Arcane Wonders Forum
Mage Wars => Strategy and Tactics => Topic started by: sIKE on January 22, 2014, 12:37:20 PM
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Ok here it is I have opened up this topic because the poor "Re: About warlord only card" topic has been hi-jack by me so badly and I wish to apologize for that.
So I have been chewing on the arguments presented. So what I think I have been trying to say is the following:
When I am building a book and selecting creatures, I tend to favor those with natural piercing over the same cost creatures with more natural dice. Most creatures 2-3 level creatures roll anywhere from 3-4 dice. I think this way (wrong though it may be). I pick up a six sided MW dice with High Armor only two side effective, giving me a 1 in 3 chance per die to land damage. I add piercing to the analysis and for each additional point of piercing for the dice we are talking about (3-4 natural) I have made two additional faces available to place damage upon a object 2 in 3 chance per die w/ piercing. Being able to land more damage quickly is very important to me.
Now if I added in another dice against high armor, each additional dice would only have a 1 in 3 change of landing damage.
But for each additional point of piercing I have taken the change to land damage to 2 in 3 per die rolled.
Yes stacking Bear Strengths are part in parcel of my builds, but cutting through armor is very valuable to me, therefore my love of piercing.
Hope my illogic makes total sense!
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It makes more sense if you're only rolling 1 die. :P
Which is better against 1 armor? Rolling 1 normal damage with piercing? Or rolling two normal damage?
Rolling more dice makes it more likely that you'll deal more damage than giving your attack piercing, but that's because of the possibility of critical damage still occurring with or without piercing. However, just because more dice is more useful, that doesn't change the fact that piercing is still useful.
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My perception is much like Imaginator's. Your post suggests that you're treating a point of piercing as opening up two faces on all the dice you're rolling. As each point of piercing can only add one point of damage to the total you roll, a better way to view it may be that the point of piercing is opening up one face on one die (and if you don't roll enough normal damage it won't even add that).
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It makes more sense if you're only rolling 1 die. :P
Which is better against 1 armor? Rolling 1 normal damage with piercing? Or rolling two normal damage?
Rolling more dice makes it more likely that you'll deal more damage than giving your attack piercing, but that's because of the possibility of critical damage still occurring with or without piercing. However, just because more dice is more useful, that doesn't change the fact that piercing is still useful.
Once again each die is an individual, the piercing buff gives each die that it effects a 33% boost (66% chance to hit), where as an additional die would still be at 33% chance to hit. Grouping dice and running statical models predicting out comes over the entire gamut of possibilities show that more dice is better. But where the game is mostly played is 3-4 dice rolled against 3-5 armor (in serious to semi competitive up to competitive games). This sweet spot is where piercing shines, especially if it is natural.
The point being when you play the guys out on OCTGN, the meta there revolves around High Armor. Both on the Mage and Creatures (Iron Golem or Rhino Hide etc.), looking to counter this I have only so many actions my mage can take each round. Natural piercing lets me counter this with only one full action. If it is my main guy (or two) I will buff with Bear Strength which helps better leverage the natural piercing. If I deem his next attack critical during the planning stage, formerly,I would pull out a melee buff incantation, but found, for the cost the additional piercing incantation buff was much more effective, in placing damage on target due to the high armor.
I truly believe that more natural piercing (Vorpal Blade for one) for mages, will change the meta at the high levels of the game making the actions of armoring up less potent when there are great counters to it that can cleave right through that armor. Therefore greatly lessening the value of stacking armor, not meaning that armor will go away but I think it will return back to a more reasonable level of 2 to 3 armor.
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Thanks Sike for moving this to a new thread.
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I truly believe that more natural piercing (Vorpal Blade for one) for mages, will change the meta at the high levels of the game making the actions of armoring up less potent when there are great counters to it that can cleave right through that armor. Therefore greatly lessening the value of stacking armor, not meaning that armor will go away but I think it will return back to a more reasonable level of 2 to 3 armor.
Oh sIKE... It's a sad day when you discover those who you have placed on a pedestal have Feet Of Clay... :)
Each point of Armour is less useful than the last. Please agree with this?
