 10^b <C 1^3 $

B(0,   3b)    ->  Halt(8b+4)
B(a+1, 3b)    ->  B(a,   4b+5)
B(a,   3b+1)  ->  B(a+1, 4b+2)
B(a,   3b+2)  ->  B(a,   8b+10)

Start  --(13)-->  B(0, 2)

This performs an unbiased pseudo-random walk. Unbiased random walks have 100% chance to return to 0. This TM eventually does, but only after 34,821 iterations (reaching $a=162$).

Code/Quick_Sim.py 1RB1RA_1LC0RE_0LF1LD_1LA1LC_1RA1RB_---0LD -n6 --print-loops=100_000
...
Steps:    ~10^15_713.71342
Nonzeros: ~10^7_857.11327