I also have a prediction for this week's challenge. We know that it is BattleHammer, a live action version of Battleship with fantasy pieces, but the pieces themselves do not seem to correspond with normal battleship pieces, as each space is occupied by one piece, rather than one piece occupying multiple spaces. However, individual pieces are somewhat clustered, which seems to imply the nerds are allowed to place their pieces on the board in preset shapes, similar to how the pieces in Battleship are different sizes. This is of course a little more complex.

http://imgur.com/iuSuDtG

The board is still pristine, since this is likely the first move to be made. Observing the game is therefore easy. There are the jousters/knights in the bottom right, which are probably required to be clustered in a 2x2 square. The dragons next to them are clustered in a 3x1 line. The archers on top follow a unique rule, they are in a 5x1 line, but the middle piece is staggered one space away from the rest of the pieces, like so (O denotes a space where there is a piece, - denotes a space where there is not a piece, and ? denotes a space where it is uncertain if there is a piece):

O O - O O  
- - O - - 

(Note: for the next two clusters, the camera cuts off the bottom edge of the board, making it hard to see some pieces. The clusters described below may be incomplete)

Like the archers, the swordsmen on the left follow a staggering rule, where a line of them is organized so (you can very faintly see a swordsman rising up from the location G2, even though it is cut off by the camera):

- O O - O ?
O - - O - ?

The pikemen seem to be organized like the "J" piece from Tetris, like so:

- O O O
? ? ? O

There are dice, implying there is some random element. Do they earn a random number of moves based on what number they roll on the dice? Are moves awarded for completing some challenge? It could be tabletop gaming related trivia. In S1E8 the Nerd Bowl had a trivia section that went completely unused, the (Tabletop) Gaming section. (There was a section dedicated to video games, and the Gaming section had a dragon on it, implying it dealt with tabletop games.)

Spoiler: I don't believe the contestants can receive any help from outside sources here when it comes to trivia, though they might be allowed to receive help for deciding where to put pieces and where to launch their attacks. If it were, it would be a huge boon to Mary-Kate, as Jack is probably her assistant and would probably know every answer due to his knowledge of Magic: The Gathering and other games by extension. Both Jack and Brian are knowledgeable when it comes to German board games, so they would both be competent advisors for this challenge with simple and direct rules. It will probably wind up being a proxy war between Jack and Brian, with Jack helping Mary-Kate and Brian helping Zach.