Mathematics in Tabletop Games

In which we discuss the application of mathematics in analyzing and designing wargames, RP Gs, et cetera.

Off and on for the past few weeks, I've been revamping my old medieval/fantasy wargame rules. I decided that in order to devise a balanced combat system, I'd have to look at the rates at which different troop types inflict damage on one another. For instance:

12 spearmen attack 8 knights with a 1/9 kill chance (5+ to hit, 5+ to pierce armor), while the knights responds with a 1/4 kill chance (4+ to hit, 4+ to pierce armor). So the decline in the spearmen's strength over t turns is ds/dt= -(1/4)k and that of the knights is dk/dt= -(1/9)s. Since k=(2/3)s, you get ds/dt= (-1/4)(2/3)s = (-1/6)s. So the spearmen lose 1/6 of their number each turn. You can do the same thing for the knights.

Now, to figure out how to factor in set morale-check casualty marks and use that to determine the average turn length of a round of such combat.

So...does anyone else take nerdiness to the next level by combining math with tabletop games, or am I alone in this?

You would be *amazed* how much Mathhammer I've done over the years.

Usually disproven by my dice hating me, but there you go.

yeah, I've come to enjoy using anydice.com for this. Great for crunching dice curves.

I owe you one for that. Thanks!

My pleasure.

You can use Pythagoras to estimate ranges for guess-range weapons.