Where before a Mage was content with 4 armour (excess is diminishing returns), Vorpal Blade and Critical Strike will polarise builds
(a) no armour Defences (please let there be a Defence chest piece) but sadly Falcon Precision is a Silver Bullet
(b) even more Armour, full 7 (2x Leather, Cloak, Hauberk, Rhino) which Voltaric Shield and Veteran's Belt favours
I contend that, without any alternative route being offered to us, they will only exacerbate the arms race!
So then because some builds go Full 7 Armour, this means all builds must have Piercing tech as a tax etc.
A vicious circle of Cruise Missiles and Anti-Ballistic Missiles reminiscent of something from last century...
I sometimes look at design decisions that have been made and I wonder if it's been fully thought through...
Ok, I better retract my claws and stop there... (Neutered I feel, neutered!)
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Trust me, I have played against Charmyna and book clones based off his tactics and strategy's (which he is very very good at developing his playing skills using both) that staking more dice against more armor has diminishing returns. Making armor useless on the other hand is quite handy. The opposing mage spends actions and mana growing his armor repertoire and with I save my mana and other actions for other things, then with good timing I cast Piercing Strike for 2 mana, and ignore all his armor and put the hurt on him.
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Piercing is still quite useful, no ones disputing that. But an extra effect die is generally even more useful. Now that I think about it, +1 attack die probably costs more mana in general than piercing +1. I'll have to check some card text to verify that though.
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I contend that, without any alternative route being offered to us, they will only exacerbate the arms race!
So then because some builds go Full 7 Armour, this means all builds must have Piercing tech as a tax etc.
A vicious circle of Cruise Missiles and Anti-Ballistic Missiles reminiscent of something from last century...
Acid attacks will also help against high armour (and Voltaric Shield), so if high-armour became prominent in the meta players have another option besides Pierce (choices likely dependent upon training and chosen strategy).
I think that players might just focus more of their books to countering anti-armour cards since that also helps high-armoured non-mage creatures, like Iron Golems. Plus cards like Wand of Healing, Dissolve/Explode/Steal Equipment, Dispel/Purge Magic are useful even if the opponent isn't focusing on piercing/corrode.
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Good point, Aylin: Acid's Corrode and Dissolve would indeed be better, debuff defender and not buff attacker.
And then Water emerges triumphant... So no change there...
Corrode is a good example of how the designers are already solving this arms race.
(I wasn't too pleased with Veteran's Belt, maybe they thought it was an equaliser for Voltaric Shield).
Apart from War Mages (Warlord, Paladin, Warlock - "War" in his name!), I don't like mages being armoured.
It goes against my Gygaxian upbringing! (We already play a Vancian magic system of use-and-forget spells.)
Do these mages know the Spell Failure % for wearing a Dragonscale Hauberk? Urgh.
The designers really do read all these concerns voiced on this forum by fans.
In a very real way, the most active and insightful fans are shaping this game.
Which is actually a buzz, the charm of being part of the Mage Wars community.
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Yes these new features are great,
(I wasn't too pleased with Veteran's Belt, maybe they thought it was an equaliser for Voltaric Shield).
Interesting that this is basically takes damage that can't be absorbed by armor and make it so that it is absorbed by said armor. In my opinion, making Piercing even more valuable as it subtracts X from the target’s armor when determining the amount of damage dealt. reducing the value of this belt.
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Before I get into this discussion lets get a few things out of the way.
First we all agree that the Dice/Armor statistic table in General discussion is what everyone in this discussion is using to assert their reasoning that +X dice is better than +X piercing.
Link- http://forum.arcanewonders.com/index.php?topic=13562.0 (http://forum.arcanewonders.com/index.php?topic=13562.0)
Second We all agree that Statistically +X Dice will roll and inflict more Damage After Armor deductions than +X Piercing will inflict, Following Said Table.
Third we agree That some Players expierence anecdotal evidence that seems to support that +x Piercing maybe at least as good, if not Better, than +X Dice.
Once Most Agree I will continue With an Interesting Hypothysis which contains something I think we all have overlooked.
Hedge
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Once Most Agree I will continue With an Interesting Hypothysis which contains something I think we all have overlooked.
Really? From the guy who loves to be the devils advocate? I have to agree for you to proceed? Here we go, I hereby use my scepter of OP ownership and decree that everyone agrees with you. This time. Don't get used to it.
