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Ok, I expect that most people here will have done some math hammer at some point in time, to work out, say, how many orks your tactical squad can kill in one round of shooting, or something similar. It can come in useful, and even win you the game occasionally.

All well and good. However, what if you need to know how likely it is that the squad will kill the 5 boyz before next turn when they're going to charge and destroy your whole plan? All you know is how many you're likely to kill which, while giving you some idea, won't tell you the exact figures.

What's more, it takes ages to work out how many you're likely to kill if you haven't done it in advance, and unless you brought a calculator to the battle, it's pretty much impossible. Even the calculators on most smartphones take forever to get to the answer.

So what should you do? Simply guess the probability and possibly make a mistake?

Luckily, I've come up with a solution. With the graphs attached, you can work out the chances of killing 5 orks with 17 bolter shots (7 guys rapid fire, serg. and heavy weapons fire their bolt pistols, flamer hits one) by simply working out that there's a 1/3 chance per shot of killing an ork (2/3 x 1/2) and looking at the graphs. Have them on your smartphone or print the most common ones off, and you have a game-winning set of probabilities literally at your fingertips, which could easily win you the game, telling you at a glance that it's far more likely to succeed than fail, so you probably won't need to divert any more resources.

Of course, this is a simplistic example, as all examples should be, and most players should be able to tell straight away that the marines have the advantage. With more complex examples, however, it can work just as well, telling you, again, at a glance that your 12 splinter shots from that venom are likely to take the last wound from the carnifex with a 3+ save, but still have almost 1/4 chance of failing (0.2433). This kind of precision can easily win a game.

The boring, nerdy bit: All the numbers are to 4DP but this is easy to change, and all the copyright really means is that I don't want you making money from it without paying me some of it.
The formula used throughout may seem complex, but if you look carefully you should be able to edit it easily to make any graph you want. Also, I've only gone up to 24 because it doesn't often get above this in shooting, but feel free to add more to it whenever you want, simply by adding more numbers and space (by inserting rows) and dragging the formula across.
Also, sorry but I've only got the old excel, if this causes any troubles.

The top numbers represent the number of attacks/shots being fired. The number of dice that need rolling. The left numbers are the times that the roll will succeed. Remember to use the graph that's the correct chances.

Replies welcome. (All flames will be sent to satan as per our agreement .)

This is all well and... full of decimal points, but you don't have to be so complicated with graphs and what have you. Especially as the best you can do with statistics is estimate expected values (which the dice won't always agree with).

For that, you can just use standard deviation. Or, better yet, the quick, bastardized version of standard deviation I usually use. Basically, you just multiply things together, and you get more or less the expected value. It doesn't tell you how far you deviate before you walk outside of the bounds of the standard deviation, but it's basically as good.

Take your example. You have 5 boyz still with a KFF and you want to kill them in one go with some space marines. How many marines should you shoot in order to expect to down the boyz?

the KFF blocks 1/3 of the shots, so .666 successful wounds will kill. The toughness to weapon strength means that .5 hits will wound. The BS of the shooter means that .666 of shots fired will hit their target. Thus, for a single shot, you should expect to kill about .22 ork boyz. Put another way, it should take about 4 or 5 shots to kill a single ork boy. To be more exact (dividing 1 by .22), it should take 4.454 shots.

So, you want to kill the 5 boyz? multiply by the shots per boy and you get 23. Assuming that the marines are double-tapping, this means that for the elimination of all 5 boyz in a single shot to be the most expected result (without going overboard), you need to have 12 bolters unload on the boyz.

12 bolters, 24 shots, 16 hits, 8 wounds, 5 boyz dead, with a little extra (a third an ork) just in case.

This way you don't need to be constantly consulting a bunch of graphs for something which is still applying to a specific set of die rolls about which statistics can only ever give you general information.

Statistics is not limited to calculating expected values. The OP calculated the probability of acheiving certain results, which is not an expected value.

