# Basic Math in Warmachine & Hordes

Most table top games have random element. Warmachine is no different. I want to help you to understand the basic math ruling this game. This post should give you general idea how to predict the outcome of your attacks which should improve your model trading.

D6 vs 2D6
If you roll a single D6 you have equal chance of receiving each result.

You have 16,66 % (1/6) for rolling: 1
You have 16,66 % (1/6) for rolling: 2
You have 16,66 % (1/6) for rolling: 3
You have 16,66 % (1/6) for rolling: 4
You have 16,66 % (1/6) for rolling: 5
You have 16,66 % (1/6) for rolling: 6

But if you are rolling 2D6 the chances of getting each result is different:

You have 2,77 % (1/36) for rolling: 2
You have 5,55 % (2/36) for rolling: 3
You have 8,33 % (3/36) for rolling: 4
You have 11,11 % (4/36) for rolling: 5
You have 13,89 % (5/36) for rolling: 6
You have 16,67 % (6/36) for rolling: 7
You have 13,89 % (5/36) for rolling: 8
You have 11,11 % (4/36) for rolling: 9
You have 8,33 % (3/36) for rolling: 10
You have 5,55 % (2/36) for rolling: 11
You have 2,77 % (1/36) for rolling: 12

As you can see the biggest probability is near the middle of this spectrum and the lowest is on it ends.

Now if we are looking for total amount be equal or higher than our goal:

Rolling 12+ chance: 2,77%
Rolling 11+ chance: 8,33%
Rolling 10+ chance: 16,66%
Rolling 9+ chance: 27,77%
Rolling 8+ chance: 41,66%
Rolling 7+ chance: 58,33%
Rolling 6+ chance: 72,22%
Rolling 5+ chance: 83,33%
Rolling 4+ chance: 91,66%
Rolling 3+ chance: 97,22%

So for estimation of hitting chances we can use table above. But for damage output we can use an extended version of this formula.

Number of attacks x Probability of hitting (as a fraction) x (7 + P+S/POW of attack – ARM of target)

This is simplified formula. So it won’t work for cases where you have ARM>P+S/POW+7 and for small numbers of attacks it may be not precise. And it is only estimation of damage! Outcome may wary a lot. But for fast counting attacks that you need this formula is really helpful.

For your comfort it is a good practice to round nearest result for: Number of attacks x Probability of hitting – part
If you have weapon master you can estimate 10 points instead of 7. 10 points is rounded down.

Fishing for spikes

Probability is fluid thing. After first roll chances may change drastically. If you have shots/spells/attacks which may open a window for assassination or a good trade without putting your pieces in danger you may take even low chance rolls. If you spike your chances will grow and you make get advantage of the situation.
You should search also for low chance shots to work up an overall advantage. Small things matters in this game. Every grunt, chip damage or even continuous effect may have big impact on the outcome. The only moment when you don’t want to roll those attack is when you are bleeding on clock and need to focus on most vital plays.

It’s a trap!

Image this situation: You were flipping a coin 50 times you got 49 tails and now you flip is last time. What is the chance of flipping tail again?
You are counting? You shouldn’t be. It is 50%. The past is irrelevant for probability. You are in the place you are. Next rolls are not depended on previous ones. If you are counting probability of a chain of events you need to remember that after each roll your chances of success raise or fall. You need to have in back of your head that when you are taking 90% chance assassination after few bad rolls you may be facing a 10% chance of success and you need to adjust to the situation.

When to go all in?

One of the most important skill in this type of game is to know when to take even small chance play. The general idea is to play it safe when you have an advantage. So the advantage will push you through the game. If you are playing for behind you need to find a way to get back on your feet and sometimes you will be force to take more risky plays.