:o
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Once Most Agree I will continue With an Interesting Hypothysis which contains something I think we all have overlooked.
Really? From the guy who loves to be the devils advocate? I have to agree for you to proceed? Here we go, I hereby use my scepter of OP ownership and decree that everyone agrees with you. This time. Don't get used to it.
:o
It really wasn't your agreement I was waiting for, because from the discussions you had here and in other threads I can Reasonable conclude that you already agree with all three. Also I don't have time at this minute to type it all out I will have the time in a few hours though.
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I was just being farcical...
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Ok I'll chime in on this. I've been reading it in other threads enough :) Which is better dice or piercing? Both. That's like asking which is more useful a hammer or a screwdriver. Yeah you'll probably hammer more stuff but when you need a screwdriver.....
Personally I go with large dice pools in any game I play cause hey I got a nice dice bag and rolling a bunch of dice gets me drunk on imagined power.
Comparing more dice to a hammer and more pierce to a screwdriver isn't exactly an accurate comparison. Pierce does what more dice does, but not as well and only against targets with enough armour. The main benefit to it is that it's cheaper than more dice (ex: Piercing Strike vs. Power Strike).
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I don't think that +x Piercing can be better than +X dice, But I believe that the difference between the two might not be as profound as the model describes. So much so that the difference is insignificant.
The Statistic model is correct, but for one small snafu. It does not take into account the HP of the targets or rather the lack there of. The model assumes that all damage is used at 100% efficiency. Once we think about it we know that this is not true. Piercing increases the efficiency of the dice on armored tagerts by increasing the amount of damage the target will suffer on the bottom end, but does not increase the chances of inflicting in excess of the creatures HP.
I will use the 4d6 +2 P(A) and 6d6(B) set against a 2 Armor 8 HP creature in explaining the hypothisis.
The first strike from A will always be at 100% efficiency. However, B's can be as low as 67%. It is rare though to roll all Crits. On the second strike, if it is not killed by the first, B has a greater chance of producing significant damage that is wasted because of the low amount of HP. If we continue this out for a whole game would the difference be even quantifiable.
My Gut tells me that this should affect the model in some way and the problem might even need to be approached from a different angle. Something along the lines of The Probability for 1, 2, 3.... Strikes to kill a set list of creatures with varying stats. As I said I don't think it is possible for piercing to be better, but then again there might be some "magical" combination of dice, piercing, armor, and HP that does.
There almost always is Overkill Damage, but could some amount Piercing mitigate it to make a lower amount of attack dice just as good as adding the same amount of attack dice?
Hedge
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I will use the 4d6 +2 P(A) and 6d6(B) set against a 2 Armor 8 HP creature in explaining the hypothisis.
The first strike from A will always be at 100% efficiency. However, B's can be as low as 67%. It is rare though to roll all Crits. On the second strike, if it is not killed by the first, B has a greater chance of producing significant damage that is wasted because of the low amount of HP. If we continue this out for a whole game would the difference be even quantifiable.
Hedge
If the 4D +2 Piercing nets 2 piercing damage against a 2 armor 8 HP creature then it stands to reason that +2 dice added to that same roll will score damage whether there are critical or normal results. Looks pretty efficient to me.
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I will use the 4d6 +2 P(A) and 6d6(B) set against a 2 Armor 8 HP creature in explaining the hypothisis.
The first strike from A will always be at 100% efficiency. However, B's can be as low as 67%. It is rare though to roll all Crits. On the second strike, if it is not killed by the first, B has a greater chance of producing significant damage that is wasted because of the low amount of HP. If we continue this out for a whole game would the difference be even quantifiable.
Hedge
If the 4D +2 Piercing nets 2 piercing damage against a 2 armor 8 HP creature then it stands to reason that +2 dice added to that same roll will score damage whether there are critical or normal results. Looks pretty efficient to me.
Yes it will add more, sometimes more than is required. Making it a less efficient use of the damage. The Current Dice/Armor model, to be accurate, relies on all damage being 100% Efficient. Meaning no damage is ever inflicted beyond the creature's HP. This does not happen in the real world.