That said, this chart would read a lot better if you calculated survival probabilities instead, which is just 1 minus the cdf. It's much more useful to know, for example, the probability that 10 Tactical Marines wipe out 5 Boyz than the probability that the kill exactly 5 Boyz. Yes, you can calculate these more relevant probabilities from your charts, but the whole point is to have the numbers at a glance.

MrEconomics wrote:Statistics is not limited to calculating expected values. The OP calculated the probability of acheiving certain results, which is not an expected value.

Well then what's the point?

What's the point of knowing the odds of something happening unless you mean to do something with those odds. You can only make decisions based on what they expect to happen. The odds themselves don't seem to have utility.

I'm "intelligent" and can figure out whatever mathhammer I need to mid-battle.
Sounds arrogant though.

Of course it would be a Tau player that comes up with this. Nice work P_gray99

I fully understand and appreciate this, and math hammer for what it is.

That said, I absolutely hate using it. Not just because I hate math, which I do, but because it, to me, and I'm sure a lot of other players, ruins the game when you calculate everything out.

I've been playing tabletop games since '92, and GW systems since '94, and I've never once stopped and calculated out a bunch of hit/wound probabilities. It just takes all the fun out of it for me.

For me, the game is about tactics, strategy, taking chances, and when to hold back. I'm sure I'll lose some games to people with iPhone apps that allow them to assign a probability to each action. And I don't care.

Painting and miniature building is an art, not a linear science, and I treat my games the same way. If I'm calculating a move, then I'm not having fun playing to my own personal satisfaction.

I generally go by the following maxim: Marines generally hit what they shoot at and generally kill what they hit. Guard, not so much, but they have a LOT of dudes shooting.

That said, if math hammer works for you, and there's a lot of potential there, great, no slam from me, but it's just not my bag, baby.

YMMV.

kustom wrote:That said, I absolutely hate using it. Not just because I hate math, which I do, but because it, to me, and I'm sure a lot of other players, ruins the game when you calculate everything out.

For me, the game is about tactics, strategy, taking chances, and when to hold back. I'm sure I'll lose some games to people with iPhone apps that allow them to assign a probability to each action. And I don't care.

Well, but that's what 40k IS. Tactics and strategy is little more than playing odds in one way and not another. There are no "right" odds to play, which is why the people who know the best mathhammer don't always just win games straight away.

That said, like in any other game of chance there are better odds to play which give you a better chance of success, depending on what the circumstances are. People who are able to do a little bit of simple fraction work in their head on the fly are able to more clearly understand their choices.

Whether you should shoot a pair of missile launchers at a chimera with its front armor facing you, or another chimera that you get a side shot on, but is obscured by the first don't give the same odds of a wrecked chimera. Being able to calculate which has a higher expected damage can help you make better decisions in this case, and that's just one example amongst many that can come up.

For example, I've done a lot of work with guard power blobs, and I've spent a fair amount of time doing the math to see what a power blob can and cannot beat. Knowing if I have a reasonable chance of wiping out that terminator squad with just the one blob or if I'm going to need two to finish it off can make a big difference. Knowing in advance, thanks to mathhammer, what I should expect my units to be capable of is very helpful on the field.

When I first read this subject I thought I had taken a wrong turn into a Techpriest lecture... but Aliaros broke this down so us grunts could understand the logic thread. "Knowing in advance, thanks to mathhammer, what I should expect my units to be capable of is very helpful on the field." Having an idea how effective a unit can be before deploying it on the field just makes good tactical sense, and if Mathhammer is a part of that strategy, by all means, smash away. I would just be a bit put off by someone who kept checking a "cheat" sheet or an iphone during a battle. Play the game and smash the math in your head, the game can run long enough with out consulting graphs and charts.

Right, and you can gain expectations other ways, like through your own experiences, for example. The problem, though, is finding a replacement for mathhammer that's also objective. You may have just been really lucky with a certain weapon the first dozen times you used it. That might give you a skewed view of things. On the other hand, if you start bringing autocannons and have to fire over 100 shots before you finally take down a vehicle (like I did), you might come to a certain conclusion that really only applies to a narrow set of circumstances (my luck), rather than to broader principles. I still don't like autocannons, but I like them for more objective reasons than "once I used them and they were terrible".

