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Post by Trollock on Sept 29, 2017 14:26:07 GMT
On the things of more dices: For sure the best way to use them is on things that can do multiple attacks. That said, sometimes piling up dices could be interesting exactly for the reason of the OP. More dices have chances to spike higher, and since high spikes count more than low spikes, in general more dices will net more damage against high armored targets than fixed numbers or low number of dices at parity of medium damage roll. That still does not change teh fact that adding +1 d6 to a roll will result in +1 d6 to damage. It does not mean anything how many other dice you roll. What CAN matter is the total expected "power" of your attack. Giving +1d6 of damage to a model with P+S 5 will likely not matter. he will still do 0 damage to a heavy in all likelyhood. Giving +1d6 to something like a POW 18 beast will almost guarantee that you do +1d6 of actual damage. Giving +1d6 to a P+S 10 weaponmaster will also usually cause +1d6 of damage caused, cause the chance of him not breaking ARM with his normal dice is pretty low but it could happen. My point is that it is NOT better to give +1d6 to a POW 10 weaponmaster than to a POW 14 normal model. Infact it can be argued that it is very slightly worse since the chance that the weaponmaster fails to bear ARM with his "normal" dice is slightly lower than for the POW 14 model. The easiest way to think about it though is to imagine hat the extra dice you roll is red. every time you roll damage, you can look at the red die and say "oh, that is a 4. If i hadnt had +1d6, my result would have been exactly 4 lower". It then becomes pretty silly to assume that just because you roll a lot of white dice next to the red one it would some how start rolling higher
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Post by Aegis on Sept 29, 2017 16:12:05 GMT
On the things of more dices: For sure the best way to use them is on things that can do multiple attacks. That said, sometimes piling up dices could be interesting exactly for the reason of the OP. More dices have chances to spike higher, and since high spikes count more than low spikes, in general more dices will net more damage against high armored targets than fixed numbers or low number of dices at parity of medium damage roll. That still does not change teh fact that adding +1 d6 to a roll will result in +1 d6 to damage. It does not mean anything how many other dice you roll. What CAN matter is the total expected "power" of your attack. Giving +1d6 of damage to a model with P+S 5 will likely not matter. he will still do 0 damage to a heavy in all likelyhood. Giving +1d6 to something like a POW 18 beast will almost guarantee that you do +1d6 of actual damage. Giving +1d6 to a P+S 10 weaponmaster will also usually cause +1d6 of damage caused, cause the chance of him not breaking ARM with his normal dice is pretty low but it could happen. My point is that it is NOT better to give +1d6 to a POW 10 weaponmaster than to a POW 14 normal model. Infact it can be argued that it is very slightly worse since the chance that the weaponmaster fails to bear ARM with his "normal" dice is slightly lower than for the POW 14 model. The easiest way to think about it though is to imagine hat the extra dice you roll is red. every time you roll damage, you can look at the red die and say "oh, that is a 4. If i hadnt had +1d6, my result would have been exactly 4 lower". It then becomes pretty silly to assume that just because you roll a lot of white dice next to the red one it would some how start rolling higher We are going a bit into the fields difficult to reach in WM, but let's say you have to kill a AS Centurion under Stryker1 Feat (ARM 29). In that case, is better to give the extra dice to a POW 6 weaponmaster that will charge (so total 6+5d6 = total medium damage roll 23,5), or to a POW 13 shooting model (total 13+3d6 = medium damage roll 23,5)? In that situation, piling up dices is better, since both rolls need to spike to damage the Centurion, but the 5d6 roll has a lot higher chances to spike high enough to make that extra dice count, while the 3d6 roll can, at best, do 2 damage to the centurion if all 3 dices are 6. Again, corner cases, but there are actually cases where piling up dices is worth more, at parity of medium damage.
