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We tacitly assume that strength can be measured by one number and that the numbers can be compared using a transitive relation like 'greater than'. However, this needs not to be true, see here for a simple game with dice:

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

So here is a new chess variant challenge: Chess with nontransitive armies

Design a chess variant with different armies such that, whatever army your opponent chooses first, you can choose another army having an advantage over your opponent's army. (To avoid the first move problem assume 2 games where either army moves first once)