Mathhammer can also give you a more nuianced look at things because numbers are more articulate than anecdotes. It is probably not going to make much of a difference if you fail to make a certain choice when a different one would have been 2% more likely to yield a favorable result, but, to be fair, that's how people win money at vegas. Playing slightly better odds over and over in the big picture nets you more success.

The only problem, of course, is when you take expectations too far, which is easy to do when you're being backed by cold, hard numbers. "Yes, but what the statistics say SHOULD have happened when I did this..." is a quick path to madness, one which I've walked many a time...

All of which is definitely agreed with.

Ailaros, I definitely respect you opinion, in fact, you're one of the main reasons I have given powerblob IG a chance, and have done great with them, and your posts have been some of the most well reasoned I've seen while lurking this forum.

That said, and I may be old school, but I believe there's a certain amount of "what can I expect out of this unit" that each player should weigh before plonking it down on the table, or writing it into their army list.

If Math hammer gives a player that "Oh, well, I'm not really sure if this is good or not, let me find out before throwing this or that out there," then so much the better.

However, I play by the looser "common sense" rule than mathematical averages.

Will 10 Marines knock out 10 Orks in the shooting phase? Depends on what they're armed with, but either way, they'd have to be darn lucky, so I know, if I need them 10 Orks DED, I'm going to have to task more firepower to see it done.

I'm not going to whip out some homebrew Java app or stop the game to calculate how many of my tac squads I need to punch that guy's troops out, I select the most efficient weapons I have at my disposal based on the stats and my experience, and what I have on hand (limited math hammer, I know), and go to town.

I think Math Hammer is like the internet... sure, you can find out "statistically" or "what other people think", but it takes away the experience of knowing and playing your units as best you can based on actually doing it.

Again, not trying to flame, just my .02.

I appreciate the work you went through to do this but i have to say that if someone pulled out a mathhammer aid in a game against me i would be pissed. I do mathhammer in my head when i play people, they know what i am working out, but i can promise you that most of my foes would be pissed at me if i pulled out a mathhammer aid in battle too.

MrEconomics wrote:Statistics is not limited to calculating expected values. The OP calculated the probability of acheiving certain results, which is not an expected value.

That said, this chart would read a lot better if you calculated survival probabilities instead, which is just 1 minus the cdf. It's much more useful to know, for example, the probability that 10 Tactical Marines wipe out 5 Boyz than the probability that the kill exactly 5 Boyz. Yes, you can calculate these more relevant probabilities from your charts, but the whole point is to have the numbers at a glance.

This is indeed what I created the new math hammer for. Also, I'll start another sheet with the inverted probabilities as well, alongside another for the chances + the chances above it etc. should be easy enough.

junk wrote:Of course it would be a Tau player that comes up with this. Nice work P_gray99

I see where you're coming from, lol. Thanks

kustom wrote:That said, I absolutely hate using it. Not just because I hate math, which I do, but because it, to me, and I'm sure a lot of other players, ruins the game when you calculate everything out.

I've been playing tabletop games since '92, and GW systems since '94, and I've never once stopped and calculated out a bunch of hit/wound probabilities. It just takes all the fun out of it for me.

For me, the game is about tactics, strategy, taking chances, and when to hold back. I'm sure I'll lose some games to people with iPhone apps that allow them to assign a probability to each action. And I don't care.

Yeah, I understand how math hammer is boring for some people and doesn't suit their style of play. If you don't like it, don't use it, and I expect this will mostly be used by tornament players etc. Still, if a quick glance now and again wins the game, why not?

sennacherib wrote:I appreciate the work you went through to do this but i have to say that if someone pulled out a mathhammer aid in a game against me i would be pissed. I do mathhammer in my head when i play people, they know what i am working out, but i can promise you that most of my foes would be pissed at me if i pulled out a mathhammer aid in battle too.

