How fast could AlphaGo mine bitcoins? This question resulted out of a shower thought. In my naive understanding, both, training neural networks and mining bitcoins require a lot of math crunching that is best offset to ASICS and GPUs. AlphaGo is powered by a lot of horse power, but more importantly by a lot of custom ASICS. 

According to Wikipedia, one Tensor processing unit currently clocks in at 180 TFLOPS. The latest AlphaGo version used 1920 CPUs and 280 GPUs to run it's neural network. (The hardware it was trained one is likely a number of times larger than that)

Assuming you would task that cluster to mine bitcoins instead of powering a neural net. At which rate could it mine bitcoins and would it be profitable?
As you said, AlphaGo is "just" a collection of CPU's and GPU's. CPU's can mine at a few dozen megahashes (millions of hashes) per second. GPU's can mine at several dozen gigahashes (billions of hashes) per second. ASIC miners mine at several terahashes (trillions of hashes) per second. So a miner is a 100 to a 1000 times better/faster than a GPU which is a 100 or a 1000 times better/faster than a CPU.

So mining with AlphaGo would be insignificant. You would be better off with even one ASIC miner. If mining with CPU and GPU farms was profitable, people wouldn't bother with ASIC's.