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This is an article i wrote for the more advanced players who use mathhammer frequently.

When a player works out mathhammer, 99% of the time they will use averages rather than the actual odds.

My goal is to show people that averages aren't always the best thing to go by, and that people should use the Odds instead.

For the people that are confused...

Averages - The average number of models you will kill.

Odds - The chances of you killing a model(s).

Lets take an example....

Lets say you have a 10-man unit of Tactical Marines who are rapid firing on a single Terminator.

Lets assume that 9 of them have Bolters, and that the Sergeant has some other weapon (lets ignore his weapon for the purposes of this example).

Now, first we will use the common mathhammer that 99% of people use... Averages.

9 Marines will have 18 shots

12 hit

6 wound

1 failed save

Now is where the problem comes in...

People will assume they should be able to wipe him out at this stage, which is a VERY POOR assumption to make.

Quite often they will be dissapointed when they dont kill it, and say things like "dam, he should have died".

To prove why averages are a bad guide, lets work out the same situation with the actual Odds...

For a single bolter shot to kill a Terminator, the chances are 2/3 to hit * 1/2 to wound * 1/6 failed saves.

(2/3)*(1/2)*(1/6)= 1/18.

If there is a 1/18 chance for a single bolter shot to kill a Terminator, then there is a 17/18 chance for a single bolter shot NOT to kill a Terminator.

So for the chances of 18 bolter shots NOT to kill a Terminator, the chances are...

(Odds for single shot to miss)^(Number of shots)

(17/18)^18 = 35.7%

Therefore, there is a 64.3% chance to kill the Terminator with the 18 shots, and a 35.7% chance that you wont.

To further prove the advantages of Odds vs Averages, lets look at another example....

Lets take a squad of IG Veterans with 3 Meltaguns, and a Platoon Command Squad with 4 Meltaguns.

Lets assume that they are shooting at a T4 Independant Character with no Invulnerable save, with the hope of killing him outright.

Assuming you will only need the 1 Meltagun to hit (we will ignore the To Wound roll for simplicity purposes), which are you better off with?

The main thing here is to compare the BS with the number of shots.

First of all, lets use Averages to see what will happen....

3 shots at BS4

Average of 2 hits

4 shots at BS3

Average of 2 hits

Now people will say "wait, there is no difference between them, the odds are the same"..... WRONG!

Lets look at it using Odds....

(Odds for single shot to miss)^(Number of shots)

3 Shots at BS4

(1/3)^3 = 3.7%

Therefore, there is a 96.3% chance that at least 1 Meltagun will hit, and a 3.7% chance that they will ALL miss.

4 Shots at BS3

(1/2)^4 = 6.3%

Therefore, there is a 93.7% chance that at least 1 Meltagun will hit, and a 6.3% chance that they will ALL miss.

Yes, thats correct, you are actually almost TWICE AS LIKELY to miss 4 BS3 shots than you are of missing 3 BS4 shots, even though they will both score 2 hits on "average".

So in conclusion, averages are still ok to work out a majority of mathhammer as quick as possible.

But when it comes to needing that 1 wound, destroy that 1 tank, or anything else that is crucial to the outcome of the game, by using Odds rather than Averages you can calculate a far more accurate probability to maximize your tactical movement and target priority as much as possible.

I hope you found my article an interesting read, and hope that you will consider calculating Odds rather than Averages when the game is on the line.