Again, this isn't for everyone, but just because they do this doesn't mean that they stop playing dangerously. Of course people will still take risks! It's just that they won't take risks if they didn't actually want to. Don't use it if you don't want, and save 119kb. It's basically just an update to math hammer, so if you didn't use math hammer .1 don't even think of using this more complicated version. Each to his (or her) own.

Thanks for the replies .

For me, the game is about tactics, strategy, taking chances, and when to hold back

This statement does not invalidate the use of mathhammer, it supports it.

Good Tactics means moving your models in a way you know will should beneficial. This can only be determined with math hammer. A good guess or hunch, made without knowing the odds, is a quick way to defeat, unless you are 'lucky' and guessed right.

Knowing mathhammer also lets you know about taking chances. If you dont know the odds, how can you be taking chances? IE, if you have a 30% chance of sucess of winning the game with one move, versus a 15% chance of winning the game with another move, which move are you going to be taking your chances with?

While I would be against pulling out a statistics device during gameplay, this is because it would slow down the game. That has as much to do with liking/disliking math hammer as someone abruptly having a 5 min conversation with another friend in the middle of the game. Call that for what it is, poor behavior. Dont drag math hammer down because of that.

I whilst I would consider myself intelligent, I do admit I was a terrible, terrible math student.


But damn dice math is easy.

DevianID wrote:

For me, the game is about tactics, strategy, taking chances, and when to hold back

This statement does not invalidate the use of mathhammer, it supports it.

Good Tactics means moving your models in a way you know will should beneficial. This can only be determined with math hammer. A good guess or hunch, made without knowing the odds, is a quick way to defeat, unless you are 'lucky' and guessed right.

Knowing mathhammer also lets you know about taking chances. If you dont know the odds, how can you be taking chances? IE, if you have a 30% chance of sucess of winning the game with one move, versus a 15% chance of winning the game with another move, which move are you going to be taking your chances with?

While I would be against pulling out a statistics device during gameplay, this is because it would slow down the game. That has as much to do with liking/disliking math hammer as someone abruptly having a 5 min conversation with another friend in the middle of the game. Call that for what it is, poor behavior. Dont drag math hammer down because of that.

A good point, and well put. Thanks for the support!
I have tried to make the graphs easy to find what you want so that only a quick glance is needed, and it won't slow the game down overly. Still, if an opponent is getting annoyed at you for using this, don't. This is just the same, however, as thinking for a short while with the old math hammer. Use this new version where you would the old math hammer, and don't use this were you wouldn't use the old math hammer.
Also, it seems that only some of the people here are understanding what math hammer is for, and you've just hit the nail on the head. Thanks

Jihallah wrote:I whilst I would consider myself intelligent, I do admit I was a terrible, terrible math student.


But damn dice math is easy.

Not this. It isn't simply a 1/6 chance of getting a or a . 22 dice with a 4 in 9 chance of success is far more complicated.

p_gray99 wrote:

Jihallah wrote:I whilst I would consider myself intelligent, I do admit I was a terrible, terrible math student.


But damn dice math is easy.

Not this. It isn't simply a 1/6 chance of getting a or a . 22 dice with a 4 in 9 chance of success is far more complicated.

Call me special then. Figuring out lady average really ain't that hard, and better than hoping for lady luck to come to this pub.

Agree, it's not that hard. If you toss 22 dice, you can easily figure out how many hits, wounds and unsaved wounds you are going to get. All you need to do that is the ability to divide by 2, 3 and 6. Then, if you are vaguely familiar with a bell-curve and know that you are less likely to stray far from the average the more dice you toss, you can pretty much guess the chance. The exact chance isn't that relevant, as it's still possible that you roll all ones with 22 dice.

Jidmah wrote:Agree, it's not that hard. If you toss 22 dice, you can easily figure out how many hits, wounds and unsaved wounds you are going to get. All you need to do that is the ability to divide by 2, 3 and 6.

no, this is normal math hammer. Mine is far more precise, more reliable, and therefore far better.

