Mathhammer vs TableHammer; Relationship

[Mileposter]

For the rest of that definition in the Oxford English Dictionary- "or expected". It's that expectation that the thinking gets really skewed.

[M@verik115]

While you are arguing, I am gonna go help my uncle Jack off a horse. 

[NatBrannigan]

Well I would expect half my lasgun shots to hit the target, I might be disappointed or pleasantly surprised though.

 

Anyway, enough with the delightful pedantry, we're arguing the same point that Math is far from everything and people do make (in my opinion) bad choices when they look just at the math because they're thinking spherical Guardsmen in a vacuum.

 

Space Marine Aggressors are beyond good for instance, outrageously so. But good luck getting them near a viable target alive!

[BitsHammer]

Personally I try to restrict Mathhammer to choosing one set of wargear over another, or comparing average damage outputs between two very similar choices.

 

An example of this was the Power Maul vs Power Sword vs Power Axe load out in 6th and 7th. For Sisters the Maul was mathematically better because the increase in strength meant rolling wounds more often which was more important than ignoring more saves for them but on Marines it was usually the reverse that held true: their stats meant that swords were more useful than mauls in most cases.

 

To me this is the best use of mathhammer. It lets you find that sweet spot in options that works best for a given model against a wide range of targets allowing you to build better TAC lists.

[Firepower]

Yup, rarely is my mathhammer employed for anything beyond picking the 'right' stabby thing or shooty thing.  Mostly stabby things, naturally.

[Claws and Effect]

Well I would expect half my lasgun shots to hit the target, I might be disappointed or pleasantly surprised though.

 

Anyway, enough with the delightful pedantry, we're arguing the same point that Math is far from everything and people do make (in my opinion) bad choices when they look just at the math because they're thinking spherical Guardsmen in a vacuum.

 

Space Marine Aggressors are beyond good for instance, outrageously so. But good luck getting them near a viable target alive!

Play Raven Guard and watch that problem disappear. ;)

[totgeboren]

Personally I try to restrict Mathhammer to choosing one set of wargear over another, or comparing average damage outputs between two very similar choices.

 

An example of this was the Power Maul vs Power Sword vs Power Axe load out in 6th and 7th. For Sisters the Maul was mathematically better because the increase in strength meant rolling wounds more often which was more important than ignoring more saves for them but on Marines it was usually the reverse that held true: their stats meant that swords were more useful than mauls in most cases.

 

To me this is the best use of mathhammer. It lets you find that sweet spot in options that works best for a given model against a wide range of targets allowing you to build better TAC lists.

 

And this was the reasoning behind the very long thread about guardsmen. A guardsman squad and a tactical squad are "two very similar choices", having almost the same options, versatility, mobility, and on a points basis resilience.

 

It doesn't make sense to compare a Fire Prism to a Guardsman. When does it stop making sense?

Terminator vs guardsman is probably not that meaningful. Comparing a Multimelta and an Assault cannon might make more sense. The offensive output of a squad of Havocs or a squad of Obliterators might also make sense.

In 7ed comparing a squad of 20 Chaos Cultists with the Mark of Nurgle to a squad of 30 without the mark (so same cost) made sense (giving your cultists the mark of nurgle made them worse by every metric).

 

But I have seldom seen anyone make a bad call on the table due to mathhammer. The other way around is far more true, like giving marks to cultists in previous editions. Paying points to make your units worse is of course ok if you are pushing your theme, but often people saw "+1 T" and though, "wow, this will make my cultists much more resilient!".

 

That is far more common. Or in 4ed, picking a lascannon for anti-tank when you could have an assault cannon instead. The anti-infantry gun was leagues better at anti-tank than the anti-tank gun. Similar in 7ed, where high-rate-of-fire weapons were much better at taking out vehicles than dedicated single-shot anti-tank weapons. And by better, I mean that the same model has a higher % chance of killing their target if they have one gun over the other.

 

And all this is mathhammer.

[MrZakalwe]

That is far more common. Or in 4ed, picking a lascannon for anti-tank when you could have an assault cannon instead. The anti-infantry gun was leagues better at anti-tank than the anti-tank gun. Similar in 7ed, where high-rate-of-fire weapons were much better at taking out vehicles than dedicated single-shot anti-tank weapons. And by better, I mean that the same model has a higher % chance of killing their target if they have one gun over the other.

This edition's version of that is when people load up Devastators with missile launchers when an even split of lascannons and heavy bolters will put more wounds on pretty much any target in the game while costing less points.

[Frater Cornelius]

Mathhammer can’t take into account player stupidity and lack of common sense :P

[Wargamer]

Mathhammer can’t take into account player stupidity and lack of common sense

It can, if your model is complex enough. But there's the rub - you ultimately get to the point where you're creating something that is so damn complicated it actually becomes more practical to just play a game of 40K and test it that way.

