When adjusting fuel control on a reciprocating engine, why is there a slight RPM rise (50-RPM rise) when pulling the mixture control to idle cutoff? Why if more than a 50-RPM rise, carburetor is set too rich?
Engine are usually run slightly richer than a stoichiometric mixture, to ensure reliable running and avoid overheating the pistons and valves. When you cut off the fuel, it goes from slightly too much fuel to none - and so it's briefly at a stoichiometric ratio.
The engine runs slightly faster at this ratio because it's not wasting energy heating up unburnt fuel.
If you see more than a 50rpm rise, it was previously running further from stoichiometric than necessary (as determined by the engine manufacturer, and many years of experience), reducing power and wasting fuel.
The idle circuit is set to be richer than necessary to help the engine run better when cold. This is because you start with prime, not a choke, so there is nothing to keep the mixture extra rich for cold running once the primer fuel in the intake has been used up.
If you don't set the idle mixture richer than necessary, the engine will die after running a few seconds at minimum idle without extra prime, unless you immediately wind the RPM up to above 1000, which is not really good on a cold engine that is just starting to get oil circulation going (I keep RPM as low as possible until there is significant oil pressure showing to indicate the main bearings are being pressurized and the cam lobes are getting splashed). The alternative is to pump the throttle to squirt fuel from the accelerator pump, or keep slowly stroking the primer to keep it running until the oil pressure is fully up and you can raise the idle RPM.
So as Robin's answer mentions, the mixture passes briefly through stoichiometric, or close to its "best power" idle mixture range as it continues to no fuel at all, causing the RPM rise.
On Marvel Schebler carburetors, there is finger screw knob at the back of the carb body below the float bowl that moves the idle jet in and out. You can reach in and turn it with your fingers. You set this knob by trial and error until you get the (roughly) 50 RPM bump in RPM when going to idle cutoff.
Some private owners will set the idle mixture at a more lean setting, to reduce lead fouling of spark plugs, without having to fuss with the mixture every time the throttle is at idle. The problem with this is, as mentioned, it's harder to keep it running on a cold morning.
My own homebuilt, with a Lycoming O-290, was set like this by the previous owner when I bought it, which I figured out after pondering why there was no RPM rise at idle cutoff, and why I needed to keep adding prime after starting on a cold day. Since I run on auto fuel now and lead fouling is no longer an issue I've restored the normal rich idle setting.