Mar 18
That diagram, though, is a simplified method of choosing a shot. It includes only our preference for the location of the cue ball after the shot; there are other factors it doesn't take into consideration. Here I'll talk about several of them, including:
In this diagram, the height of the terrain represents our opponent's preference for the cue ball to land in that spot (assuming we miss our shot). In this situation (again, this diagram isn't necessarily realistic, but used to illustrate an idea), we'll assume that our opponent wants us to leave the cue ball so that he has a shot on the 12 (purple striped) ball. This means that if we were to play a safety in this situation, we want to miss our shot, and leave the cue ball anywhere except the peak at the end of the table.
And most pool players, when taking a shot, are trying to accomplish one of the two objectives shown in the prior two diagrams. They're either playing offensively by trying to make a ball, or they're playing defensively with a safety. But that doesn't have to be the case; sometimes we can take a shot that, if we make it, will leave us an excellent next shot, and if we miss it, will leave the opponent a very difficult shot. We can visualize this with the composition (difference) of the two terrains:
The peak that was previously at the end of the table in our offensive terrain matched our opponent's peak, so our preference for that shot may now be lower. The peaks in the new diagram are those locations where we will have a fairly easy next shot if we make the object ball, and our opponent will have a difficult shot if we miss.
This terrain still isn't accurate; it should also take as input the difficulty of the shot. This can can be done by weighting the two terrains by shot difficulty when composing them -- if the shot is simple, and we make it 80% of the time, we should weight the offensive terrain more heavily than the defensive terrain. If a shot is more difficult, we should weight the defensive terrain more heavily.
Recognizing the difficulty of a shot is hard because it has a psychological aspect. We must accurately gauge our own skill level. If we overestimate our abilities, we'll weight the terrains incorrectly, which will lead us to the wrong decision. Humility is important.
And we could go on. Remember that this terrain looks only at the cue ball, and ignores the other balls on the table. This is natural for a pool player; in general, we try to hit as few balls as possible (unless we have a need to move one into a better position.) The diagram should probably be in n+2 dimensions, where n is the number of balls on the table. That would be tough to draw.
What use is all this? I'm sure we could write a nice little pool-playing bot that takes all these aspects of shots, and some known variance (its current skill level) into consideration, and minimaxes them.
A pool bot is pretty useless (I don't see us carrying around little terrain generators until we have holographic iPhones or something), so here are some things I've learned from thinking about the game in this way:
Eight-ball terrains (part 2)
Last time, I talked about how we can visualize our shots during a game of pool in a three-dimensional terrain like this:- Our opponent
- Shot difficulty
- Our skill level
- You don't always have to decide between making a shot and playing a safety; sometimes you can do both
- Humility is important; recognizing you're not good enough to make a shot enables you to make a better decision
- Visualizing your terrain, and possible opponent terrains actually helps your game
- Don't try to talk about this stuff at the bar