Hedge
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Does your meta operate under Trivial Pursuit rules? (I'm joking with you, not mocking)
I suppose if I had both I could use the inferior 4D +2P on weaker targets and the much more powerful 6D attack on the mage. OR I can just be more efficient and use both on the mage, wishing I had 2 Six dice attacks instead of one.
Edit: If we are going to talk efficiency then you have to give real examples with differing opportunity costs. If I have a choice of one and only one attack, I will choose 6D over 4D +2P every single time. Telling me, I might do too much damage if I go +2 dice is not a winning proposition for piercing.
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Does your meta operate under Trivial Pursuit rules? (I'm joking with you, not mocking)
I suppose if I had both I could use the inferior 4D +2P on weaker targets and the much more powerful 6D attack on the mage. OR I can just be more efficient and use both on the mage, wishing I had 2 Six dice attacks instead of one.
You still do not understand the initial premise. That the statistical model that tells us +x Dice is better than +x Piercing is Flawed. How much so is the question.
Hedge
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I understand it just fine, but if the opportunity costs are the same, then why do I care if I might do too much damage to a target? I understand the concept of distributing attacks in an efficient manner.
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I understand it just fine, but if the opportunity costs are the same, then why do I care if I might do too much damage to a target? I understand the concept of distributing attacks in an efficient manner.
It isn't about any of that.
Hedge
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I understand it just fine, but if the opportunity costs are the same, then why do I care if I might do too much damage to a target? I understand the concept of distributing attacks in an efficient manner.
It isn't about any of that.
Hedge
Look up all the creatures and conjurations that have exactly 2 armor and ones that have 8 HP and could be buffed to 2 armor. Now check to see how many of those have exactly 8 hit points AND 2 armor then consider how often those are used. If you're going to calculate +2 dice overkill it's also fair to calculate how often +2 piercing is wasted against resilient targets and +1 armor targets and when not enough normal damage is rolled for piercing to have an effect, especially, against high armor targets.
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Hedge, overkiling a creature isn't a problem. You're overlooking a lot of things, such as enchantments that can save a creature from a killing blow (Healing Charm and Bull Endurance), the overall usefulness of Piercing (useless against any Resilient, Incorporeal, or generic 0-armour creatures), and most importantly that the important thing isn't how much average damage is done but rather the probability of killing a target in a given number of attacks.
In your example, with the 8-HP/2-Armour target, the 4-die/2-pierce attack is less likely to kill to kill the target in two attacks than the 6-die/0-pierce attack. In a standard distribution, ~49.9% of the data will fall below the average. Roughly speaking, this means that the 4-die/2-pierce attack has a ~24.9% chance of rolling less than 4 damage on 4 attacks (where the mean is), but the 6-die/0-pierce attack has less than a ~24.9% chance of rolling less than 4 damage on both attacks (since the mean is above 4, one could roll below average on both attacks [say exactly 4 damage on both] and still kill the creature).
There are also other cases to consider, such as one attack rolling poorly but the other rolling above average. However, at any value of HP and 2 Armour the 6-die attack will have a greater probability of killing the creature than the 4-die/2-pierce attack does for pretty much the same reason as above. Plus the 6-die attack is more useful against things without armour as well.
Piercing does have value, but it isn't nearly as valuable as more dice. But the situations where going for more pierce rather than more dice are fairly uncommon and require that, for the same price, you would get more piercing than extra dice.
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I am not going to continue with this topic until such a time as I can explain myself fully. If someone wants to defend the premise I posted Have at it or if you have question I may answer them, but I am not going to argue the point any further at this time. I have read your rebuttal Aylin and agree with what you say on its own, but It just doesn't defeat my premise, in my mind. I don't know I may just be off on some tangental thinking or some such thing. My other Gamer Friends tell me I don't look at things the same as most other people. So it may be one of those things that I can't communicate myself.
Also I have read many of your discussions with Sike and other and you always have good and sound logic behind your conclusions. Like I said I know it is impossible that the piercing is better, but something just keeps nagging at me that there isn't as big of a gap as the statistic model dictates.
I just wish I had someone to play against so I can get so practical experience instead of theoretical. I have only played three games since Gencon.