 

Mathhammer is meant to be a way to simulate potential scenarios. You can absolutely simulate things like bad choices or bad rolls, but most proponents of Mathhammer recognise that you really want to aim for a middle of the road simulation, because otherwise you're wasting time and effort.

[Karack Blackstone]

Mathhammer is math.

Tablehammer is what happens.

 

Probability is the attempt by math to predict that which may occur on the table; the single biggest issue is, as many have pointed out already, may, should, and might all apply.

 

Dice are not 100% predictable. Fate, Chance, and Luck are all old-world concepts that can be argued to still apply to this day; if your Fate, Chance, and Luck say you are to lose however many wounds on any given save roll, well, the only way to find out is to roll the dice.

 

Good luck.

[Wargamer]

The theory behind Mathhammer is that all the bumps and dips balance out in the long run. Yes, you might utterly fluff your hit rolls, but you might then get exceptionally lucky wound rolls, or vice-versa.

 

I suspect the nay-sayers against Mathhammer would do well to roll some dice and keep a tally of how well they do - the more rolls the better - and then compare to what Mathhammer says they should get. It might just prove enlightening for some.

[Mileposter]

I enjoy Mathhammer, when applied properly.

 

My dislike is that many of those who claim to apply Mathhammer properly... Aren't.

 

My aversion of Mathammer is entirely due to those who wield it. Those who do not utilize it as a diagnostic tool but instead brandish it like a weapon. There is a habit for those who fall onto Mathhammer to view damage output as the only measure of a model. There seems to be a steady recurrence of those who tout Mathhammer to take the numbers of probability as entitlement. And there are many of those who use Mathhammer to generate unreasonable expectations (even if their Math is accurate) about the game and performance.

 

I like Mathhammer, when those who use it treat it as possibility rather than probability. Because the attitudes between them are vast.

[Frater Cornelius]

Dunno. To me this seems to be the same issue as economics and all that jazz. All those complex mathematical models and still it can only give you a very vague approximation. Humans are not rational and thus can not be quantified in a mathematical model. Even if they could, there are so many variables to consider, some of which can’t even be quantified themselves. How do you take into account movement, reading your opponent, feinting or even jusf a hunch or intuition? It is not that I distrust math. I distrust the human using the math correctly.

 

Edit: Besides, most mathhammer is not accurate. Only resorting to probability will never yield as accurate of a result as a binomial distribution or a similar distribution model will. I have written about it somewhere in the SM and AdMech section a while back. Most simply do not know how to use this, making the use of mathhammer very general and vague to be preached as the gospel.

Edited January 31, 2018 by Frater Cornelius

[ERJAK]

 

 

Yep. There are plenty of people in the hobby who are mathematicians and statisticians. And plenty of said people have done plenty of mathhammering to build perfect army lists that...immediately fall over due to any number of extraneous factors including the 'stupidity' factor that math seems to have problems dealing with.

 

Except the ones who win tournaments consistently because they have stacked the odds in their favour time and time again?

Yeah, duh. Why did you pose this like it was some big mystical thing? Yeah, really solid math hammering+skilled table play (often incorporating mathhammering) is mandatory to winning big tournaments. Again, DUH. Some people have great mathhammering and terrible, sloppy table play and lose because of it. 3rd duh.

 

I feel like you should probably attempt to contribute something useful to the conversation instead of...whatever you thought this was.

[totgeboren]

 

 

Yep. There are plenty of people in the hobby who are mathematicians and statisticians. And plenty of said people have done plenty of mathhammering to build perfect army lists that...immediately fall over due to any number of extraneous factors including the 'stupidity' factor that math seems to have problems dealing with.

Except the ones who win tournaments consistently because they have stacked the odds in their favour time and time again?

Yeah, duh. Why did you pose this like it was some big mystical thing? Yeah, really solid math hammering+skilled table play (often incorporating mathhammering) is mandatory to winning big tournaments. Again, DUH. Some people have great mathhammering and terrible, sloppy table play and lose because of it. 3rd duh.

 

I feel like you should probably attempt to contribute something useful to the conversation instead of...whatever you thought this was.

 

 

I wrote that because what you wrote is simply improbable in the extreme, and also incoherent. Your statement implied some mystical correlation between being good at maths and consistently losing at a game that heavily relies on probability manipulation.

You wrote that "There are plenty of people in the hobby who are mathematicians and statisticians". Ok, we can both agree here. But this means people educated in these fields right? It implies an ability to work as a professional in said fields if you are defined as a "statistician". At the very least it implies someone who is competent in the fields to successfully do the relevant calculations in the first place.

