Dots for fun and profit

Dots is a simple game for two players. You make a grid of dots on a piece of paper (we used to play with a roughly ten-by-ten grid, although there’s no rule about how big it should be). The players take turns drawing a line connecting two dots. If you complete a square, you put your initial in the middle to mark it as yours, and you get to go again. The game ends when the whole grid is filled with lines. The player who owns the most squares wins.

At first, it can be difficult to see which moves allow your opponent to finish a square. Thus, some games are decided by simple one-move oversights. But with a few games under your belt it’s relatively easy to avoid those mistakes. If both players are at that level, the game comes down to who gets the biggest runs of squares, more or less at random. There is, however, one trick that will let you win just about every game if you know it and your opponent doesn’t.

Typically the board develops in such a way that there are big clumps of almost-finished squares. If you can claim one of them, you get the rest in a domino effect. The natural play is to take all the available squares, then look for the least damaging move to pass it back to your opponent. The trick is to not take all the squares. You can leave the last two for your opponent. They get those, but then they’ll have to give you the next big clump and you can repeat the process, claiming all the big tracts and giving away just two piddling squares in return.

Of course, you only get to do this once before your opponent realizes what’s up and uses the same approach in future games. At that point the game just comes down to whoever’s move it is when the good moves run out, which is awfully hard to control.

Which, if you think about it, is kind of weird. Ties are rare in dots. In fact, depending on the size of the grid, a tie might be impossible. There’s no hidden information. So at any point in the game there should be a “correct” result: one side or the other could force a win with perfect play. On the very first line, there are probably some moves that win and some moves that lose. But how do you know which are which? There doesn’t seem to be any way to know, or even to have a better chance of being right. In dots the early part of the game is a tedious formality where both players go according to their whims until the rubber hits the road in the late game. Many of the moves are probably horrible mistakes, but there’s no way to know.

Chess and Go, like dots, are too complex to be solved, but they offer players more satisfying ways to guess at good moves. A good player can often tell who’s winning with just a glance at the position. Some formations of pieces work better than others and, to an expert, a good position “looks good.” In dots, a good position is just one move away from a bad position (if the other side were to move, the result would be reversed). It doesn’t seem possible to develop any sort of feel or intuition, as one can in chess or Go.

As such, dots has little to teach us as game players, except that knowing a simple trick can give us a huge advantage, even if we don’t understand the game deeply. But the edge we get from these tricks is likely to disappear quickly if our opponents are smart and observant.

From the game design perspective dots is more interesting. It shows that for a game to be satisfying, it must be too complex to solve definitively, but still admit of shortcuts, guesses, or heuristics. The players can’t know for sure what the best moves are, or the game would get stale, but they must have ways of approaching good moves, or feeling that they do. We have to feel like we’re getting somewhere, but if we ever get there, the game stops being fun.

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