Jidmah wrote:Then, if you are vaguely familiar with a bell-curve and know that you are less likely to stray far from the average the more dice you toss, you can pretty much guess the chance. The exact chance isn't that relevant,

yes it is, if you need your 22 shots to take out 2 terminators and don't know whether you'll need to assault afterwards. You may work out that on average you'd kill one and a bit terminators with 4s, 3s and a 2+ save, but if the game isn't going your way you'd want far more precise chances of whether you'll kill two rather than simply none or one. With a glance, working out there's roughly a 0.65 chance of failing, you suddenly know you've got enough chance to manage if you're already unlikely to win.

Jidmah wrote:as it's still possible that you roll all ones with 22 dice.

Yes, but there's nothing maths can do about this. It's chance. It's what makes the game fun, even when you know the exact chances. I really don't see what your point is here.

22 Shots(assuming boyz) will result in 7 hits, about 4 wounds and zero to two wounds at the core of the bell curve. An assault of those 11 boyz will cause 33 attacks, 16 hits, 8 wounds and 0-3 wounds if no boyz died. So I better get some more boyz to kill those terminators over here, or add more shooting to make sure they go down.

I didn't use calculator, a codex or looked at a curve to do that, and still know what to do. That's my point, the exact chances of those 11 boyz killing 5 terminators are largely irrelevant, as I'm not trying to gamble my way out of the game, but to make tactical decisions. No matter how perfect your numbers get, lady luck will screw you over (or not), so ballpark numbers are fine.

If you toss 22 dice, you can easily figure out how many hits, wounds and unsaved wounds you are going to get. All you need to do that is the ability to divide by 2, 3 and 6. Then, if you are vaguely familiar with a bell-curve and know that you are less likely to stray far from the average the more dice you toss, you can pretty much guess the chance.

The second bit is true, but we are talking binomial distribution, not normal. Depending on the individual chance of success you can have very different curves to a classic normal probability curve.

Its also worth noting that often you may be wanting to stray from the average. If you are after killing a particular squad then knowing that non of your guys have an expected chance of doing that is not terribly useful, you want to know who has the greater probability of getting sufficiently better than average so you can maximise your chance of not having to put more shooting in afterwarrds.

Take 4 guys with S8 Ap3 weapons firing at marines. And you also have 10 S4 Ap5 guys who can rapid fire the marines. Both squads have exactly the same expected result of 20/9 dead marines.

If you want to kill X marines and have the best chance of having one squad left to act with who do you use to shoot first.

For X = 1-3 the 4 guy squad has a slightly higher chance of achieving your goal than the bolter squad. At X = 1 ( well within expected) the bolter squad is twice as likley to fail to achieve your goal than the 4 man squad. However, If you want to kill 4 guys then the bigger bolter squad has nearly twice the chance of success than the 4 man squad.


Admitedly working that out in game is probably beyond most, but probability beats simple average when you are looking at a specific goal. Thats because at that point you are not wanting to know the average anymore.

Guys, be men and stop bitching. If you don't like it don't start saying gak about it. Get over it and look at stuff you will like. Use your heads and theirs no point arguing that mathhammer is awful. Some people like it others don't.

puree wrote:

If you toss 22 dice, you can easily figure out how many hits, wounds and unsaved wounds you are going to get. All you need to do that is the ability to divide by 2, 3 and 6. Then, if you are vaguely familiar with a bell-curve and know that you are less likely to stray far from the average the more dice you toss, you can pretty much guess the chance.

The second bit is true, but we are talking binomial distribution, not normal. Depending on the individual chance of success you can have very different curves to a classic normal probability curve.

Its also worth noting that often you may be wanting to stray from the average. If you are after killing a particular squad then knowing that non of your guys have an expected chance of doing that is not terribly useful, you want to know who has the greater probability of getting sufficiently better than average so you can maximise your chance of not having to put more shooting in afterwarrds.

