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Is terminator armour twice as good as power armour?
Let's assume we get saves. Getting hit by guardsmen/warp spiders etc. Lets forget that termies have an invulnerable save, powerfists, and all that jazz. Just look at 2+ save vs 3+ save.
Say you roll 6 dice, on average losing 2 in power armour and 1 in terminator armour.
That would make terminator armour twice as good as power armour right?
And yet, terminator armour is only better than power armour when a 2 is rolled.
Which is only 1/6 of the time.
So, wouldn't that make terminator armour only 1/6 better.
I wouldn't think so. There's something I'm missing here.
However, power armour saves 2/3 of the time. If terminator armour was twice as good, wouldn't it be saving 1 1/3 of the time? Technically impossible. So wouldn't it be:
(5/6) / (2/3) = 1.25 times better?
You can't use both 1.25* better and 2* better.
If we said it was 2* better, then a 5+ save would not be 2* better than a 6+ save, even though you save twice as much. Why? Because we have to be consistent.
A 5+ save would be:
5 dead / 4 dead = 1.25 times better.
While if we said terminator armour was 1.25* better, 5+ saves all of a sudden become 2* better.
So which bloody method do we use!
A question from a very confused person :/.
I believe your math is funky. Im pretty sure you gotta divide the 2 fractions by each other which is multiply by the reciprical or something like that. I really have no clue what im talkin about exept for when I say that Im almost certain that the termies without considering the Invulnerable save are 1/3 better than a marines save. the thing is they also have that invulnerable save, a powerfist, and a storm bolter not to mention an extra attack and other cool stuff.
A very interesting question. First we must assume we need to roll six saves against lasguns. Power armor will grant you a save on a 3+, or two-thirds of the time. Terminator armor will save five-sixths of the time (a 2+ in this case). Now we must determine the average saves.
Power armor: 6 * 2/3 = 4 saves made
Terminator Armor: 6 * 5/6 = 5 saves made
Now we subtract the lower result from the higher, because we are trying to figure out how much better Terminator Armor is than Power armor. The result is one, or course. Then we devide one by the lower result (the Power armor result) to figure out the fraction or percentage.
1 / 4 = .25
We have now determined that Terminator Armor is 25% (or one fourth) better at shrugging off lasgun wounds than power armor. Clearly, Terminator Armor is not even close to being twice as good as power armor when it comes to this.
Victorus aut mortis,
-Archetype
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thats not realy a question you can answer like that. Chance wise your 1/6 more likely to pass a save in termi armor 1/3 more likely to pass an ap 1 2 or 3save. so with termi armor you have a 33.3333...% chance of passing a save from a weapon with ap 1 2 or 3. were as you have a 0% chance of surving that shot with power armor. now with power armor you have a 33.333..% chance of failing a save right?( assuming your capable of making a save, ap 4 or worse)only on a 1 or 2 will you suffer a wound. terminator armor hower will on fail a save on a roll of a 1 or 16.666666...% chance. have of 33.333... is about 16.5. so yes terminator armor is twice as good, if the weapon allows saves. were as power armors useless if it doesn't.
I belive i did this right if there is any won out there better at math then me please correct me
Rheagar fought nobly
Rheagar fought valiantly
Rheagar fought honorably
And Rheagar died.
Your problem is coming from the phrase "times better than". Simply put, this phrase is not appropriate for a discussion of probability.
The average number of deaths per wound against terminators is 1/6 while against power armoured models it is 1/3. Thus, terminators will lose, on average, half as many models per wound as marines (or sisters or whatever, models with 3+ saves from now on will be referred to as 'marines' just as models with 2+ saves will be referred to as 'terminators).
The probability of a single marine dying to a single wound is similarly twice as high as the probability of a single terminator dying to a single wound. However, it is important to note that the probability of various numbers of models dying to the same number of wounds will vary significantly, and as the numbers of models and wounds increase (assuming you're looking one wound per model), the terminators become exponentially less likely to be wiped out than the marines. For example, two marines have a 1/9 chance to die to two wounds, while two terminator have a 1/36 chance to die to two wounds. Here, it is four times less likely that both terminators die than it is that both marines will die.
However, if a single marine suffers two wounds, there is a 5/9 chance that he will die. If a terminator suffers two wounds, there is an 11/36 chance that he will die. So, the marine is 20/11 times more likely to die than the terminator. In other words, as the number of wounds per model increases, the chances of the terminator living drop decrease faster than the chances of the marine living. (this seems odd at first, since it seems like the model with the worse save would become more likely to die faster with the addition of extra wounds. However, if you consider the fact that as the number of wounds approaches infinity, the chances of each model dying approaches the same number, zero, it makes more sense that the Terminator drops faster. To use a metaphore, it has more ground to cover in what is, effectively, the same distance.)
In addition, you are correct in saying that the terminator armour will only produce a better result on one out of six outcomes, or that on approximately one out of six rolls, your marine will wish he had terminator armour.
Do any of these represent the proportion by which terminator armour is 'better' than marine armour? The answer is yes, in that being 'better' than other armour could be expressed in any of these ways, and no in that being 'better' than other armour could be expressed in any of these ways.
In short, the phrase 'better than' in this case, carries with it no default meaning. Since that is the case, it would be necessary, every time you use that phrase, to state specifically what it meant--and if you were to take the time to do that, you might as well skip the phrase entirely and just say what it means. The important thing is to know what is expressed by each bit of math you do, not to know which bit of math is associated with the phrase 'better than'--the answer to that question (not to be redundant, or anything :-p) is that, in general, none of them are but also that any could be.
thats quite well put.
Rheagar fought nobly
Rheagar fought valiantly
Rheagar fought honorably
And Rheagar died.
You all forgot one thing - TDA has a 5+ invulnerable save, while PA has none such. This means that a Terminator has also 33% of survivng things like Lascannon hit or a Power Weapon-equipped enemy, while PA has 0% in the same cases.
Against normal fire, PA has 66% chance of survival, while TDA has 83%.
Factoring that together, the PA has 66/200 protective factor, while TDA 116/200. In percentages, this means 33% for PA for surviving a hit from a completely random weapon, and 58% for the TDA.
Naturally, this calculation excludes things like Daemon Weapons or Phase Weapons which do not allow even Invulnerable saves.
Bean summed it up nicely. And the 5+ invulnerable wasn't forgotten, merely discounted for simplicities sake.
Your also forgetting another important factor - AP. The ability to actually get the save is very important, and there are a considerable amount of AP3 weapons (Battlecannons, Rail-Rifles, Krak Missiles, Staff of Light etc...) that are normally extremely dangerous that you now can save against. So basically, only the weapons with the best AP in the game (for this purpose AP1=AP2) can now deny you your saves. Another important factor you have with a +2 save.