Hedge
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I am not going to continue with this topic until such a time as I can explain myself fully. If someone wants to defend the premise I posted Have at it or if you have question I may answer them, but I am not going to argue the point any further at this time. I have read your rebuttal Aylin and agree with what you say on its own, but It just doesn't defeat my premise, in my mind. I don't know I may just be off on some tangental thinking or some such thing. My other Gamer Friends tell me I don't look at things the same as most other people. So it may be one of those things that I can't communicate myself.
Also I have read many of your discussions with Sike and other and you always have good and sound logic behind your conclusions. Like I said I know it is impossible that the piercing is better, but something just keeps nagging at me that there isn't as big of a gap as the statistic model dictates.
I just wish I had someone to play against so I can get so practical experience instead of theoretical. I have only played three games since Gencon.
Hedge
I have also experienced times during which I was unable to express myself adequately, so I am aware of how you feel. However, I would also like to apologize for my rude behavior to you in the other thread. I should not have allowed my frustration to seep into my posts.
I'm not really sure what I could say that would help to alleviate or at least address your nagging feeling. Statistics is my least favourite subset of mathematics due to how unintuitive it is, and I'm absolutely terrible at explaining it.
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Like I said I know it is impossible that the piercing is better, but something just keeps nagging at me that there isn't as big of a gap as the statistic model dictates.
It is just due that you are human. Humans mind tend to refuse statistic evidence.
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STATISTICS has been described as "the science which tells you that if you lie with your head in the oven and your feet in the fridge, on average you'll be comfortably warm"....
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STATISTICS has been described as "the science which tells you that if you lie with your head in the oven and your feet in the fridge, on average you'll be comfortably warm"....
I know you meant it as a joke, but... *deep breath, sigh* ...really???
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STATISTICS has been described as "the science which tells you that if you lie with your head in the oven and your feet in the fridge, on average you'll be comfortably warm"....
That's an example of kurtosis, I believe?
No, it's not, I just checked it.
Go on somebody, what's the polarised "U" distribution (where mean = Normal Distribution) called then?
I am sure that Good Statistics don't lie.
Its reputation is harmed by Bad Statistics that marketers like me use for nefarious "messages"...
Back to the OP:
I'm obviously in the Sane Camp here :)
You can see that the value balance was appreciated by designers:
Power Strike or Bear Strength vs. Piercing Strike or Critical Strike
Rajan's Fury (situational melee) vs. Tooth and Nail (even ranged)
Are there any situations when +1 Piercing would better (more certain) than +1 Die?
Let's test Hedge's point when excess damage in the distribution curve is irrelevant
Please tolerate cruddy Probability Theory (opening myself to be slaughtered here)
All I remember from my school days is AND = multiply, OR = add, NOT = 1 minus
SCENARIO
I'm attacking something with 1 Armour and 1 Life left with a 3 dice Falcon (0 piercing)
You really don't make any weaker attacks than that in the game really
Would I prefer +1 piercing (Tooth and Nail) or +1 dice (Rajan's Fury)?
With +1 Piercing
Chance of failure = rolling all 3 dice blank = 1/3 x 1/3 x 1/3 = 1/27
Chance of success = 1 - 1/27 = 26/27
With +1 Die
Chance of rolling all 4 dice blank = 1/3 x 1/3 x 1/3 x 1/3 = 1/81
Chance of rolling exactly 1 die with 1 normal damage other 3 blank = 4x (1/6 x 1/3 x 1/3 x 1/3) = 2/81
The "4x" is because any of the 4 dice could be the 1 normal damage
Chance of failure = 1/81 + 2/81 = 1/27
Chance of success = 1 - 1/27 = 26/27
So with 3 dice, in this situation, it seems like +1 Piercing is equal to +1 Die
But what if we attacked this 1 Armour 1 Life object with 6 dice?
Would 6 Dice +1 Piercing or 7 Dice be better?
6 Dice +1 Piercing = 1 - (1/3)^6 = 99.86%
7 Dice = 1 - (1/3)^7 - 7x(1/6x(1/3)^6) = 99.79%
So with more dice (often the case), hitting that Death Threshold is better with +1 Piercing
I've cheated with Excel below (who needs maths when you can simply formula)
When attacking this 1 Armour 1 Life target, what is the probability of killing it?
