There is still a disconnect here as we are talking about two different things. Forget I ever mentioned botnets for a moment. Your proposed system is highly ineffective if I wanted to setup 3 computers so I can play a 6 player game with 3 out of the 6 players at the table being accounts under my control. I could then use that to my advantage in a non-obvious way that is hard to detect.
That means you need to either rent or own the physical hardware, tho - that is expensive. Compare that to regular online poker, where you can just rent a VPS farm very cheaply, because online poker bots don't need 100% cpu, which will get your VPS shut down by the hosting company.
True, but I still think it is ineffective towards multi-accounting. I think you need layers that make the most effective solution. Otherwise, the poker network will be seen as being shady. Social identity confirmations, web of trusts, and certificate authorities should be used in conjunction to computationally extensive identities IMO. All except computationally extensive identities could be
optional, but there would be a way for people to tell who have successfully identified through what types. If someone doesn't want to play against someone that hasn't been through the identification process then they shouldn't. I suggest we leave it up to the players to make this decision for us, but build in the tools for them to choose.
Back to your idea. I had thought about computationally secure identities, but not the way you suggested with continual PoW instead of simply generating a computationally intensive identity hash. So, that brings forth a couple more challenging problems. Mental poker protocols require some extensive CPU usage. I think it would be better to have the PoW done with a GPU-mine-able algorithm. One thing that is puzzling me though... how would you be able to tell if someone is actually mining in a transparent and provable way? Some people may want to mine with a pool, how do we stop them? If the network gets popular with a lot of players, then it may take solo miners forever to find blocks. Also, I was planning on using DPoS to utilize the efficiency, smart coins, electable witnesses, etc... How would you tie that into a PoW scheme?
Just some initial thoughts. Sorry if it seems like I'm being tough on you. This is the way I want people to do to my ideas too... tear them apart to get the best design possible! I appreciate you taking the time monsterer.