Superimposed Board Games

Under "Simultaneous Checkers," [po] suggested the superimposition of a chess game upon a game of checkers. So I'll take this a bit further.

First, take an odd bunch of games that can be played on a large board (14x14): Chess, Checkers, Stratego, Snakes and Ladders, and maybe Scrabble, but you can throw in others. Naturally, some of the sub-games will not require every single square, but there should be as much overlap as possible. The objective is to win >50% of the subgames.

Players alternate turns, at the start of which they will roll a die. Now here's the kicker: after the roll, player two gets to choose which subgame player one will play. If applicable, the value on the die will be used.

I'm aware you could do this with separate boards, but it's both more ergonomic and chaotic this way.

EDIT: I suppose I should mention that the pieces from one subgame have no effect on the pieces of another subgame, which was also mentioned in the annos from Simultaneous Checkers.