# +1 Pierce +1 Die
1 66.667% 77.778%
2 88.889% 90.741%
3 96.296% 96.296%
4 98.765% 98.560%
5 99.588% 99.451%
6 99.863% 99.794%
7 99.954% 99.924%
8 99.985% 99.972%
9 99.995% 99.990%
So is this the (not-so-subtle) difference between Statistics and Probability?
Statistics deals in averages (but we don't care about the excess damage)
Probability deals in an intended outcome, it's binary, it works or it doesn't
I feel it is linked to Burn = 3 damage fallacy (because infinite series says so)
I always treat Burn as 1.5 damage because that's the median, not the mean
I don't want my Burn damage to be upweighted by the unlikely outlier events
Mathematicians on this forum will no doubt enlighten us Lesser Humans on the error of my thinking here...
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I always treat burn as zero damage and then I'm pleased if I get something else. In (mage) war you have to be prepared for the worst case scenario.
Sorry for the minor diversion, back on topic now.
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I always treat burn as zero damage and then I'm pleased if I get something else. In (mage) war you have to be prepared for the worst case scenario.
Sorry for the minor diversion, back on topic now.
This is overly timid, and likely wastes resources and causes you to undervalue agression. It also doesn't tell you how to evaluate your opponent's burns on your creatures.
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I feel it is linked to Burn = 3 damage fallacy (because infinite series says so)
I always treat Burn as 1.5 damage because that's the median, not the mean
I don't want my Burn damage to be upweighted by the unlikely outlier events
Mathematicians on this forum will no doubt enlighten us Lesser Humans on the error of my thinking here...
If I have time later I'll look over the rest of your post, but from a cursory glance I didn't see any problems.
But estimating the value of Burn at 1.5 assumes it will survive, on average, for just under two turns. (Nitpicking, 1.5 isn't the median of the series either.)
The series in question:
(3/2) * Sum(n=1 to Infinity) (2/3)^n
Expanding:
1 + 2/3 + 4/9 + 8/27 + 16/81 + 32/243 + 64/729 + 128/2187 + 256/6561 + 512/19683 + ...
~= 1 + .667 + .444 + .296 + .198 + .132 + .088 + .059 + .039 + .026 + ...
So the average damage you can expect from your Burn is determined by how many turns you think there is left in the game:
1: 1
2: 1.667
3: 2.111
4: 2.407
5: 2.605
6: 2.737
7: 2.825
8: 2.884
9: 2.923
10: 2.949
When there aren't many turns left in the game, ~2.5 is a good estimation (~3-5 rounds left), but 3 is a good estimation for when there are 7 or more rounds left.
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@ ringkichard
Not burn on my own creatures, just burns I inflict. 2/3 chance is definitely not good enough for me to count on, so I just think of burn as bonus damage.
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@ ringkichard
Not burn on my own creatures, just burns I inflict. 2/3 chance is definitely not good enough for me to count on, so I just think of burn as bonus damage.
So what math do you use on your own creatures with Burns? Debonus Damage?
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I don't usually find it that useful to quantify burn tokens on my own creatures. You only roll one die at a time per burn token and at that level the statistics aren't very predictive. For example, let's say there's a burn token on one of my creatures. On average, it should do three damage. So in the upkeep phase I roll a 2. What's the expected damage output of that burn token in all future turns? Because of the way the statistics work, it's still three damage, even though it's already done 2. So I just classify burn tokens as "indeterminate amount of future damage" without worrying about how much damage I should expect the token to do.
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I don't usually find it that useful to quantify burn tokens on my own creatures. You only roll one die at a time per burn token and at that level the statistics aren't very predictive. For example, let's say there's a burn token on one of my creatures. On average, it should do three damage. So in the upkeep phase I roll a 2. What's the expected damage output of that burn token in all future turns? Because of the way the statistics work, it's still three damage, even though it's already done 2. So I just classify burn tokens as "indeterminate amount of future damage" without worrying about how much damage I should expect the token to do.
Interesting, so how do you determine when/if it is worth to remove them outside of Upkeep?
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I ask myself two questions.
1. Is this creature's long term survival critical to my plan?
2. If I remove the burn tokens, is the creature likely to survive long enough to be useful?
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+2 Dice > +2 Piercing, always
So with 3 dice, in this situation, it seems like +1 Piercing is equal to +1 Die
...
