# Pentagonal 3D5

This game is played on an 5x5x5 cell board with the following setup (the initial red stone is a neutral stone or using Lundberg's terminology, a free space):

 DROP - On each turn, each player drops a stone on an empty cell. GOAL - Wins the first player making a 5 in-a-row (orthogonal or diagonal in any 3D direction) with friendly and (eventually) neutral stones .

Some words from the author: After several months of analysis, Edward Jackman & I have come up with a possible variant of the 5x5x5 Tic-Tac-Toe game that may work for everyone.  [...] Edward demonstrated the 'strong draw' nature of the basic version of this game by giving me 3 moves to start and was able to block my best attempts at winning.  We quit about 1/2 way through the game after all the main lines were blocked by him.  Of course he was only demonstrating a certain style of play where the 2nd player was hell bent on creating a draw.  This is kind of unordinary for about 99.95 percent of the play I have witnessed with my board game called "Pentagonal" [...]. Now I'm cognizant of the fact that many games have been "killed" by elite abstract strategy gamers by ripping them apart and reducing them to a simple algorithm that removes all attraction to playing them at all. But I believe we have found the solution that may make some of you'all think a bit.

My original variant was to use a single 'free-space' in the center of matrix, which has the most lines or planes passing through it (11).  So what we have come up with is an extension of the free-space concept.  The center space should still always be a free-space, unless you are playing a novice and want to give them somewhat of an advantage.  But here is the interesting part: the difficulty of this game can be adjustable.  Both players then start alternately placing free-space pieces on any position they like, accept you cannot create more than 3 free-spaces on any line (or obviously the 2nd player would win).  It appears that 5 may be sufficient, but this may be incorrect.  Once one player wants to start playing, they place their piece down, but using yet another equalizing rule, the other player can then replace this piece with their own.  Play then continues in the traditional fashion, but since there are probably several 2 space lines in several directions, it is probably unproductive to try and just play the blocking game by either player.  It is most fun when both players are playing to win anyway!

The question still in our minds is this: Just how many free spaces does it take to satisfy the true analytic minds out there?  Edward had proposed that all of the major '6' spaces be made into free-spaces:

V           W           X           Y           Z
a b c d e   a b c d e   a b c d e   a b c d e   a b c d e
1 F . . . F   X X . . .   O . O . .   X . . . .   F . . . F
2 . . . . .   . F . F .   . . . . .   . F . F .   . . . . .
3 . . . . .   . . O . .   . . F . .   . . O . .   . . . . .
4(O). . . .   . F . F .   . . . . .   . F . F .   . . . . X
5 F . . . F   X . . . .   . . . . .   . . . . .   F . . . F

Jim     Edward
1)  X2c     X1c
2)  Wa1     Wc3
3)  Ya1     X1a (forced)
4)  W5c     Y3c
5)  Z4e     V4a

...but if you continue the above game, you will see the first-move-win nature of this configuration.

Edward also has suggested an interesting pattern:

V           W           X           Y           Z
a b c d e   a b c d e   a b c d e   a b c d e   a b c d e
1 . . . . .   . . F . .   . F . F .   . . F . .   . . . . .
2 . . F . .   . . . . .   F . . . F   . . . . .   . . F . .
3 . F . F .   F . . . F   . . . . .   F . . . F   . F . F .
4 . . F . .   . . . . .   F . . . F   . . . . .   . . F . .
5 . . . . .   . . F . .   . F . F .   . . F . .   . . . . .

but we have not played this configuration yet.  Edward has also come up with a rather unique concept in making the outside of the matrix a 'virtual wrap', where one side is connected to the other side, or top to bottom, and making it a 4 in a row game, thereby circumventing a middle block, but I don't think that will work very well. So if any of you care to exercise your analytic prowess and figure out the best range of the number of free-spaces needed, you may get a free copy of the game board matrix I have patented and is in the final production run of 500 (out of 2500 total). I feel it is between 5 and 9, but Edward thinks it is more.

I feel this board matrix may be viewed as an abstract "deck of cards" that can accommodate numerous games, most of which have probably not yet been invented yet.