Take 4 guys with S8 Ap3 weapons firing at marines. And you also have 10 S4 Ap5 guys who can rapid fire the marines. Both squads have exactly the same expected result of 20/9 dead marines.

If you want to kill X marines and have the best chance of having one squad left to act with who do you use to shoot first.

For X = 1-3 the 4 guy squad has a slightly higher chance of achieving your goal than the bolter squad. At X = 1 ( well within expected) the bolter squad is twice as likley to fail to achieve your goal than the 4 man squad. However, If you want to kill 4 guys then the bigger bolter squad has nearly twice the chance of success than the 4 man squad.


Admitedly working that out in game is probably beyond most, but probability beats simple average when you are looking at a specific goal. Thats because at that point you are not wanting to know the average anymore.

Thanks for the great example, and explaination.
As I have been saying, old math hammer is imprecise and slow, compared to this if you have a smartphone to hand. Why would you use the old system when this works so much better? Averages have their place, when deciding whether to take a unit or not for example, but on the battlefield when you have precise goals you want precise chances so as to redirect forces to the best places, but also to not make a stupid mistake with risks when anyone knowing the risks would do something else.

ninja13 wrote:Guys, be men and stop bitching. If you don't like it don't start saying gak about it. Get over it and look at stuff you will like. Use your heads and theirs no point arguing that mathhammer is awful. Some people like it others don't.

Thanks. I've been saying for a while that some people like it and others don't; please just go away or make suggestions over how to help it if you don't like it.

puree wrote:

If you toss 22 dice, you can easily figure out how many hits, wounds and unsaved wounds you are going to get. All you need to do that is the ability to divide by 2, 3 and 6. Then, if you are vaguely familiar with a bell-curve and know that you are less likely to stray far from the average the more dice you toss, you can pretty much guess the chance.

The second bit is true, but we are talking binomial distribution, not normal. Depending on the individual chance of success you can have very different curves to a classic normal probability curve.

Its also worth noting that often you may be wanting to stray from the average. If you are after killing a particular squad then knowing that non of your guys have an expected chance of doing that is not terribly useful, you want to know who has the greater probability of getting sufficiently better than average so you can maximise your chance of not having to put more shooting in afterwarrds.

Take 4 guys with S8 Ap3 weapons firing at marines. And you also have 10 S4 Ap5 guys who can rapid fire the marines. Both squads have exactly the same expected result of 20/9 dead marines.

If you want to kill X marines and have the best chance of having one squad left to act with who do you use to shoot first.

For X = 1-3 the 4 guy squad has a slightly higher chance of achieving your goal than the bolter squad. At X = 1 ( well within expected) the bolter squad is twice as likley to fail to achieve your goal than the 4 man squad. However, If you want to kill 4 guys then the bigger bolter squad has nearly twice the chance of success than the 4 man squad.


Admitedly working that out in game is probably beyond most, but probability beats simple average when you are looking at a specific goal. Thats because at that point you are not wanting to know the average anymore.

Just for myself, I'll do that example before hitting a calculator, like I did for my boyz:

4 Devastators with rockets hit about 3 of them, all wound, no armor save. I expect 1-4 dead marines due very few combinations causing a very narrow curve, making straying from the average very likely, while no dead marines being more unlikely than 4 dead marines.

10 Tacticals Marines with bolters hit about 14, 7 wound, one third will not be saved. I expect 1-3 dead marines, as with that many combinations you'll have a much broader curve and thus are unlikely to get a result far from the average.

As the devastators are more likely to stray from their norm, I'd have them shoot first and then act accordingly to their result. Marines are also unlikely to get spectacular results, so there is a low chance of accidentally overkilling something.

