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Ok, what exactly *is* Mathhammer? Is it actually a tool, or just a fancy way of saying 'using probabilities in gaming'? Is it the specific method of dropping fractions each step of the way in determining probabilities?
I read the article on Dakka and it just explains probabilities so it didn't really help me understand what exactly this mathhammer is.
Any help would be greatly appreciated.

Blood Angels assault squad charges Tau. Blood Angels get first turn.

Blood Angels:
1x 10x Assault Squad
Power Weapon, Meltabomb
// 270 points

Tau:

3x 10x Fire Warriors
// 300 points

Tau deploy 5.999" from their own table edge. Blood Angels deploy 23.999" from theirs. Blood Angels move up 12". They are 18.002" apart.

Tau fire. 30x 3/6 (to hit) x 4/6 (to wound) x 2/6 (armour save) = 3.3333, call it 3 dead Blood Angels. The Tau have more points the BA get more luck.

BA move up 12" and shoot their Bolt Pistols.
10 x 4/6 x 4/6 x 3/6 = 2.222, 3 Tau die.

The Tau move up and Rapid Fire.
27 x 2 x 3/6 x 4/6 x 2/6 = 6 dead Blood Angels.

The last Blood Angel, the Veteran, Charges the Tau. The Tau all die.

Mathhammer!

Note that in reality you would have to take into account the fact the Veteran could get killed. You would also have to choose if you wanted to use discrete probabilities or variance (an average) to describe how many were killed.

It does not matter, really. But what is known as Mathhammer can give you an edge in list building, especially for shooty lists.

Besides, it can be fun. Not as much fun as painting, of course.

Ok, so I take it from these posts that Mathhammer is just using probabilities in gaming and not a fancy schmancy tool that does everything for you. Bummer! Maybe I should write one. Is there one out there already so I don't waste my time?

It is easy enough to do with Excel. There are probably a couple others out there. Somewhere down my priority list I am doing my own version/ contribution I can send you a link when it is finished if you like.

But yes, it is just probabilities.

Ok, thanks for the info. I'll probably whip up a spreadsheet as well.

or you could have a fancy TI 89 (or 92) just do it for you. that would work too.

What it does is give you probabilities. The point of tactics is to get the balance of probabilities on your side if you can. They are not certainties.

So does anyone include survivability into their probabilities, or are they just one-way...to wound/kill an opponent model?
I have been spinning the wheels trying to think up how to include survivability into the equation.
I was thinking of taking the chance to fail an armor + invuln save and multiplying it by the model cost or cost-per-wound.

So a termie with a stormshield would be 2+/3+:
(1 - 0.83) + (1 - 0.33) = 0.167 + 0.66 = 0.83

An LC/shooty termie would be 2+/5+:
(1 - 0.83) + (1 - 0.66) = 0.167 + 0.33 = 0.50

Whereas a standard marine would have a 3+:
(1 - 0.66) = 0.33

I am not quite sure how to use these calculations yet.
Possibly a multiplier against their wound/kill percent to give their overall combat effectiveness.
Is anyone doing anything like this?

Your terminator example is perfect. For example, the best way to kill Terminators is to just suck it up and take them out with small arms fire. Or say I like to charge Terminators with Scorpions they will always come out ahead. Better to charge than to be charge.

So per-point, Terminators are more than twice the cost of marines but their armour save is only twice as good.

Of course that is also why those 3++ saves are so good. It is also why H.B.M.C.'s group's suggestion to increase Terminator toughness to 4(5) makes sense, because it protects them against small arms fire.

It is also why say Honour Guard are actually not that bad, so long as they do not get shot with plasma weapons.

Another example is an Ork KFF. Especially with vehicles, a KFF can get it's points back many times over. Or else the combination of Eldrad + an Avatar, making the Avatar almost unkillable. Guide, Fortune and Doom can all be mathhammered in general.

Of course with defensive upgrades if all you take is defensive upgrades then your opponent's offense will be front-loaded compared to yours.

The solution to the Honor Guard is to add a Libby with Force Dome to give them a 5+ invuln save. the Honor Guard hit so hard (esp with the Chapter Banner) that you don't need a full 10-man squad. I don't have my spreadsheet on me, but I think a squad of 6-7 HG averages 10 kills on an assault with the Chapter Banner. It seems the growing trend is to get the assault, but not win on your turn, but win on your opponents turn so they cannot shoot you.