 

But then you wrote that, of the people who are competent in the fields of mathematics and statistics, plenty (that is; many, a significant portion, the majority) consistently fail on the table-top due to lacking the cognitive abilities required to assess and take into account such factors as resilience and model movement in the game of 40k. If you have the faculties to do the most intellectually demanding part of 40k analysis, you will likely do just fine in understanding that your opponent will shoot back at you. It is improbable in the extreme that what you wrote is true.

 

You essentially said that math-hammer increases your chance of failing on the tabletop. And this is just flat out false.

 

It is incoherent because to even do math-hammer-stuff, you need to be able to calculate how resilience impacts different guns and movement. Otherwise you can't do say weapon comparisons in the first place. Otherwise you could not say that X gun is a better anti-tank gun than Y, or that gun X is better than Y if you also fulfill condition Z.

 

And sure, taking movement on a table with terrain into account can be complicated to quantify. But by comparison, it's not complicated to asses. "I need to be able to move x number of times, likely one in the open, if I am to reach my target, given my Move value. Consider what my opponent is likely to bring, will my unit make it?".

Or: "I hope I get a table with lots of terrain, because my unit Z is squishy-but-killy".

 

People who fail due to math-hammer are either those who are not statisticians and mathematicians, who do not understand how to calculate statistics, or who made some other mistake.

 

I often make armies that are based around a theme (fluffy armies), but I am fully aware that I am not stacking the odds in my favor. Without thinking I often make remarks like "Aw man, you only had a 11% chance of managing that, I was sure my dude would be fine!" and similar during game-play.

Still, I see 40k more as an opportunity to tell a story than having an intellectual bout.

But I have also made armies that I math-hammered to be as potent as possible (latest to win vs an Eldar player who made much stronger armies than the rest of us in the group), and the change in general effectiveness is just staggering in many cases. And as expected it's just easier to play and win if you mathhammer before the battle. It is probable.

 

But it might not be as fun.

 

If you don't enjoy mathhammer, that's fine. But there was no need to say that people who do enjoy mathhammer are generally bad players.

Edited February 1, 2018 by totgeboren

[D3L]

I feel like you should probably attempt to contribute something useful to the conversation instead of...whatever you thought this was.

In the same vein my good frater, it's probably best you stop embarrassing yourself w.r.t Maths

 

Not understanding is fine, not utilising is fine, and no one will judge you, but if you wish to understand what is happening and how the laws of large numbers affects your game, well, then it's probably time to pick up the mathshammer ;-)

[WarriorFish]

I'm sure I can speak for many when I say I'm a little tired of topics requiring closure due to consistent poor behaviour on display. If you can not disagree with someone in a civilised manner please reconsider your post. Please participate in the manner expected on the B&C or more drastic action may be required. Thanks.

 

 

[Claws and Effect]

I only use the most rudimentary mathhammer, mostly because going any further feels like I'm doing math homework instead of playing a game.

 

I suppose I could go that in depth and give myself the best mathematical chance of winning. But if I were to do that it would very much feel like I was prioritizing winning over having fun.

 

If my opponent is a fun person to play with I can still have a blast getting curbstomped. It's only when I get curbstomped and my opponent gloats about it that it ceases to be fun.

[CMDR_Welles]

Mathhammer?

Tablehammer?

 

I remember a time when we all just played Warhammer... It was a simpler time, it was a fun time.

 

Can't we return to those days? No one worried about "optimum", or "best", and just concentrated on playing with the models they had, liked, and enjoyed painting and playing with.

 

I miss the days before tournaments. People played campaigns, or recreated famous battles, or sat and had fun discussing the games they had played, and the heroes they had created.

[Wargamer]

Just to demonstrate, and to put my money where my mouth is, I decided to do a Mathhammer / Tablehammer comparison.

 

So for this example I'm going for Incinerators vs Uber Guys (T8 3+ save). Mathhammer suggests that an overcharging Incinerator should deal 3.3333 wounds at 16-30", and 6.6666 at 1-15".

 

The logic is simple: 5 shots > 3.333 hits > 1.66666 wounds, each wound causes 2 damage, giving 3.3333 damage per volley. Rapid fire range doubles the shots, thus doubles the damage.

 

So here's what I got:

 

16-30"

1 - 4 hits, 1 wound, 2 damage.

2 - 1 hit, 1 wound, 2 damage.

3 - 4 hits, 3 wounds, 6 damage.

4 - 2 hits, 2 wounds, 4 damage.

5 - 4 hits, 2 wounds, 4 damage.

6 - 2 hits, 2 wounds, 4 damage.

7 - 4 hits, 3 wounds, 6 damage.

8 - 3 hits, 3 wounds, 6 damage.

9 - 4 hits, 1 wound, 2 damage.

10- 2 hits, 2 wounds, 4 damage.

11 - 4 hits, 0 wounds, 0 damage.

12 - 3 hits, 3 wounds, 6 damage.

