# Defining Variance Hammer

Warhammer 40K, or indeed any miniatures wargame (or any game with dice) is an excercise in probability. When designing armies, thinking about what units to take, or discussing the local meta-game, you often find people making statements like:

“On average, this squad should wound three Space Marines, one of which should fail their saves.”

I’ve seen this called Theory Hammer or Math Hammer. But all of that logic is built on what is known as the Law of Large Numbers. In the sense of Warhammer 40K, this law states that as the number of dice you roll increases, the average of those dice rolls will equal the theoretical average (things like a 4+ save working 50% of the time).

And, over a tremendous number of die rolls, that’s true. But any particular game isn’t necessarily a large number of die rolls (in the Law of Large Numbers sense of the word “large”). And any particular shooting phase definitely isn’t. We’ve all had that happen – the miracle roll of all sixes to save a squad from inevitable doom. A squad of Guardsmen who nail every shot.

That’s because a mean has variance, an expression of statistical variability. Variance Hammer is my term for exploring this variability, that some parts of Warhammer 40K can exploit this variability, be particularly condusive to “Go big or go home” – or my particular favorite phrase for games, “The dice gods favor the bold.”

This blog is my musings on that, the hobby in general, and generally trying to apply math, statistics and simulation to one of my favorite games.

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