## Probability and Dice Wars

There's this Flash game that I play called Dice Wars. It's sort of like a stylized and abstracted version of Risk.

(Note: it's pretty addictive. Fun, but can be a major time sink.)

I've been playing it intermittently for years. There was a time, a few months ago, when I won at least two-thirds of the time.

These days, I win less than half the time.

It seems unlikely that I've gotten worse at playing over time. I don't feel like my strategy has changed.

The game's code was written in Flash, years ago, so it seems unlikely that the computer-players' code has been improved; and the game doesn't keep a persistent state, so the computer players can't learn to get better over time.

Also, attacks that used to almost always succeed seem to be failing fairly often. For example, when I attack with 8 dice against 5 defending dice, I should have a 95% chance of success, but that attack seems to me to be failing about a third of the time these days. And when I attack with 3 dice against 2 defending, which should have a 77% chance of success, that seems to fail about half the time.

Thus, I am led inescapably to the conclusion that the way probability works has changed, and we're now living in a region of space where things have different probabilities than they used to.

(...To be clear: I'm joking. The answer is probably a combination of my strategy changing in subtle ways that I'm not aware of, and observer bias on my part. It's vaguely possible that the game relies on a random number generator that behaves differently on my current computer than it did on my old computer, but that seems unlikely—and if that's what's going on, then it seems like it should affect the computer players just as much as it affects me.)

(Update: I wrote this entry in mid-June, but didn't get around to posting it 'til late July. Sometime in July, the pattern I had observed went away, and I started winning most of the time again. Obviously this means that we've left the skewed-probabilities region of space. ...I also came up with another possible explanation, which is that even unlikely things happen sometimes; probability isn't a guarantee that the outcome will match the expected distribution.)