I make a lot of use of mathhammer, but one of the things you have to understand about it is when it is useful and when it is not. You can't really come up with an equation that will tell you how much a particular unit should be worth or which unit is better overall. The randomness of the dice and the uncertanty of the battlefield make that impossible. However, what it can help you with is determining what's more useful for a given situation and help quantify how much better it is.
For example, I recently ran numbers for a star cannon vs a scatter laser. Against marines out of cover, the star cannon kills .81 marines per turn (shooting with a bs of 3) while the scatter laser only gets .55, however if the marines are in cover the star cannon goes down to .41 while the scatter laser stays at .55 (since they were getting their normal armor saves anyway). So with this you can see that without cover, the star cannon is by far the better weapon but it's effecitveness goes down to being slightly worse when shooting at targets in cover. While this doesn't tell you which you should have in your army, it does tell you which is better (and by how much) in the cases of cover and no cover when shooting at MEQ's. It is now up to you to decide how often you are likely to see each situation and army your army accordingly.

You can also use it to run mini simulations like Tacobake did earlier where you match up theoretical units. While it won't tell you what the outcome will be every time, it gives you an idea of what to expect. If you want to get more fancy than simple expectation values, you can start using more advanced statistical models for it (I recently added binomal distribution to my spread sheet) but that's only if you really want to embrace the nerd side of the hobby.

I wrote a thing on my old blog if people really want to read it. Note I was actually under the effects of medication at the time.



http://tacobake.blogspot.com/2007/06/40k-eldar-strategy-in-defence-of-war.html

(it was written for 4th ed)

pavonis wrote:So does anyone include survivability into their probabilities, or are they just one-way...to wound/kill an opponent model?
I have been spinning the wheels trying to think up how to include survivability into the equation.
I was thinking of taking the chance to fail an armor + invuln save and multiplying it by the model cost or cost-per-wound.

So a termie with a stormshield would be 2+/3+:
(1 - 0.83) + (1 - 0.33) = 0.167 + 0.66 = 0.83

An LC/shooty termie would be 2+/5+:
(1 - 0.83) + (1 - 0.66) = 0.167 + 0.33 = 0.50

Whereas a standard marine would have a 3+:
(1 - 0.66) = 0.33

I am not quite sure how to use these calculations yet.
Possibly a multiplier against their wound/kill percent to give their overall combat effectiveness.
Is anyone doing anything like this?

Sorry to nitpick, but some of your math is odd.

For example, the shooty termy you have combined (1-0.83) or "chance to fail base save" + (1-0.67) or "chance to pass invulnerable save." I'm not sure if you meant to do that, but I'm not sure why you'd combine two different probabilities. Why not "chance to fail base" and "chance to fail invulnerable?"

I see what you are saying. Good catch.
So the numbers should look like this:

The TH/SS termie should have been:
(1 - 0.167) + (1 - 0.333) = 0.833 + 0.667 = 1.500

The shooty termie should have been:
(1 - 0.167) + (1 - 0.667) = 0.833 + 0.333 = 1.166

The standard marine would be:
(1 - 0.33) = 0.667

pavonis wrote:I see what you are saying. Good catch.
So the numbers should look like this:

The TH/SS termie should have been:
(1 - 0.167) + (1 - 0.333) = 0.833 + 0.667 = 1.500

The shooty termie should have been:
(1 - 0.167) + (1 - 0.667) = 0.833 + 0.333 = 1.166

The standard marine would be:
(1 - 0.33) = 0.667

Yessir.

I just wasn't sure if you had a reason for crossing the math like that, not being a statistician or anything.

But again, now it comes down to the application of those modifiers.

In fact, should you multiply the success rates?

(1-0.167) * (1-0.667) = 0.833 * 0.333 = 0.277

Would that be the "fail rate" of a standard terminator under? I dunno, haven't had enough stats classes...

But what is known as Mathhammer can give you an edge in list building, especially for shooty lists.

Not only list building, but also during the game where you need to take down an enemy unit by shooting or cc.

If you really want to find the survivability of a unit, you have to find it's survivability vs every weapon, and then average the results.

This is a pain, so i just do it for weapons I know I'm going to face.

I use math mainly in list building and then some quick in my head math for figuring out what units to prioritize duing a game. Math hammer is very valuable in deteriminng the most effective units and load out.

I think there's really just two scenarios of weapons you need to figure out. 1) the horde army which is just a mass of shots and 2) TEq/Anti-vehicle weapons to force your termies to make invuln saves. There is a little grey area on the roll to wound based off different strengths, but not as common. Why point those at a termie when you could make them count for more against a MEq or GEq unit.

The modifiers I have above would either go against the point cost per wound value or against the cost of the model to find it's true cost. Then you can find the models that are most efficient for the points. For example, Honor Guard are almost all in the green (which on my spreadsheet means their cost per wound is lower than their point cost, though they can cost up to 50pts per model, but they will average killing 1-2 opponent models each turn in CC). You only need 6 HG (with relic blades and chapter banner) to average killing a 10-man tac squad or 7 non-SS termies in one turn on an assault. Yea, best wargear scenario, but even without upgrades, it's almost 6 marines or 3 non-SS termies. Half it for SS termies. The downside to them is they have no invuln save without a librarian for 100-150 more pts. At which point termies outprice them and even the same points in assault squads comes fairly close.

