So, now that you have rapidly charged your supercapacitor from https://hackaday.io/project/174806-supercapacitor-rapid-charger
What are you going to do with it? Replace the batteries in your favorite wireless game controller! Why? because you can charge and discharge the supercapacitor at least 500 000 times!
So, here is the picture of the project below. The 450F supercapacitor is on the left, the DC/DC controller is the perfect purple PCB in the middle (to go from 0.6~3V, to 3V needed for the controller), and runnin' with the hood off is the Wii controller.
The game controller uses about 125 mW, so with 450 F, you can get a few hours of gaming. Here are the envelope calculations: the energy available is approximately 0.5 * 450F * ((3V^2) - (0.6V^2) = 1944 J. At 0.125 W, that means ~15000 seconds of run time (not taking into account the changing efficiency of the converter).
Here is a detailed picture of the DC/DC converter. The component is U1 (Torex XCL103D with the 3V output). Yes, it is that tiny! The inductor is included in the package.
That's it. There is nothing else. It is that simple to interface the capacitor to the controller.
When the supercapacitor discharges down to ~0.6V, the DC/DC converter shuts down, and the Wii automatically pauses since the controller lost contact. So, then take a bathroom break while the supercapacitor recharges (2~3 minutes). :)