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twity
Junior Strategist
Posts: 179
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Post by twity on Sept 29, 2017 18:50:41 GMT
I have also seen some people who are very good at math make mistakes because they have lost sight of what the actual goal of rolling the dice are. For instance, when buying attacks needing a 5 to hit (83.3%) logic would dictate that each bought attack is worth 83.3% of the damage done, while boosting damage is worth 3.5 damage. So if you are doing an average of anything greater than 4.2 damage per swing (say dice -1) you should simply but another attack. However if they only have two HP left, a boost would give a 0.833 chance to kill while a bought attack would give a (30/36) * (35/36) chance to kill, which is lower.
The opposite can be true too, sometimes you need to kill something to win, and anything less than lucky is irrelevant. You might at well go for several unboosted 9's or you will lose.
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Post by Trollock on Sept 29, 2017 19:21:42 GMT
That still does not change teh fact that adding +1 d6 to a roll will result in +1 d6 to damage. It does not mean anything how many other dice you roll. What CAN matter is the total expected "power" of your attack. Giving +1d6 of damage to a model with P+S 5 will likely not matter. he will still do 0 damage to a heavy in all likelyhood. Giving +1d6 to something like a POW 18 beast will almost guarantee that you do +1d6 of actual damage. Giving +1d6 to a P+S 10 weaponmaster will also usually cause +1d6 of damage caused, cause the chance of him not breaking ARM with his normal dice is pretty low but it could happen. My point is that it is NOT better to give +1d6 to a POW 10 weaponmaster than to a POW 14 normal model. Infact it can be argued that it is very slightly worse since the chance that the weaponmaster fails to bear ARM with his "normal" dice is slightly lower than for the POW 14 model. The easiest way to think about it though is to imagine hat the extra dice you roll is red. every time you roll damage, you can look at the red die and say "oh, that is a 4. If i hadnt had +1d6, my result would have been exactly 4 lower". It then becomes pretty silly to assume that just because you roll a lot of white dice next to the red one it would some how start rolling higher We are going a bit into the fields difficult to reach in WM, but let's say you have to kill a AS Centurion under Stryker1 Feat (ARM 29). In that case, is better to give the extra dice to a POW 6 weaponmaster that will charge (so total 6+5d6 = total medium damage roll 23,5), or to a POW 13 shooting model (total 13+3d6 = medium damage roll 23,5)? In that situation, piling up dices is better, since both rolls need to spike to damage the Centurion, but the 5d6 roll has a lot higher chances to spike high enough to make that extra dice count, while the 3d6 roll can, at best, do 2 damage to the centurion if all 3 dices are 6. Again, corner cases, but there are actually cases where piling up dices is worth more, at parity of medium damage. I think we are talking past each other a bit here... It is true as you say that having a POW 6 with 5 dice damage will do more than a POW 13 with 3 dice damage against a high ARM model on average. Im talking about the effect of the extra die you add. That die will still only be able to show a 1, 2, 3, 4, 5 or 6 with an average of 3.5. It does not matter how many other dice you roll. As you show here, it is possible to construct an example where you are extremely unlikely to do any damage at all, where a guy who has many dice has a bigger chance of breaking ARM at all. However, one has to resort to extremes (POW 6 vs ARM 29) and the damage caused will likely be negligible anyway. One could also say that the POW 13 with 3 dice has a 100% chance of breaking ARM 15, while the POW 6 dude with 5 dice could fail. These are both super extreme cases that usually have no meaning in the game. Most of the time, you expect to do at least 1 point of damage and then these edge effects disappear. But i get your point. there is a slight difference when you are unlikely to break ARM at all. The same thing applies the other way though (the ARM 15 dude above) so i guess we could call the actual difference very small. The base point here was that on every single podcast basically when they go through a caster's spell and find battle lust or the like, they always jump to the "oh, we could put that on weaponmasters to get 5 dice damage! it will be amazing!" This is not because of the math shown in your example but because of a misconception that adding 1 dice to 4 dice is some how way better than adding 1 dice to 3 dice which is not the case
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Post by ziggyqubert on Sept 29, 2017 19:45:12 GMT
If you are interested in seeing how different models perform in various situations, I've written a web app to run all the math warhammer.ziggyqubert.com/warmaHordesCalc/this uses a brute force method to calculate the stats, basicly it rolls the dice multiple times and averages the results, as oposed to using a formula to calculate what the averages should be. i.e. if you want to see how often a wrastler kills a juggeanaut you enter the relevent stats (their is a shortcut for thoes) and abilities select the number of iterations and click run, it will then roll the dice for the wrastler attacking the juggeanut that many times and average the results (and provide the raw dice rolls) it gets around the problem of having to figure a formula for all of the various things that can happen on an attack
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Post by droopingpuppy on Sept 30, 2017 10:28:34 GMT
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Post by NephMakes on Dec 20, 2017 2:12:36 GMT
Dice probabilities are not very complex topic overall. The thing is that you need to do some calculations to get a proper result. That is why people use approximations in gaming.
