If Consistency is weakened to eventual, then either you have no defined Consistency (i.e. no Consistency ever) or you have an equation for probability of Consistency. If there exists such an equation, then you have to explain how and the probability of either Availability of Partition tolerance is lost when the probability of Consistency is attained. The onus is on your to justify these claims analytically, including convincing arguments about the game theory. Else you can just put it into the wild and observe (and who knows what will happen).
I don't agree with the red part, it's impossible to have an equation for probability (has anyone ever had it?) because it depends on network topology which is infeasible to measure (it even changes every minute).
Consistency in Bitcoin is the fact that the objectivity is the longest chain. There only state of inconsistency is the probability of an orphaned chain, which declines over time except if the adversary has greater than 50% of the sustained network proof-of-work hashrate.
Bitcoin has eventual consistency, probability of an orphaned chain has nothing to do with it unless you consider the case of spherical Bitcoin in vacuum.
Availability in Bitcoin is given by even if there are no other active nodes, then sender and/or recipient of the transaction can extended the longest chain and the Consistency remains valid (except for the caveat of the 51% attack).
Availability in Bitcoin is nine nines, ability to extend the longest chain is irrelevant there.
Partition tolerance is lost in Bitcoin because if there is network partitioning then double-spends can occur on each chain without being detected until these chains are merged. Bitcoin can't tolerate multiple chains, and only allows the longest chain. There is no way to merge these chains, because double-spends can infect other downstream transactions, combined with inputs from legitimate transaction graphs.
Partition tolerance in Bitcoin is pretty high, this is achieved with the help of coinbase maturity parameter, if it was set to zero we would see more transactions not reincluded into the longest chain after a reorg.
So what we can say is Bitcoin fulfills the CAP theorem, except it has theoretically unnecessary caveats in Consistency due to 51% attack and delay due to probability of orphaned chains. The Consistency delay also causes transaction confirmation to be significantly delayed. The goals of my Sync (or BlocSync) block chain overhauled design has been to eliminate those caveats, while relaxing the Consistency and/or Availability during partitioning of the network in order to provide some Partition tolerance.
51% attack is an attack for another case of spherical Bitcoin in vacuum. Ittay Eyal and Emin Gun Sirer
showed that Bitcoin can be successfully attacked even with 33%/25% of hashing power.
PS: Looks like we are NOT on the same page. I suggest to spend one day to come to a common denominator of our points of view and after that continue discussion about tangle and CAP.