it does sound like not enough fuel (compared to the amount of air) is getting through the carburetor and into the engine.
The closed choke restricts air intake and "corrects" the mixture.
So, if fuel is now getting into the float bowl, the thing to check for is a clean float bowl and that the main jet's hole is open and clear. A tiny bit of floating crap will get sucked up and partially clog that jet..
Lean = lots of air compared to fuel..
Rich = less air or more fuel in the mix.. same difference..
A 1:10 (fuel:air) means 1 pound of fuel to 10 pounds of air. (it's measured by weight .. a lot of air weigh quite a bit..)
A 1:3 mixture is much richer than above.. (only 3 pounds of air instead of 10 pounds of air is mixed with that same 1 pound of fuel.)
1:14 ... this is leaner than both the others.. a larger amount of air (14 pounds) is being mixed with that same 1 pound of fuel
When starting the engine needs a very rich mix, like 1:2 or 1:3.
Idling requires less fuel and more air (leaner) like 1:8 or so. Normal running is leaner still.. somewhere around 1:13.