Diddling With Dice

by MXSavant 04/28/05

I don’t know a gamer who has not at some time had a love-hate relationship with dice. Those pesky little purveyors of randomness that make a game seem more like the real, chaotic world we are stuck with when we come “back” from the imaginary worlds where we like to play. Dice are as old as humanity. Loaded dice have been recovered from ancient tombs, and the Roman emperor Claudius was said to have written a treatise on how to win at dice.

Knowing a little bit about how dice work, including (but not limited to) some basics of probability can help you play a better game, no matter whether you favor Silent Death, Noble Armada, Carnage, or any other game that uses dice.

If you have a fair six-sided die (D6), each outcome has an equal probability of happening: 1/6. All six possible outcomes add up to 1. With a D8, each outcome has a 1/8 chance, and so on. But in Metal Express games, more often than not you find yourself rolling two or three dice. What then? In order to find the probability of an outcome that depends on multiple outcomes, you multiply the probabilities of the two outcomes. So, for rolling snake eyes with two D6, you multiply 1/6 time 1/6, which equals 1/36.

However, this is not the whole story, because if you’re trying to roll a 7, there are six possible combinations of two D6 that add up to 7. So, you add 1/36 + 1/36 + 1/36 + 1/36 + 1/36 + 1/36 = 6/36, or 1/6. That boils down to about a 16.6% chance of rolling a seven, as opposed to about a 2.8% chance of rolling snake eyes or boxcars.

If you take two or three dice and roll them many times, recording the outcomes, you’ll find that the number of times each outcome happens graphs into a sort of bell-shaped curve which statisticians call the standard distribution curve. I wrote a simple computer program using a pseudo-random number generator to simulate rolling three D8 10,000 times. I plotted the result and got the following graph:


Now just because the odds favor something doesn’t mean it will happen on the next roll. Probability deals with what it more or less likely to happen. It’s still a matter of chance. So, for instance, you might think that if you are having a run of bad luck, it will be followed by an equal run of good luck. Nope. Previous events don’t influence the next roll. The odds are th e same for each new trial; heads or tails. But the distributions of dice rolls and so forth will eventually reveal themselves after many, many trials.

So how does this help you?

Using my nifty program I did large trials of lots of different three dice combinations one is likely to find in Metal Express games, such as 2D6 + 1D8, 2D8 + 1D10, etc., etc. I looked at the data produced by each trial to see if I could find a pattern in where the tip of the curve was. What I found was that if you take the highest possible total from your combination of dice (for instance, 2D8 + 1D4 would be 20), multiply that by .6 and round off the decimal. The result is a pretty close approximation of where the tip of the curve is.

So, for our example of 3D8, you would set it up like this:

24 x .6 = 14.4 Round off the decimal, and you know that your most likely total will be somewhere in the neighborhood of 14.

This means that if you are throwing 2D6 + 1D8 the odds favor you rolling 12 or close to it, since the curve will also give almost as good chances for an 11 or 10. Now you can make more intelligent estimates on the fly as to whether you’ve got a decent chance of hitting a DV of 13 or whatever. Remember, this is just a rough rule of thumb I arrived at by trial and error. I didn’t try to derive this in closed form or anything like that. But try this trick in your next game and see how it works.

Something else to remember is that if have a given chance of making a certain throw, trying it twice in the same turn will improve the odds of hitting at least once. So, if you’re lining up a shot on someone’s heavy fighter and the odds are less than ideal, you might decide to improve the odds by having more than one fighter take a shot at the same target.