So with more dice (often the case), hitting that Death Threshold is better with +1 Piercing
from a cursory glance I didn't see any problems.
Thank you, Aylin, but it wasn't me you offended (edited out). As for...
Nitpicking, 1.5 isn't the median of the series either.
I know
However, when you have an infinite series like burn, surely median damage is a more reliable indicator?
In this case 3/2 damage = 5/9 probability.
Therefore median = 3/2 x 9/5 x 1/2 = 27/20 damage = 1.35 median damage.
The reality is, if you test 100 burn counters repeatedly in a Monte Carlo simulation, half the time, they will deal less than 135 damage and the other half of the time, they deal more. With the ability to deal a significant amount in outlier cases. Median identifies its 50th percentile, unbiased by the high damage of those outlier observations which raises the mean.
Now, I don't really understand math (I don't know how long I can keep up this Colombo act) but infinite series burn seems related to Damage Threshold.
For those who want to understand burn better, please reference Zuberi's thread
http://forum.arcanewonders.com/index.php?topic=13139.0
Where Kich made probably my vote for the most laugh-out-loud post on this forum.
This is why, today, the warlock foundation is announcing a very special pledge drive to help at risk burn tokens get through those first critical turns so they can thrive and meet their full mean potential. Just two complete rounds is all it takes for a burn token to do (1.5 * 2) = 3 expected damage. When a warlock comes to your door with her lash of hellfire, we do hope you'll give generously.
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Deckbuilder, I'm not sure where you got 5/9 as the probability for 3/2 damage... in the thread you linked to you list it (correctly) as 2/9. I'm also not sure what exactly you're taking the median of. None of the methods I am aware of for finding a median work for a monotone infinite sequence. What exactly was your thought process?
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Instead of comparing Dice vs. Piercing in a 1:1 ratio it would be better to compare them at a 2:3 ratio. After all the question is ultimately whether using Power Strike vs. Piercing Strike is better, or whether Bear's Strength vs. Critical Strike is better, right? In both cases you are comparing +2 dice with +3 piercing. Hence a 2:3 ratio.
This is probably the source of the statistical vs. intuitive disconnect that a few people are mentioning. From a gameplay perspective there's no card that gives only +2 piercing.
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Piercing +3 will add from 0 to 3 extra damage.
Melee +2 will add from 0 to 4 extra damage.
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Piercing +3 will add from 0 to 3 extra damage.
Melee +2 will add from 0 to 4 extra damage.
<3
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Not playing the lottery will earn me between 0 and 0 extra dollars.
Playing the lottery will earn me between 0 and 10 million extra dollars.
:P
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Not playing the lottery will earn me between 0 and 0 extra dollars.
Playing the lottery will earn me between 0 and 10 million extra dollars.
:P
Yeah i kbow it is bot that simple.
Basically, if you roll 4-7 dices and your target has exactly 3 or 4 armor you will do slightly (around 0.5) more damage than +2 dices. Else, +2 dices will yield more damage.
Conclusion, more dices > piercing
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Not playing the lottery will earn me between 0 and 0 extra dollars.
Playing the lottery will earn me between 0 and 10 million extra dollars.
Statistics like this require the use of expected outcomes. If I don't play the lottery I spend zero dollars, and I have a 100% chance of gaining zero dollars, so my expected outcome is zero dollars.
If I do play the lottery, I pay 1 dollar, and my expected outcome is either zero dollars (999,999,999/1,000,000,000 chance) or $1 million (1/1,000,000,000)*. The expected outcome is (-1 + [0 x (999,999,999/1,000,000,000)] + [10 million x (1/1,000,000,000)].
So your expected outcome is -99.99 cents.
* I made up the statistics for the payoff. They're not really important, since as long as (chance of payoff) x (monetary value of payoff) is less than (price of ticket), your expected payoff will always be less than zero. In cases where this is not true, you could theoretically guarantee a positive result by buying all of the tickets. This has famously been done in the past a handful of times for exceptionally large payoffs, but the organization running the lottery typically finds out and refuses to honor the holder's tickets, saying that they've violated the spirit of the game.
