Math- Can't Truss' It

You know an article is going to be awesome when the title contains a Public Enemy quote.  Those of you that have been following my work on Dick Move already know that I'm a sucker for math.  I enjoy a good round of mathhammer nearly as much as a game of Warhammer.   Statistics and probability are things that you really need to have a grasp on to elevate your game.  Knowing the odds of killing an enemy, surviving a reckless action, or passing a leadership test are invaluable in my own decision making process.  I won't lie and say that I always calculate the exact odds of accomplishing what I want, but I know that if I want to take down a Landraider with missile launchers, it's going to take more than just a handful of shots to do it. 

Don't fret if you're not math savvy.  Heresy Online has a good 40k combat calculator that can help you out of a jam. 

Having said that, I will also let you know that I am extremely mistrustful of the application of probability to a game of Warhammer.  Frankly, you are rarely going to be rolling enough dice at one time for the outcome to logically follow predicted outcomes.  Perhaps something like Khorne Berzerkers on the charge come close, but keep in mind that rolling 20 is less likely to behave as we would assume, but rolling 1,000 dice would probably yield pretty close to average results.  Rolling an infinite number of dice will yield average results. 

Here is a real life example based on a series of highly improbable events that happened to me recently.  It's centered around these assholes here:

Yeah, these assholes

This past weekend I got a chance to play my first game of Warhammer Fantasy 8th ed against my good buddy Hoagy.  He already went to the trouble of making up a battle report, so if you're interested in reading it or seeing more pretty pictures of mostly unpainted miniatures on my desert board you can read it here.  For me, the game was fraught with bad luck from the outset.  Turn 1 saw my cannon misfiring itself to death after my Lvl 4 Life Wizard miscast and killed 3 greatswords while resurrecting 3 crossbowmen- not a good trade off to say the least.  Over the course of the next few turns I lost both my other artillery pieces (a mortar and a Helstorm Rocket Battery) to misfires- it was a small game and I was more interested in trying out as many things as possible than having a cohesive army, so I didn't have a lot of artillery and didn't get to spam anything. 

Anyway, let's crunch the numbers on my suicide artillery.  I took a total of 5 shots over the course of the game.  3 of those were fatal misfires. 

• 1 result on the artillery die is a misfire, so the probability of rolling a misfire is 1/6
• 1 result on the misfire chart (a roll of 1) results in a wrecked piece, so the probability of being wrecked is 1/6

Noting the above, the probability of an artillery piece getting killing itself with a misfire on a single shot is 1/6 * 1/6 = 1/36

This also means that the probability of not killing itself (inclusive of non-destructive misfires) is 1 - 1/36 = 35/36. 

Since in my particular case I got 2 shots off and died on 3 others the odds of that happening were:
(1/36)^3 * (35/36)^2=  1,225/60,466,176 = .00002026... or odds so low that my calculator just had to resort to scientific notation.

I stood a 0.00203% chance of exploding my 3 war engines over the course of 5 shots.  Ordinarily when you fire a cannon or what have you, you assume that you're going to the shot off.  Statistics even tell you that you have a 35/36 (97.2%) chance of at least not destroying yourself.  Seems like a pretty safe gamble.  Hell, I'd take odds like that in Vegas all day long.  Sadly, just because something is likely to happen doesn't mean that it is guaranteed to happen.  Despite the fact that there was nearly 100% certainty that I would not lose all of my own units to misfires, it happened.  Shit happens. 

And that my friends is the moral of the story.  Shit happens.  Despite your best efforts and confidence in  statistics, you can't expect all of your rolls to behave as predicted.  Even if you know that firing 10 lasgun shots at BS3 will yield 5 hits on average, it is still possible or even likely that you will get 4, 6, 10, etc hits when you roll.  At the same time, even though I know that shooting a single missile at a Landraider at BS4 only stands a 11.11% chance of glancing, so it's not worth the effort if there are other viable targets.  If anything is to be learned by this, it's that knowing your stats will help you to make logical decisions, but don't be surprised when things don't work out quite as you expected.

So there you have it.  Anybody else pulled off any ludicrous rolls?  Got advice for applying stats to your game?  Inevitable math errors to bitch about in my calculations?  Sound off in the comments section.