"does that mean that it is possible to design a single best kdice-playing robot?"
Well, purely theoretical, yes, that should be possible, at least for a kdice with 2 players. The entire game-tree and the odds for certain events are known.
However, first of all, this tree is simply immense, too big to search through completely. And secondly, it contains loops, which may be difficult to evaluate (although I expect that most of them become infinite series as in this 2vs2 example).

I've been messing around with creating an expectiminimax AI (basically minimax on a chance-based game) and even on simple boards (2x2 or 4x1) with 2 players searching only 2 turns ahead will take a significant amount of time. So practically speaking I'd say a perfect AI is near impossible.

But I am really interested in how well kdice players understand these statistics. From seeing how non-trivial the solution to the 2vs2 problem is, I expect that there might be similar intricacies in for example fighting the 8vs8 endgame (or even the question whether stacking up for the 8vs8 endgame is optimal).
Sadly though, in it's current form Kdice hardly rewards smart players, any statistical advantage can easily be overthrown by social context.
Having a 2 player kdice would allow to see who really plays better, but it would probably require tens or hundreds of games to get a reliable result.

I meant complete information. Perfect information is what you would get from a psychic who forecasts the weather. The expected value of perfect information is the difference between its value and the value of the information we currently have.

the brain and Vermont:

If a strategy incorporating randomness is in the universe of complete information, it would have to be considered in the proof for the 2 v 2 case. But I have redone my math for a probabilistic strategy in the 2 v 2 case and I find a corner solution (p1 > 1), regardless of what probability Player 2 might select in regard to a 2 v 3 attack if Player 1 chooses to attack. But there might be other more complicated situations with interior solutions.

"Perfect information is what you would get from a psychic who forecasts the weather."

Not in the context of game theory, which if we actually want to analyze kdice the way you're talking about, is what we'd use.

It has to be considered, but that doesn't make it valid. Again, if there is a play this will net the win 55% of the time, you make that play always and your score goes up. Making it only 44% of the time (means your score would not be as high.) This is pretty straightforward. The type of probabilistic play you're talking about using is applicable in incomplete information games, but not here, unless you can predict the die rolls.

Wow, that was a grammatical mess. Where is that edit post button?

Vermont:

It looks like we have come to agreement on three things:

1. Perfect information does not apply to game theory.

2. Probalistic strategies have to be considered in a proof, but we have not yet identified an interior solution probablitistic strategy.

3. It would be nice if we had an edit post function.

A probablistic strategy would only occur if at some point there is a choice between a set of actions which will all lead to the same payoff.

But this is only true if you are playing an optimal opponent (which is a common assumption in most AI's). If you want to maximize against a given probablistic opponent, then yes, you need to consider it.

For example, if I knew I was playing someone who would let me build up to 8+6 then attacking 2vs2 is not the best choice since I can gain a 1.3% chance of winning. But the optimal strategy in a general case (regardless of opponent) will garantuee me at least 64.1% chance of winning.

joke off then

I would flag for 2nd and take my dom.