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Hi:
This is a question/test of my knowledge for all you mathematicians out there. I've gone to the tactica section and read through several "Mathhammer" threads, but I'm not sure I fully get it. With due respect to the clearly knowledgeable and well-thought-out presentations there, I fear that many of them go into far too much detail for my needs. I only wish to occasionally use this to get a ROUGH outline of how a unit will behave against MEQs, TEQs, GEQs, etc.
I'm posting here and not in the tactica sub-forum because this is more me asking if I've got it right, as I write for a living, and don't lay claim to being any kind of number-crunching genius. If this method of mine works, it's something that is relatively quick, simple, and doable even in my rusty, drafty ol' head. This is NOT designed to be a guide, although if it turns out I've got it right, anyone here is welcome to use it.
This method assumes a few things:
1) I am using 40k here, as I play 40k, but I imagine this would work for WHFB, Warmachine, pretty much any tabletop game that uses dice.
2) With due respect and thanks to Onlainari's guide on "real" Mathhammer, I'm not interested in modeling luck. I know that this method of mine may seem simplistic, but I feel seeking out a perfect system that takes any and all possible contingencies into account is best left to the Las Vegas "Jimmy the Greek" types, and, for me, gets into way too much hair-splitting. I'm prepared to accept the idea that this method is not expected to be perfect, merely something to help, say, decide between two different units I'm considering for my army. In short, getting TOO specific risks ruining the fun factor.
3) Pursuant to #2, I'm assuming range (where applicable) is not a factor. I also calculate with BASE STATS in mind (e.g., standard tactical marine carrying a bolter, no power weapons, powerfists, iron halos, etc.), and understand I may need to adjust this method when/if other factors such as wargear, charging, etc. come into play.
4) I'll be using many common 40k stats below, but note they will be assigned to fictitious units/equipment, since posting stats from actual codices/army books is against forum rules. Please bear this in mind when composing comments.
Ok, disclaimers are done. Whew!
Now, as far as I see it, the basic idea behind Mathhammer probability is to measure desired results against all possible results.
For example, two models are in melee. Model GIJoe has a WS of 3, and strength 4. Model Cobra has a WS of 4, strength 4, and a 3+ armor save.
If GIJoe is attacking Cobra, we consider that he needs a 5+ to hit, a 4+ to wound, and Cobra needs a 3+ to save. When we compare these numbers to a normal d6 (which I use throughout this post), we see that to hit, GIJoe's player wants to roll a 5 or a 6, NOT a 1, 2, 3, or 4. This means only 2 of the 6 possible outcomes of that roll are desirable. Hence, we have a ratio of 2/6, or after simplifying, 1/3.
Knowing this, we can assume also that one out of every three attacks is LIKELY to hit (note that's not a GUARANTEE, as luck is a factor). Therefore, if there were, say, a mob of 20 GIJoes in cc with 20 Cobras (Cobrae?), we can guesstimate that, with 20 attacks, the Joes can expect to hit 6-7 times.
Moving on to wounds, we see that it's basically a 1/2 ratio (3 desired outcomes vs. 6 possible outcomes makes for a 3/6 ratio, or 1/2), meaning the Joes can EXPECT one out of every two hits will result in a wound. So continuing our hypothetical 20-on-20 battle, assuming 6 hits, we can EXPECT to see three wounds.
Finally, since the Cobra save is 3+, that works out to a 4/6 ratio, simplified to 2/3, meaning for every three wounds, Cobra can EXPECT to make two saves. In this example, there are three wounds, meaning Cobra will lose only one save, and thus lose only one model.
Now, let's pretend that the standard GIJoe has a BS of 4 and carries a standard-issue Spud Gun rifle that has a strength of 5 with an AP of 4 and fires one shot per turn. Again, assume range is irrelevant. For this example, the entire GIJoe 20-man unit is in range of the entire Cobra 20-man unit, and there is no intervening terrain.
So in the shooting phase, the Joe unit fires 20 shots at BS4. Since the player needs a 3+ to hit, this turns into a 4/6 ratio, or 2/3, meaning two out of every three shots is EXPECTED to hit. With 20 shots, this works out to 12-14 hits, and if we were to round up, let's say 14 ("Yo, Joe!")
Since the Spud Gun has a strength of 5, Joe needs a 2+ to wound, which turns into a 5/6 ratio, or five wounds for every six hits. With 14 hits, that works out to be roughly an EXPECTED 10-11 wounds.
