Below are my 2 latest incarnations of tail cutouts. As LeeD mentioned the cutouts need to be tuned to the boards width and outline and generally as you go narrower in the tail you would reduce the cutout size or eliminate them completely. I am not an engineer and only have a fairly simplistic comprehension of the theory and have arrived where I am through that simple understanding and trial and error. Those who are way more qualified than me please jump in and call BS if anything I am saying is crap.
Planing hulls generate a higher proportion of lift from the leading edge of the planing surface and the amount of lift decreases the closer you get to the trailing edge, especially the outboard surfaces of the rear. So it makes sense to me that to get the most efficient lift to drag ratio you need to balance the width of the leading edge with that of the tail. On a pintail speed board for example you have already removed a lot of surface area from rear of the board with the narrow tail so are less likely to need cutouts at all to get the lift drag balance optimised. Wider boards though and especially wide tailed boards designed for lighter winds where you want the tail width to enable larger fins and bigger sails, you can get noticable top speed gains with cutouts by removing surface area from that low lift area of the board. It is worth remembering though that although the board is producing less lift from the rear end of the planing surface it is still producing some lift so cutouts will impact the way the board trims. So for me that has been where the bulk of the trial and error has been, tuning the tail cutout size and shape along with the outline with the aim of getting the right balance between lift, drag and board trim. Strap placement and mast track position along with rocker all come in to the equation so it gets very complicated and you can really screw up.
What is the perfect cutout shape????? I am sure lots of people have strong opinions on that and I am not even going to try and go there. What I am currently doing appears to work great on my boards and as I always have I will continue to learn something every-time I try a variation. It's all good fun.