I am a crypto miner hobbyist, and I am trying to mine this coin called duino coin with my arduinos, and I was wondering if there is just a general way to make arduinos run faster. I am working with an Arduino uno, and 2 nanos. Just wondering, and any help is greatly appreciated.
- Not going to happen.
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No, not substantially.
OK, so as I understand, the DUCO concept favors the slow, old-skool Arduino's like the ones you've got there. The ones you have are based on an ATmega328P controller, running at 16MHz. You could make a custom board using the newer ATmega328PB and clock it at 20MHz. It'll be 25% faster than your present Nano/UNO. If you're feeling really adventurous, you could even try to overclock it by getting some faster crystals and see how far you can push it. Maybe you can eek another 10-20% of performance out of it.
The cost in components and electricity required to build these custom boards are likely never going to be recouped by mining coins. And you're likely not the first one to try this approach, either. But it can be fun, I suppose.
Thank you for the much more informative answer. 
There is a maybe yes. If you can switch to an ESP32 it is a lot faster and from your side the coding is about the same, Speed (throughput) depends a lot on the code as well as processor speed.
Further, if you can use a device with built in WiFi you won’t need a host.
Yes, indeed, but I suspect the algorithm penalizes the use of an inherently faster core. It's hard to find concrete info on this, but it's implied on the GitHib pages of DUCO.
Some of the parts have two cores, that should get past that problem, if not modify the algorithm.
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