Even more spelling fixes

No functional change.
Clarify definition of capture_or_promotion()

No functional change.
Further simplify Bitboards init()

No functional change.
More readable init of MS1BTable[]

Because now it uses lsb(), the BSFTable[] must be
already initialized.

No functional change.
More work on Bitboards::init()

No functional change.
Research at intermediate depth if LMR is very high

After a fail high in LMR, if reduction is very high do
a research at lower depth before teh full depth one.
Chances are that the re-search will fail low and the
full depth one is skipped.

Passed both short TC:
LLR: 2.95 (-2.94,2.94) [-1.50,4.50]
Total: 11363 W: 2204 L: 2069 D: 7090

And long TC:
LLR: 2.95 (-2.94,2.94) [0.00,6.00]
Total: 7292 W: 1195 L: 1061 D: 5036

bench: 7869223
Update History and Counter move on TT hit

We already update killers so it is natural to extend to
history and counter move too.

Passed both short TC
LLR: 2.95 (-2.94,2.94) [-1.50,4.50]
Total: 52690 W: 9955 L: 9712 D: 33023

And long TC
LLR: 2.96 (-2.94,2.94) [0.00,6.00]
Total: 5555 W: 935 L: 808 D: 3812

bench: 7876473
Sync history and counter moves updating

Change updating rule after a TT hit to match
the same one at the end of the search.

Small change in functionality, but we want to
have uniform rules in the code.

bench: 7767864