One hand tied

The next principle from combinatorial game theory that I'd like to look at is the “one hand tied” principle, whose name comes of course from the schoolyard taunt:

I could beat you with one hand tied behind my back.

In combinatorial game theory (I'm really testing my aversion to acronyms here), we use this principle to prove that one player has a winning strategy. By restricting that player's available moves, if we can show that she still has a winning strategy, then she certainly must have one in the full game. The point is that the restriction may well simplify the analysis (and keep in mind that all we care about in such an argument is who wins -- not by how much). So, does this one have any relevance to poker?

It's a bit of a stretch, but I'd claim that there are some games (ultra low limit cash games, low buy in MTT's, but most especially sit and go tournaments at odd times), which are so good, that it's actually a mistake to do anything but “play with one hand tied”. By simplifying your game, you can avoid out thinking yourself, avoid having yourself marked as a tricky, or just as bad skilful, player, and generally stay under the radar. It's a matter of establishing and maintaining an image. When the time comes, you might make a “lucky” move to take someone out, but ideally the remaining competitors will still just think you're one of the crowd.