Friday, January 29, 2010

Tricky Last Moves and Schedule Change

There are two parts to this post. The first is actual content, but the second is some metaposting about the schedule. The short version is that I am switching to a Tuesday-Friday schedule instead of MWF. I am simply too busy to keep up with posting on my three busiest days of the week, so I will instead post twice per week.

Often, the end of a game is not when the difficult decisions arrive. There are certainly some sneaky final chess positions (I used to see them in the paper) but often either the last moves are a bit obvious or Chessmaster has already forfeited the game to you. (I'm not a good chess player... perhaps I'm completely wrong about this!)

Assume it's your turn and it's the last turn of a game. If that game is Amazons, it doesn't seem hard to determine if you've won. Similarly for Mancala. Each potential move is simple enough that you can try them all and see what the outcome is. In some games, however, there may be a large number of different potential final moves. What do you do in this case?

I picked up the game Cave Troll over the winter break and found myself taking way too long on the last turn of the game. The scores were close, and I had to figure out how to spend my four "actions" on my final turn to maximize the gold I would collect. Worse still, depending on which actions I might use, the game might not even end that turn!

Although I might have had a reasonable number of options for one action, say x, now I have a similar number of options for each of my four actions: meaning about x^4 in total. If we generalize this game, the number of actions might be one of the generalized variables, making it x^n options. Oof!

Which games are hard to make last-turn plays on? Are there lots of good examples of this?

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