I have a feeling that given any symmetrical board arrangement with no luck involved where the goal is to achieve some given geometric sequence in order to win that the person who goes first (assuming perfect logic) will either win or at worst tie.

Don't ask me to prove that, because if I were to successfully prove that the singularity would arrive and we'd all disappear in a puff of algorithmic smoke.

Mongrel wrote: There will be a fix to the map soon enough to infuse balance. But right now we're solving a math problem.

Hold please.

If it's concluded that it's not balanced (which somehow you also said above that you were 99% sure that it was...which is it?) then that solves the math problem.

Yertle wrote:

Mongrel wrote: There will be a fix to the map soon enough to infuse balance. But right now we're solving a math problem.

Hold please.

If it's concluded that it's not balanced (which somehow you also said above that you were 99% sure that it was...which is it?) then that solves the math problem.

I asking the opposite question, sort of. The question is, given perfect play, can black always win?

Just because a board is imbalanced doesn't ensure that the first player always wins.

IRoll11s wrote: I have a feeling that given any symmetrical board arrangement with no luck involved where the goal is to achieve some given geometric sequence in order to win that the person who goes first (assuming perfect logic) will either win or at worst tie.

Don't ask me to prove that, because if I were to successfully prove that the singularity would arrive and we'd all disappear in a puff of algorithmic smoke.

Has connect four ever been worked out?

Mongrel wrote:

IRoll11s wrote: I have a feeling that given any symmetrical board arrangement with no luck involved where the goal is to achieve some given geometric sequence in order to win that the person who goes first (assuming perfect logic) will either win or at worst tie.

Don't ask me to prove that, because if I were to successfully prove that the singularity would arrive and we'd all disappear in a puff of algorithmic smoke.

Has connect four ever been worked out?

Cram's Connect Four also involves luck, which makes it a bit different (but yes I think it favors player 1 too).

Yertle wrote:

Mongrel wrote:

IRoll11s wrote: I have a feeling that given any symmetrical board arrangement with no luck involved where the goal is to achieve some given geometric sequence in order to win that the person who goes first (assuming perfect logic) will either win or at worst tie.

Don't ask me to prove that, because if I were to successfully prove that the singularity would arrive and we'd all disappear in a puff of algorithmic smoke.

Has connect four ever been worked out?

Cram's Connect Four also involves luck, which makes it a bit different (but yes I think it favors player 1 too).

Sorry, meant RL connect four.

I remember this being announced a few years back. If you google connect 4 solution, you get a bunch of stuff (different people have apparently written up solutions). 1st player can force a win.

No move here that is smart for either of us right?

Unless there was a territory bonus per 19 territories, no.

That's the board state I've been trying to achieve in some of my games, but usually it just means I give up easy wins (not unlike the end result in ALL of my games)

There is a chess quote that applies here as to whether or not Five is balanced.

"When I'm white I win because I am white, when I'm black I win because I am Bogulyubov."
-- Bogulyubov

Any 2-player game that does not involve luck has a strategy that guarantees a win or a draw for one player or the other. I have no proof to back this up, but I don't think doing so is equivalent to singularity.

Here's a wikipedia article about games that have been solved (Where solved means a strategy has been found.) - including checkers and connect four.

http://en.wikipedia.org/wiki/Solved_game

Most of doing this involves computers of course. What makes a board balanced for us humans is how non-obvious the perfect strategy is.

GAH! DANG DANG! Amidon, I was about to freakin post that quote. It's my favorite. I also like to sneak up on people and say "Bogolyubov" in their ear sharply and loudly.

I was reminded of this as I soundly defeated Mongrel ;)

I lost, as I was not Bogulyubov.

Here is an answer to the darts game of Nygma and partial answer to five:

http://en.wikipedia.org/wiki/M,n,k-game

Darts:
Player two cannot have a winning strategy with perfect play. Even though we are allowing two "stones"(darts) placed at a time, the same argument will work showing that either player 1 is the only player that can win or the game ends in a tie with perfect play by both players.

Five:
I believe a modified argument would work for five, the unlimited fortifies and ability to take away spaces modifies the game significantly however.
So, player two should not have a winning strategy as player 1 can use it first. If a modified argument works, then either player one can always win (I am sure this is correct with an adaptive approach as many of you believe given the correct first turn for black) or the game ends in a tie (based on the assumption of perfect play by both players).

The ultimate question for five is "Is there a first move for black that can always be played to victory or does every start that black has have a perfect counter?" We are assuming the former.

For darts, we aren't allowing one at a time. Player 1 throws one dart, Player 2 throws 2 darts Player 1 throws 2 darts Player 2 throws 2 darts etc etc.

And this is also in the fix for five. Player 1 moves once Player 2 two times then two times for each subsequent turn. So player one cant have the configuration as player two unless he wants to burn a move in his second turn, but doing so would make HIM player two.

From Alpha's link I went here

http://en.wikipedia.org/wiki/Connect6

Connect6 is a get 6 in a row game. Player one places 1 stone then alternating placing two stones. May be fun here - any idea on how to work out the end-game?

Also this quote is on that page:

Herik, Uiterwijk, and Rijswijck give an informal definition of fairness (Herik, Uiterwijk, and Rijswijck, 2002) as follows: A game is considered a fair game if it is a draw and both players have roughly equal opportunities for making mistakes. From this, it is argued that Connect6 is fair ...

Cool! So Nygma and I essentailly came up with Connect5 (darts). If there's are yearly tournaments, forums and grandmasters for connect6 games then my guess is darts would do well.

No idea how to work out endgame, unless you mean, how does one prevent stalemates? We got that covered.

I hadn't looked at Darts. I was thinking that you could not use your "get an army and attack a capital" way of ending the game, but I see that you gave a bank of armies to work with. Which I should have because, honestly, I had thought of that earlier. But I don't get how you worked around the stalemate. I got as far as +1/n territories being set high. Care to elaborate how you did it?

Rijswijck is my uncle but he disavowed me when it became clear that there was no strategy against my irrational behavior and poor play.