Friday, August 28, 2009

Word Choice: suboptimal

I realized I was using the same word to mean two different things, recently. That word was 'suboptimal' and I was describing move options in a game.

On one hand, I said that a move was suboptimal if there was another move that definitely was a winning move.

On the other hand, I said that a move was suboptimal if it was definitely a losing move.

These both sort of make sense, and I think this is part of the beauty of combinatorial games. I can say that a move is a winning move and even if the game is not over on that turn, it's (mostly) clear what I mean: the next player does not have a winning strategy. Furthermore, the term strategy does likely not have to be defined for those that have never seen the actual definition (have I?). People play games, and thus have an idea of what these terms mean.

The term suboptimal does make sense... but, taking a look at it, it doesn't necessarily mean what it perhaps should. In the first definition, it doesn't say anything about the "suboptimal" move not actually being a winning move. There's not necessarily anything "sub" about it. I probably shouldn't use it this way any more (I won't cry for too long).

I am, however, attached to this second definition! I've used it and plan on continuing to use it. Why is this? When I'm reasoning about game states, I often want to say "Player 1 won't make this move because it's suboptimal--Player 2 would have a winning strategy after that move---and Player 2 won't make that move either on their next turn, because Player 1 would also have a winning strategy from there."

How can it be suboptimal for both of them? One of them already must have a winning strategy, and the other does not, so it's not actually any worse for that losing player. Although we may not know yet which player that is, it is still not suboptimal for one of them. It seems better to replace this term with, simply, "losing move". A player shouldn't make that play because it's a losing move, not that it's necessarily suboptimal.

Still, there's another part of the usage for suboptimal that gets lost: that move doesn't extend the length of the game. Often, making these suboptimal plays is equivalent to giving up; the game is now going to end quickly, and with the opposing player having a clear view of which plays to make to finish you off. If you avoid the suboptimal play, you may not have a winning strategy any more, but there are places the opponent may "trip up" and give you the advantage again.

Thus, as a player, even if you're in a losing position already, you still probably don't want to make the suboptimal plays.

Have a good weekend! I'm doing a good job of updating MWF, so I will try to keep that up! This, of course, may change in coming semesters...

No comments:

Post a Comment