I agree with the brain, a 2 player version of kdice would be great. Pure tactics, no diplomacy. And it's already coded in the tournaments. There should just be opened for 2 player tournaments, buy-in 500, winner takes all. Like in poker.

Another thing I have been thinking a little about is the full-stacked 1v1 endgame. Is it good to 7v8 sometimes, is it good to take weak neutrals, etc.

1. Perfect information does not apply to game theory.

- I'm not sure if you're being sarcastic or just misunderstood what I was saying, but it definitely does apply to game theory: http://en.wikipedia.org/wiki/Perfect_information

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

- You can consider them, but they would be rejected. I've already explained why. As a simple example, if you know the best move in a checkers game (which you could, since it has been solved,) making it only a certain percentage of the time would decrease your odds of winning. This does not change just because kdice involves die rolls.

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

-What, like any other forum? Craziness!

Having this first mover advantage, i should move first, right? And attack from round one.

If this is not the right answer, then i say... wait till this discussion is long enough... send him the link... let him read it till he lags out... hit end turn and then win... you still reading this? you lagged out.. you dont even need go back and double check... you loose...

"if you know the best move in a checkers game (which you could, since it has been solved,) making it only a certain percentage of the time would decrease your odds of winning."

Depends on the opponent. If a computer only played one move for every position, then a 'draw game' could be memorized even by a flawed opponent, and get that result every time. If the computer varied it's moves, the challenge to the opponent to find a draw game gets more complex.

I havent completely read all the replies to this so my mistake if someone already mentioned this. But as far as I read no one, even you brain are correct, or at least if you are correct, your answer to it is wrong. I dont know the answer, thought I am intrigued to see what it would actually be. But no one is taking into account the randomness of your restacks. If you attack first turn, there is potential of not just 2v2 for your opponent but a 2v1 (if you stacked both of yours on one die). Resulting in him having 7 dice to your 3. Likewise if you decide to stack up higher there is potential of you stacking to a 4 and a 2 stack. Which gives u statistical advantage if opponent gets an even distribution of dice. Based on this information, what I THINK is right is to wait not for an 8 +6 stack but to wait until you unevenly stack dice, and then attacking their lower dice stack.

also the shape of the map is important, as it is only possible for one of the diagonals to attack the opposite. Giving 2 options, no attacks can be made diagonally (each land only has 2 places to connect to it i.e. Hole in the middle). Or 2 of the lands can be connected to 3 places, and 2 of them are connected to 2 places. None of these factors are taken into account. The mathematical answer will be much much more complex then anyone has stated thus far. What also needs to be derived is your opponents best possible move given your move. And to assume that your opponent is smart enough to know his statisticaly best possible move and to proceed with it. Having first mover advantage I believe gives you the best statistical advantage, although I dont pretend to know the math to do it because it would be an extremely long long problem. I may email this to one of my stats professors to get him to do it and see what he comes out with.

The Fountain:
"Ok, this is given: you are playing a 1vs1 version of kdice with only 2 lands"

I dont understand the point of that post wiggin. If that is all that is given u have to explore all possibilities and possible variations of the game.

yes i think the best option is always to wait until unequal distribution of dice.

Assuming both lands start with 1 die on each land:

Player 1: End turn, possible outcomes, 3 and 1 stack or 2 and 2 stack.

Player 2: End turn, possible outcomes 3 and 1 or 2 and 2.

If you are able to attack his 1 stack you essentially win if this occurs. Which is decently high probability, someone else do the math.

If he stacks 2 and 2, and you stack 2 and 2 you end turn again, until someone has unevenly stacked their dice. Once this occurs, Player ones best option is to attack when he has the numerical dice advantage, which will happen at some point with a decently high probability.

I also believe that Player 2s best option is to attack if he is ever able to gain an equal dice attack, as that is the best he can ever hope for.

It's not each player who has 2 lands. Each player has 1 land, for a total of 2.