 

Average: 3.08333 hits (expected: 3.3333), 1.91666 wounds (expected: 1.6666), 3.8333 damage (expected: 3.33333)

 

12 batches of 5 dice are not an exhaustive sample, but you can see that it's not far out. We got less hits than expected, but did better on the wounds / damage.

 

Mathhammer isn't a guarantee by any measure, but it certainly looks like it's a good way to estimate your success or failure.

[BitsHammer]

Honestly, while it is possible to build complex mathematic models to win games (there are people who do it to win money playing Fantasy Football after all, and that has even more variables than 40k does), at the end of the day I feel that relying too heavy on averages doesn't win me games. Sure, it gives me the safe bet, the sure bet, and the optimum choice, but sometimes you have to throw all of that away and take some risks to win games.

 

Then again I'm just some dork who pushes plastic models around the table and will play games out to the very end because I always feel that even if I can't win, tying isn't impossible (pulled a win once with three models against a barely wounded Necron army thanks to objectives. Definitely a "winning the battle, losing the war" moment, but it was great to see my Sisters of Battle eke out such an unlikely win. If I was betting on averages I would have scooped two turns prior).

 

Knowing how things should work most of the time is certainly useful, but when you over-rely on it, then it becomes a crutch that can actually drag down your decision making and prevent you from being willing to take the risks you may need to take to win more games.

[totgeboren]

I guess the thing that throws people off, or causes misunderstanding is... hmmm... say someone has a 33% chance to kill an enemy with their attack (hit on a 3+, kill on a 4+).

So you wanna shoot one enemy with that attack and you have your dude who hits on 3+ and kills on 4+. How many shots would you shoot?

Most might say "3 shots, each hit on 3+ so 2 hits, each kills on a 4+ so 1 kill. Yay."

But you roll your dice and the enemy survives, and then you think "Mathhammer sucks!"

 

And this is because what you were interested in is really not how many wounds you would do on average, but how large a chance you had of slaying your enemy. And what chance was that? Well, the enemy had a 2/3 chance of surviving each shot if each shot had a 1/3 chance of killing him. So his chance of surviving was obviously not 2/3+2/3+2/3=6/3, or 200%.

 

It was (2/3)^3=~30%, which means you only had a 70% chance of killing your enemy with your three shots. With 4 shots you would have around an 80% chance till kill your enemy, and with 5 shots you would be up at 87% chance to kill the enemy.

And when you get an intuitive feel for this, it's easier to apply the appropriate amount of force to whatever problem you are trying to solve on the table, and thereby reducing the impact of bad luck.

That's how I see it at least.

[Schlitzaf]

MathHammer as others said is a good way to guestestimate outcomes. And while I and many, X Unit with Y Gear commiting to task A equates to Z Outcome with MathHammer. It should be read as “X Unit with Y Gear commiting to task A in the majority case of the G Scenerio statistically result in Z Outcome.” Someone said earlier about the Berzerker “only 60% chance of occurring”. Well yes, in the game, that means it will occur 60% more likely than than 40% chance to fail.

 

The extension of said point, is riddle me this, why do we play? If the scenerio didn’t have atleast two different probable outcomes. Why would we even bother to play? The reason we play is because, that is their is a chance. A chance to succeed and a chance to fail. How many folks have played a game where you needed Double Six’s to win? That is 1/36 likelyhood of success. MathHammer says that 35/36 likelyhood of failure. We see on the table that their 1/36 chance to success.

 

What is a ‘statistical’ anomaly is why we play. One of my favorites games I ever played. Back in fifth edition. It was an Apoc Game, 1500 Points + Free Formation. A Chaos Player brought Angron and his retinue of Bloodthristers, plus a horde of lesser Daemons and Berzerker, right before the 5th Ed GK Codex Dropped. We the Imperium, threw, 3 Baneblades, 2 Reavers, Assassin Strike Force, Grey Knight Teleport Strikeforce Formation, 10 Dreadnoughts (Ancient Battleforce), Imperial Gaurd Shield Company, Ultramrine Battle and 1st Company, Yarrick, Celestine, Lysander, Calgar, 50 Black Templars, Emperor’s Champion, 10 Hammerators, Vulcan, 2 Land Raider, an Ork Stompa, Two Vendettas and 60+ SOBs.

 

And by the end of the game? Angron survived. He marched through every single thing we threw at him. He cut us down. That should never had happened. But it did. Because no matter how statistically unlikely, it happened.

 

MathHammer is great for quick evaluation, but the reason we play is that the tabletop outcomes are never garunteed. But understanding the math let’s you weigh the situation to be best in your favor. And then sometimes Angron happens.

Edited February 1, 2018 by Schlitzaf

[totgeboren]

Hehe, yeah it's the statistical anomalies that really makes the game shine. Stuff you remember for years later. :)