But basically I made a spreadsheet with two tabs; CC and shooting and it compares every SM unit model against the GEq, MEq and TEq to find their kill rate and cost per wound. In most cases, I can just flip the sheet around to see how well my termies would survive against certain unit or weapon types. If I know how well I can kill a TEq with a weapon, I know how well I can be killed with the same or similar weapon.
I just added a third tab where I can create units with various loadouts like an assault squad with 2 flamers vs. 2 plasma pistols, and a sgt with PF or PW. I can see the total kills per unit base and on an assault.
Can you tell I took both probabilities and discrete mathematics courses in college? LOL.

Ah mathhammer, how I love thee. Let me count the ways.

Terminator vs. Guardsman, Terminator gets charge.

3 Attacks.
4+ needed to hit, chance to hit= 1/2
2+ needed to wound, chnace to wound= 5/6
No armour save allowed for Power Fist hits.

(3)(1/2)(5/6)(100)=125

Dude's getting his skull pulped.

Let's look at this in reverse shall we?

Guardsman Steelballs tries to get a hit in as the wrecking ball comes in for a landing.
1 Attack.
4+ needed to hit, chance= 1/2
5+ needed to wound, chance= 1/3
2+ armour save, chance= 1/6

(1)(1/2)(1/3)(1/6)(100)=2.778

Dude ain't hittin'

It's useful for determining the probability of a unit winning or losing HtH. If you know ahead of time that your guardians are a favorite over Tau Firewarriors you can gleefully fleet and charge them in. On the other hand you would stay away from those evil Dark Eldars! You just can't reliably beat them. Though the DE may only be a 60/40 favorite over Guardians.

Shrike78 wrote:If you really want to find the survivability of a unit, you have to find it's survivability vs every weapon, and then average the results.

That wouldn't be a realistic reflection though, you should factor in your likelyhood of meeting those weapons. You come up against lasguns far more often than lascannons, you gain a lot more by upgrading a unit to make them immune to lasgun fire then you do by upgrading a unit to be immune to lascannon fire (if it were possible).

Howard A Treesong wrote:

Shrike78 wrote:If you really want to find the survivability of a unit, you have to find it's survivability vs every weapon, and then average the results.

That wouldn't be a realistic reflection though, you should factor in your likelyhood of meeting those weapons. You come up against lasguns far more often than lascannons, you gain a lot more by upgrading a unit to make them immune to lasgun fire then you do by upgrading a unit to be immune to lascannon fire (if it were possible).

I agree, most player in their gaming spots normally would know what or who they are facing if they play often.

Mathhammer is just fuzzy math. Most of the time stuff that works on paper (math) rarely does on the table top. I usually dont rely on Mathhammer because of the mutable factors of point level, Luck, terrain, skill, and situation. I dont look at 40k as a numbers game but I can look at 2 units facing one another and know who can win a hth fight.

I use it to work through combinations and chance of hitting/surviving melee or ranged weapons.

For example, I use my own spreadsheet and if attacking with guardians against space marines:

Fortune? FALSE
To hit 4
To wound 4
Amour (7 for no armour or against an AP weapon) 3
Number of attacks 40

Expected hit % 8.3%
Expected wounds 3.3

(or about 3.5 if you include a shuricannon)

Then charge into combat against the 7 remaining space marines:

Fortune? FALSE
To hit 4
To wound 5
Amour (7 for no armour or against an AP weapon) 3
Number of attacks 40

Expected hit % 5.6%
Expected wounds 2.2

Against the 7 space marines (with seargant)

Fortune? FALSE
To hit 3
To wound 3
Amour (7 for no armour or against an AP weapon) 5
Number of attacks 8

Expected hit % 29.6%
Expected wounds 2.4

So - even after shooting first and charging guardians are most likely to draw the combat - before being run down the following turn (1.8 vs 1.0 expected wounds).

So - 170 points of guardians are brought low by a 170 point SM tactical squad - by the numbers.

tallmantim wrote:So - even after shooting first and charging guardians are most likely to draw the combat - before being run down the following turn (1.8 vs 1.0 expected wounds).

So - 170 points of guardians are brought low by a 170 point SM tactical squad - by the numbers.

Here is the thing when using mathhammer. You have to know how to apply the information you get. While the first part of Tallmantim's post here was clasic math hammer and shows you that guardians are not likely to do well against marines, the final conclusions, however, are inaccurate. It is in fact true that the guardians will probably lose combat by ~1 wound. The thing is that after that, you can't assume that the result of a one time roll (the moral check at the end) will be a failure, particularly since it is only going to be taken at -1 if the combat has an average result. In the end, I would look at this situation and say that the guardians will most likely lose in the long run, but in the first round they have ~50% chance (I'd have to run the numbers to get the precise %) of sticking arround till the second round. You will have to decide what to do with that information, but that is what this tells you.