# Mathhammer: Foundation dice arithmetic

In Kings of War, and many other wargames, you need to have a rough idea of your chances of success before committing to an action. Sometimes you may do this via pure experience (though that can be muddied with confirmation bias of course), and sometimes you may do it via maths. In Kings of War, knowing roughly how much damage you’ll do on average can be a key skill in weighing up whether a particular charge is worth it or not.

I’ve seen people turn up with printed out pre-calculated tables for their armies, showing how much damage each of their units will do in any given situation. Useful, but you can also work it out very quickly with some simple arithmetic. Some basic addition, subtraction, and multiplication is all you need. This is an extremely basic look at how you can work out the average number of hits or points of damage based on your starting attacks. It’s not meant to be complex, it’s not meant to be new for anyone who already does similar mathhammer arithmetic, it’s purely as a foundation exercise for someone who hasn’t touched this sort of probability or arithmetic since high school.

 D6 roll required Arithmetic method 1 Arithmetic method 2 6+ Divide by 6 5+ Divide by 3 4+ Divide by 2 3+ Divide 3, times by 2 Divide by 3, subtract from starting number 2+ Divide by 6, times by 5 Divide by 6, subtract from starting number

So. You have a unit that hits on 5+, then wounds the enemy on 4+ and has 12 attacks.

Work out how many hits by dividing your starting dice, the 12 attacks, by 3. This gives you a total of 4 hits. If you wound the enemy on 4+, then you divide the hits by 2, giving you a total of 2 damage on average.

4+ to 6+ is easy to calculate because they’re just simple divisions.

3+ and 2+ are slightly more complicated because they need two steps, but there are two methods of quick calculation depending on what you’re more comfortable with.

For the first method, with 12 attacks hitting on 3+, you first divide the number of dice by 3. From 12 attacks, this gives you a total of 4. Then multiply this number by 2, for a total of 8 hits:

1. 12 divided by 3 = 4
2. 4 times 2 = 8

The alternative method is to do the divide by 3 first, then instead subtract the result from your starting number. This becomes:

1. 12 divided by 3 = 4
2. 12 minus 4 = 8

Pick one of these methods, my preference is for the first, then practice. Keep coming up with a number in your head between say 6 and 30 and practice quickly dividing it by 6, 3 and 2 for dice rolls of 4+ to 6+. Ignore remainders for now and just concentrate on getting the closest number, over and over and over again. Once you’ve got the hang of that, start multiplying up the answer for 3+ and 2+. Once you’ve got the hang of that, start applying a second dice roll to the result.

Next article, we’ll start covering extra rules like Elite and look at the 2D6 probability curve.