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Starting simple, Probability is the measure of how likely a result is.

In words... to find the probability of a certain outcome you take the number of ways the result you want can occur and divide it by the total number of possible outcomes.

first things first, to understand the probability of a single roll of a single dice...

the equation looks like this...

P(X) =

__The Number Of Ways Event X Can Occur__

_______The total number Of Possible Outcomes

i.e. the probability of event X is the number of ways event X can occur divided by the total number of possible outcomes

example... to find the probability of rolling a 4

p(4) =

__# of ways to roll a 4__=

__1__

_________total # of sides___ 6

the breakdown... # of ways to roll a 4, roll a 4. Total sides = 6

to find the probability of a 4+

P(4+) =

__# of ways to roll a 4+__=

__3__

__________total # of sides ____ 6

the breakdown... # of ways to roll a 4+, roll a 4,5 or 6. Total sides = 6

Simple right? so far, yeah, it gets a lot more complicated.

To find the Probability of throwing two dice (and eventually more) all you have to do is multiply the probability of throwing each one.

example... to find the probability of getting a 4 and a 6

first step, find the probability of rolling a 4.

p(4) =

__# of ways to roll a 4__=

__1__

________total # of sides____ 6

second, find the probability of rolling a 6

p(6) =

__# of ways to roll a 6__=

__1__

________total # of sides____ 6

now take those answers and multiply them together

__1__*

__1__=

__1__

6_ 6__ 36

"the probability of two independent events is just the product of the probabilities of the two single events" not sure where i heard that, or when either, but im pretty sure it's right...

There are other ways to find the statistics of random/independent events and the next step is... Binomial Distribution. The equation for Binomial Distribution is tooo hard to type out, but trust be it makes "MathHammer" a LOT easier and is what i'd recommend using. Basically what the Binomial Distribution function does is it shows the number of times and event can occur (i.e. a roll of 5) in independent occurrences (# of different dice rolls) where you know the probability of each throw.

It is an exact probability distribution for any number of dice throws. Which means it can give you odds of throwing snake eyes, or tell you how many dice you gotta throw before you get that 5 you need. But most importantly it can help figure out what your gonna get when you're rolling 10-20-30 dice and how many of them will be a 3+,4+,5+,etc...Basically if you want to find any significant data, this is the way to go about it, and there's a ton of info on it; including tables, charts and programs.

There is another way you can also check to see how many rolls you going to need to get that 6 you want. The equation looks something like this (this is 6-7 years ago so i might be butchering this)-

i*(1-x)^(i-1) = (1-x)^(n+1)*((n+1)*x-x+1)/(x^2*(x-1)) - (1-x)/x^2/(x-1)

And if you take the limit and check recursively you'll get almost an exact answer, but thats not probability anymore. Now were talking Calculus, and im not a teacher or getting paid, so your on your own from here.

Basically this is all i really remember. And i know for a fact, a ton more people who are way smarter then i, are out there who can answer your questions. Applying "MathHammer" to an ingame senario is more important than understanding what all the math is that's involved. I just wanted to post as much math as i remember (or tried to) just so you know im not making up the fact it's not all that important. However, the most important advice i can give is in the next section.

Nothing you can read or advice you hear can be as insightful as playing a game. There is sooo much that has to be considered every turn, much less Every Phase of each turn! Honestly, i jumped the gun by talking about turns already, you have to be thinking about what your overall game plan is going to be, before you even deploy your army. And if you weren't thinking of how you were going to play when you designed/wrote up your army list it has an even less chance of winning.

By no means am i saying you need to go out and get a "power gamming" list put together. Where every unit has a purpose and each one should make back it's points worth. But what i am saying is your only going to get out of your army as much as you put into it. It's the same general idea as to why people base and paint their models, it isn't always necessary to do, but the players that do, tend to have magnificent looking models. And if my opponent put extra time into his models bases, i know he's gonna have his list memorized, and probably can recite his entire codex.

What im eluding here is that knowing your models BS is important, as much as knowing he has a 1 in 3 chance of a hit; but does he have a tactically sound advantage to taking a shot? Will the extra points you spent on that Combi-Melta be a waste, cause ill stop your tank before it ever reaches anything. Is it permissible to buy that extra Icon, for

*maybe*the off chance, you need to Deepstrike Daemons close by. I can't give you all the answers, but i can give some advise - and take it in stride,

**nothing beats experience**.

Don't expect units to accomplish things that they aren't made for, you'll waste precious points that could have accomplished something more worthwhile. Crashing a unit of "regular" troops into an Elite CC specialist squad is gonna be pointless. Know the role each of you units plays and if you pay enough attention, learn what your opponents do with theirs. Is that large unit of Termagaunts rushing towards me to charge me next turn, or are they just blocking LoS to a unit or Warriors. Personally i use rhinos all the time to block LoS, ill even go outta my way to position it so that it's blocking as much of the unit it's next to as possible, even tho it might be missing a shot with it's bolter. Especially for the units of troops i have that i want in cc, there is no point in reducing model count before you reach you opponent because you can't deploy/move around strategically.

Weight of fire is also important; depending on what weapons you have and what kind of target you've picked, it might not be tactically worth taking a shoot. I leave most monoliths alone, focus that fire on Warriors, and try to get them to phase out. Now if you have a unit of Melta Termies, deepstriking next to the Monolith would be more adventitious; instead of standing around wasting those points shooting warriors. The situation should dictate play, not the probability/chance of a lucky shoot. In addition to shooting, getting shot at is important. If you can direct your opponents shooting, so he "thinks" he is picking his targets, you've already won the battle, if not the war.

Every army has it's strengths and it's own weaknesses (which can be broken down even further into squads, and then models/HQs/etc..), 40k is about learning what those might be in any given situation. I was in Atlantic City once on vacation playing in a texas hold'em tournament and saw a royal flush. The odds of a royal flush are 1 in 649,740. I might never see one

*ever*again. So i did what any punk kid would do, i pulled out my cell phone and took a picture of it. What happened next? i was kicked outta the casino for taking a picture of the cards. Moral of this is, it doesn't matter what the odds/statistics really are, it's how you apply them. Everyone is dealt there own hand, it's how you play it.

Tactical example: I could charge a squad of Khorne Bezerkers into a unit of guants, with the basic assumption going in - ill kill enough to wipe/break them. But what's gonna happen after? are my KB's gonna be in LoS to a Dakka tyrant? am i gonna get charged by that flyrant that

*was*to far away but is now closer? or maybe because i charged i'm now out of range from a squad of geenstealers that were behind them?

Having an understanding of the Math involved is fine, but there is a

**LOT**more that goes into a game of 40k than "MathHammer". Even figuring out if you think a model is worth it's points, might be incorrect from a math standpoint, because you can't "MathHammer" out all the tactical situations in a game. My honest opinion is you'll learn more from playing more games; and this "gut" feeling that people have, tends to come from experience more than statistics/probabilities. I hope you understand the math i've tried to break-down, but more importantly don't let that be the only thing you consider when you're putting an army together, or playing a game.

Use tactics and play against your opponent (not his squads), and don't worry about the math. After all, it comes down to the roll of the dice, just pray the dice gods are on your side