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So, as I understand it... piercing is better to make your bad rolls more useful, whereas dice helps your good rolls(or burst damage) better.
I just can't help thinking that this discussion will be forever incomplete without an analysis of how veteran's belt plays into this.
If someone is up for it, please enlighten me.
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So, as I understand it... piercing is better to make your bad rolls more useful, whereas dice helps your good rolls(or burst damage) better.
I just can't help thinking that this discussion will be forever incomplete without an analysis of how veteran's belt plays into this.
If someone is up for it, please enlighten me.
If you consider Veteran's Belt, you should also consider things like Corrode, Dissolve, Explode, and Steal Equipment.
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If you consider Veteran's Belt, you should also consider things like Corrode, Dissolve, Explode, and Steal Equipment.
I am aware of said counters to it, but there are many times where the other options you mentioned are not viable. (not enough equipment removal left, corrode either unfeasible in spell points or not working well due to condition removal, etc...)
I still think the belt should be analysed on it's own in a dice vs. piercing manner as it may be a worthwhile consideration as a counter to veteran's belt strategies, but I can understand if no one wishes to do so.
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So, as I understand it... piercing is better to make your bad rolls more useful, whereas dice helps your good rolls(or burst damage) better.
Maybe I just roll so crappy, that piercing makes that much of a difference for me in my game play. Statically speaking, I maybe an the extreme low half of the average dice rolls ;)
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If you consider Veteran's Belt, you should also consider things like Corrode, Dissolve, Explode, and Steal Equipment.
I am aware of said counters to it, but there are many times where the other options you mentioned are not viable. (not enough equipment removal left, corrode either unfeasible in spell points or not working well due to condition removal, etc...)
I still think the belt should be analysed on it's own in a dice vs. piercing manner as it may be a worthwhile consideration as a counter to veteran's belt strategies, but I can understand if no one wishes to do so.
I don't have the time to go through it formally, but it would certainly favour piercing.
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I bet it would favor piercing on high armor targets, but extra dice on low armor targets. I'm not sure where the break point would be, but it's probably a ratio between attack dice v armor. Since the expected damage table is up now it probably wouldn't be that hard to figure out since the math's all done already.
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I bet it would favor piercing on high armor targets, but extra dice on low armor targets.
Its the other way around.
if you roll 10 dice vs a 3 armored target your better of getting pierce 3 than melee 2.
If you roll 10 dice vs an 8 armored target you are better off with 2 melee.
Its worth noting you need a decent amount of dice rolled in the first place before piercing strike is ever going to be worth it. At the same time the armor cannot be LOWER than 3, and cant go much higher also unless you really are rolling tons of dice.
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I'll accept that. I didn't stop to do the math and my intuitive reasoning could have been wrong.
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So what you are saying is that when the amount of dice is approximate to the amount of armor is when piercing shines.
So in the 3-5 armor and 3-5 dice range layering piercing on top would work well.
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In a veteran's belt situation, yes, especially if the overall amount of armor is low (3 pierce will negate the value of vet's belt on a 3 armor mage entirely).
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So what you are saying is that when the amount of dice is approximate to the amount of armor is when piercing shines.
So in the 3-5 armor and 3-5 dice range layering piercing on top would work well.
I think he's saying you need to be rolling quite a few more dice than armour. Probably at least 2 dice per point of armour, although I'll defer to any local mathematicians with a better idea. The idea being that you need to be reliably rolling as much normal damage as the target's armour value for piercing to become efficient
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I think he's saying you need to be rolling quite a few more dice than armour. Probably at least 2 dice per point of armour, although I'll defer to any local mathematicians with a better idea. The idea being that you need to be reliably rolling as much normal damage as the target's armour value for piercing to become efficient
My gut tells me to agree to an extent about the 2 dice per point of armor, except that it is probably slightly less than that due to the crit canceling effect of the belt. Intuitively, I'd guess it's closer to (Armor * 2) - 2 dice. If this is in the ballpark, then piercing would be the better option much more often against belt except in the extreme cases of very few dice or very high armor.
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Good point. Looking at the dice versus armour table, if you're happy with the lower standard deviation figure as a reasonable expectation you probably want (armour+2) dice against a Veteran's Belt before stacking piercing.