Let's see what traditional mathhammer says:

4 Devastators will hit 2.66, wound 2.33, kill 2.33
10 Tac Marines will hit 13.33, wound 6.66, kill 2.22
(so actually not equal, but doesn't really matter for your point)

Now "new mathhammer", using Gray's tables:
A Devastator kills marine 4/6*5/6 = 20/36 = 5/9... not on the table, I'll do the math myself

0 dead: 0.0390
1 dead: 0.1951
2 dead: 0.3658
3 dead: 0.3048
4 dead: 0.0953

So I guess it's more like 1-3, but not so far off though. A bit more than 22% chance of not killing 2 marines, a 3% chance of not killing 1 marine, 10% chance of all rockets killing models.
Assuming that 2+ always wounds on top of rounding hits up probably made my prognosis too optimistic.

Tac Marines:
A marine kills a marine 4/6*3/6*2/6 = 4/36 = 1/9

0 dead: 0.0948
1 dead: 0.2371
2 dead: 0.2815
3 dead: 0.2111
4 dead: 0.1122
more than 4 dead: 0.0633

As expected, they only have a chance of 9% of not killing at least one marine, and have a chance of about 6% of outdoing themselves. Pretty much what my napkin math suggested.

So, with the exact numbers in comparison to what I guesstimated, I wouldn't change my decision. If I absolutely have to kill four guyz there, is a 35% chance of the devastators doing something that would make any shooting by the marines futile/overkill. On the other hand, there is only a 17% chance that the marines would make the devastator's shooting wasted.

I don't want to discredit Gray's work, it's really great to think about. I just don't see the point in using such exact tables during a game - especially considering the time it takes taking them out and finding the needed numbers compared to doing some basic math while moving your models.

Jidmah wrote:I don't want to discredit Gray's work, it's really great to think about. I just don't see the point in using such exact tables during a game - especially considering the time it takes taking them out and finding the needed numbers compared to doing some basic math while moving your models.

Ok, so the only problem is time? In that case all I need is somone good at programming computers to make a system where you type in the probability and it can come up with the average and any tables you want. Should be simple, only I'm stretched to put these graphs onto a spreadsheet. Know anyone?

Jidmah wrote:
Let's see what traditional mathhammer says:

4 Devastators will hit 2.66, wound 2.33, kill 2.33
10 Tac Marines will hit 13.33, wound 6.66, kill 2.22
(so actually not equal, but doesn't really matter for your point)

They are in fact exactly equal at 20/9 each. It is just that you have introduced a rounding issue by using decimals rather than fractions (or your figures were wrong somewhere?).

[edit] Your figures were wrong,
4 Devastators will hit 2.66, wound 2.22, kill 2.22

So, with the exact numbers in comparison to what I guesstimated, I wouldn't change my decision. If I absolutely have to kill four guyz there, is a 35% chance of the devastators doing something that would make any shooting by the marines futile/overkill. On the other hand, there is only a 17% chance that the marines would make the devastator's shooting wasted.

If I knew the probabilities then I'd shoot the larger squad first, near enough a 1/6 chance of having the other squad be free to do other stuff is not bad. However, whether I would calculate it out exactly mid game is another matter.

I'm not saying probability or exepected results are better than the other. They are in fact different answers to entirely different questions. Both are valid. I wouldn't personally use a computer/phone/whatever mid game to calculate out the odds, and wouldn't expect an opponent to do so either.

Considering that the values of stats go from 0-10, armor values go from 10-14, and a die has 6 faces, that and you see the same situations again and again and again...yeah, I find it odd that people can't mathhammer enough to guide their actions in game.

I'm not really critical of the OP's program- actually I endorse it. I in fact am going to use it, to show my friends and newer players things like just how likely certain things are going to happen (powerfist killing a dread vs meltabomb for example, or the difference between AV10 and AV12 for and AC and a ML to compare them), so they can have it in their minds when they play, so I get to have a more challenging game. I think this program would be of great help to noobs- "I'm thinking of using this weapons because it looks cool and effective and I want it!" Instead of going "well... it's not a great config, and this is why..." I can say "well...its not a great config, let me show you why.

