I am actually a big proponant of choils, for a couple of reasons.
First for the newbie - the choil is the semi - circular cutout in the
blade, generally coming right to the cutting edge. They can be quite
small, as in the gents knife shown, or large enough for the full
finger to set in, as in several of the pictures.
In addition to the advantages described for the big choils, any choil
eliminates a stress riser in the steel between the bevel of the edge
and the full width ricasso. Particularly if you are a maker with a
zen for nice sharp grind lines in the bevel, you essentially have a
90 degree angle between the blade bevel and the ricasso that has the
sharpened edge at one point. Particularly after heat treating this
is a point prone to stress risers, and can crack under high stress or
extremely cold conditions. The choil allows for a smooth transition
from the sharpened edge of the blade to the full width of the riccaso.
The other option for a choilless knife to eliminate the stress riser
is to have a rounded grind forming the bevel. However, as was
previously mentioned, you don't get a well defined start of the blade
edge and it is hard to sharpen back in that area.
Generally, I find a knife not to be complete without some way to
eliminate that stress riser, and most typically that is done with a
choil.