From the original paper hardware used for initialising and training -
Training proceeded for 700,000 steps (mini-batches of size 4,096) starting from randomly initialised parameters, using 5,000 first-generation TPUs (15) to generate self-play games and 64 second-generation TPUs to train the neural networks
and hardware used for the games - AlphaZero and the previous AlphaGo Zero used a single machine with 4 TPUs Stockfish and Elmo played at their strongest skill level using 64 threads and a hash size of 1GB.
So, AlphaZero used special hardware developed by Google. It used specialized Tensor Processor Units (TPUs) rather than general Central Processing Units (CPUs) as are available commercially.
This is how Wikipedia describes the second generation TPUs they used -
The second generation TPU was announced in May 2017. Google stated the first generation TPU design was memory bandwidth limited, and using 16 GB of High Bandwidth Memory in the second generation design increased bandwidth to 600 GB/s and performance to 45 TFLOPS. The TPUs are then arranged into 4-chip 180 TFLOPS modules
They used 4 TPUs for the games, so a processing power of 180 TFLOPS. Note TFLOPS = 1000 billion floating point operations per second.
For comparison Intel's latest most powerful chip is the Core i9 Extreme Edition processor which clocks in at 1 TFLOP. A top of the line I7 that you would find in a gaming machine would typically be about 100 GFLOPs (i.e. one tenth of a TFLOP).
I think it's fair to say that AlphaZero was using an 800 pound gorilla of a hardware configuration compared to Stockfishes mouse.
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