Because (call me weird here), I'm not the kinda fella to draw up a stats graph in the middle of the game

p_gray99 wrote:

Jidmah wrote:I don't want to discredit Gray's work, it's really great to think about. I just don't see the point in using such exact tables during a game - especially considering the time it takes taking them out and finding the needed numbers compared to doing some basic math while moving your models.

Ok, so the only problem is time? In that case all I need is somone good at programming computers to make a system where you type in the probability and it can come up with the average and any tables you want. Should be simple, only I'm stretched to put these graphs onto a spreadsheet. Know anyone?

As a matter of fact, I do that for a living. However, that kind of program is much more work than it seems, and I'd rather finish painting my orks or play games than spending about a week programming that. Still, taking out a smartphone/laptop whenever you are trying to decide what to shoot, will get your opponent annoyed fast, more so in a timed event. You probably know that guy who has all his codices saved on his iPad, but doesn't seem to even know the rules for his troops? It'd be like that.

If I were to code such a program, I'd rather make it a simulation, having a billion or so groups of virtual marines shoot each other and then have the program tell you how it went.
Numbers would be close to the calculated ones, and stuff kills each other in the process.
Also much easier to expand and to check for logical errors.

puree wrote:

Jidmah wrote:
Let's see what traditional mathhammer says:

4 Devastators will hit 2.66, wound 2.33, kill 2.33
10 Tac Marines will hit 13.33, wound 6.66, kill 2.22
(so actually not equal, but doesn't really matter for your point)

They are in fact exactly equal at 20/9 each. It is just that you have introduced a rounding issue by using decimals rather than fractions (or your figures were wrong somewhere?).

[edit] Your figures were wrong,
4 Devastators will hit 2.66, wound 2.22, kill 2.22

Correct. Luckily I used the correct numbers for the calculation below that. I cant even reconstruct how I got 2.33. Maybe just a typo
While not posting them, I usually calculate everything in fractions, or if necessary as decimal with 32 digit accuracy, which should be sufficient for warhammer. I post partial results as decimal, so non-math nerds like us can still use the numbers.

If I knew the probabilities then I'd shoot the larger squad first, near enough a 1/6 chance of having the other squad be free to do other stuff is not bad. However, whether I would calculate it out exactly mid game is another matter.

I'm not saying probability or exepected results are better than the other. They are in fact different answers to entirely different questions. Both are valid. I wouldn't personally use a computer/phone/whatever mid game to calculate out the odds, and wouldn't expect an opponent to do so either.

I assumed that the 4 marines absolutely need to die, no question asked. Maybe it's last turn and they are sitting on an objective or they are threatening to melta an important vehicle if not killed. That way, even if a single one survives, there is no point killing the other three. I was also assuming that both units actually have something else to shoot. Anyways, while my tactical decision might not be perfect (after all, I'm no marine player), the estimated results fitted the exact ones close enough.

Jidmah wrote:as it's still possible that you roll all ones with 22 dice.

No, it isn't . More precisely buy a lottery ticket the day this happens.

I do like a little bit of mathematics and I do get fed up with people just calculating averages. Just not sure your work helps with this.

You can calculate averages and roughly work out the deviation from the average in game which is all your work does.

Can you work the distribution for Blood Talons please as they are just weird and a graph of their wounds would be great, it is not that unlikely they'll kill 0 but then they can kill 30 orks in one sitting?
Or draw a 3d representation of scatter, i.e. a series of rings the height of which shows how likely they'll hit that point.

Finally can give the fun example of 30 orks charging SS/TH assault termies. Essentially it is quite possible that orks will win the fight but also quite possible the termies will, however if you work out the result using averages you do not see this and may be bitterly disappointed when the orks actually lose

MFletch wrote:

Jidmah wrote:as it's still possible that you roll all ones with 22 dice.

No, it isn't . More precisely buy a lottery ticket the day this happens.

I did when i rolled 14 1's and 4 2's.


Still didn't win the lottery... maybe if I rolled 14 6's and 4 5's i might have won?