Now, we use the same save calculation as in the cc example before and find that Cobra will make APPROXIMATELY 7-8 saves, or they will lose three, MAYBE four models, which means slightly better offensive odds for the Joes in shooting.
From this, I can conclude that any player who expects to fight a lot of Cobra-equivalent (CEQ?) units and wants GIJoe units in his/her army better keep 'em out of cc, at least from an offensive perspective.
We haven't even gone into defensive roles here, but this thread has gone on long enough. You all get the idea of how I do this. So what do you think? First off, is my method a correct way to analyze probability, or have I simplified things too much? Is there a way to do it better that doesn't involve a scientific calculator?
(EDIT: Fixed some numbers that I goofed on. Thanks Caluin!)
I think the basic jist of what you're doing here is the simplest and most effective way to figure these things out, without studying advanced statistics at uni or somesuch. I'm not interested in exact hundredths of a decimal place; I want a rough idea, and simple arithmetic will get you that rough idea, which more often than not will hold true in every scenario. What difference does 0.01 really make in a game based on the luck of the dice? It's one of my biggest gripes with Mathhammer.
There is a fairly easy way of doing it: Bust out Excel and put your calculations in there.
(number of attacks/hits)*(to hit)*(to wound)*(failure to save)
The only time things are difficult is when you are working with twin linked/rerolls/etc. I used to figure all this stuff out and it involves a lot of sub equations. For example rerolling looks like (chance to hit+(chance not to hit*chance to hit)).
The equations are basic math and they arent actually difficult, they just consist of a basic knowledge of Warhammer, from there you just multiply or add things. This is basic elementary school mathematics, it has just been expanded and involves plugging probabilities into the equation.
"Mathhammer" is just a means of figuring out the overall combat ability of units, there really isn't any reason for you to sit around figuring it out yourself, it's fairly obvious which troops are better or worse at what they do, the game isn't based on calculations, it's based on the rolls of poorly made dice where each individual dice has an extreme chance of two sides showing up (unlike professional dice like I and my friends use).
The thing I am trying to say is don't sweat the math, it's only there for powergaming, or assessing which equipment, units, guns, etc will work the best. And the dice rolls in Warhammer (unless you're using Casino Dice) will not come up as perfectly random, they're off by between a few hundredths to tenths.
Last edited by archonofdeath; March 27th, 2009 at 19:19.
A youth with his first cigar makes himself sick; a youth with his first girl makes other people sick. - Mary Wilson Little
All the more reason, I think, to avoid counting down to multiple decimal points when calculating these sorts of things, since that assumes all dice are perfectly balanced, which most aren't. LN, you hit the nail on the head: Getting TOO technical to me leans in the direction of powergaming, which I've never been a fan of for reasons I won't go into here (I'm not accusing any mathhammer experts of being powergamers, just my take on it).
I guess I'm just trying to make sure I'm not being so lenient on detail as to make the entire exercise pointless. As I indicated, I can make adjustments based on charging, invulnerable saves, etc., and I imagine I could adapt this to allow for powerfists and other enhancements/wargear if necessary. The basic method, however, still applies.
Well, when your dice go on strike and refuse to roll well, you only have yourself to blame now.
I assume you're referring to my incorrect stat posting. That's what I get for posting without the rulebook right in front of me. Can you tell I don't have any BS3 units in my armies at the moment? LOL! Course, I coulda said I did that on PURPOSE to avoid posting copyrighted info. Um, yeah. That's it.
Shave you dice, for the extra edge to win! Jking, I don't put much faith in mathhammer, as some people have varying degrees of luck or there lack of.
A cracking post Canew.
This is pretty much the stats system I use when deciding theoretical winners of combats from tactical posts in votewars, since it is the only way I can see as fair, (as it eliminates luck, and of course Bob, my special High Elf Spearmen, who is yet to die.....).
I use this type of maths as a rough estimate in games too. I use it quickly in my head, (although the effectiveness may be reduced by a random percentage due to tiredness, lazyness, or just singing along to the song that is playing at the time), to work out whether a charge by one of my units is likely to yield a favourable result. It sometimes screws up royal, but I find more often than not it is a useful guide.
In conclusion I would like to state the following:
MATHHAMMER: It won't win you games, but it might help you understand why you lost.... also, maths is fun
ninja out
Thanks, Ginger. That's kinda where I was going with this. Again, no disrespect to the more in-depth mathhammer articles out there, but I think my method is a little better for a "quick and dirty" analysis.