I'm a new player, but I know a little about probabilty and statistics. I'm working on a quick-reference card that will (I hope) show at a glance what I should expect from a roll and how much boosting would help. Something like this:
I'm not sure if there's more I'd want to include on the card, but there'd be space on the reverse side if people have ideas for a plot or two that'd be useful. Tables and lists of numbers do nothing for me. I also found it interesting that the distribution of 2d6 results isn't actually a bell curve but is instead a triangular distribution. 3d6 is bell-shaped. Like so: Edit: Lrn2Post
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regleant
Junior Strategist
Sometimes things go right
Posts: 267
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Post by regleant on Dec 20, 2017 8:03:42 GMT
I can't argue the math used. e.g. the true average of rolling 2 dice @ DICE -7 = 1, not 0. I can, however, argue the assumptions. The key assumption to arrive at 1 damage instead of 0 is that you have 100 (or significant number of) dice rolls. In Warmachine, this is not often the case. When you're jack comes barging in, you get maybe 4-5 attacks. When your unit moves in, you get only 1 attack per model that can get in range. So while over the long run of the game, DICE -7 = 1, for any 1 specific attack, you should expect 0. And if it's an important roll, always boost.
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zich
Junior Strategist
Posts: 690
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Post by zich on Dec 20, 2017 9:04:55 GMT
And if it's an important roll, always boost. That is also a pretty common misconception. Don't always boost. Do the thing that gives you the highest chance at achieving your goal.
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Post by welshhoppo on Dec 20, 2017 9:47:50 GMT
And if it's an important roll, always boost. That is also a pretty common misconception. Don't always boost. Do the thing that gives you the highest chance at achieving your goal. I'm pretty sure that every failed assassination plan starts with the words "I only need a 6 to hit, I don't need to boost to hit that."
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whydak
Junior Strategist
Posts: 288
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Post by whydak on Dec 20, 2017 9:49:06 GMT
That is also a pretty common misconception. Don't always boost. Do the thing that gives you the highest chance at achieving your goal. I'm pretty sure that every failed assassination plan starts with the words "I only need a 6 to hit, I don't need to boost to hit that." Question is if you can buy next one instead of boosting
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zich
Junior Strategist
Posts: 690
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Post by zich on Dec 20, 2017 11:01:59 GMT
That is also a pretty common misconception. Don't always boost. Do the thing that gives you the highest chance at achieving your goal. I'm pretty sure that every failed assassination plan starts with the words "I only need a 6 to hit, I don't need to boost to hit that." And in that case it is still correct to buy instead of boosting (leaving aside factors like Dodge). It gives you the highest odds of success. Those odds can still fail, but that's just how chance works.
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crimsyn
Junior Strategist
Posts: 389
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Post by crimsyn on Dec 20, 2017 15:16:04 GMT
I can't argue the math used. e.g. the true average of rolling 2 dice @ DICE -7 = 1, not 0. I can, however, argue the assumptions. The key assumption to arrive at 1 damage instead of 0 is that you have 100 (or significant number of) dice rolls. In Warmachine, this is not often the case. When you're jack comes barging in, you get maybe 4-5 attacks. When your unit moves in, you get only 1 attack per model that can get in range. So while over the long run of the game, DICE -7 = 1, for any 1 specific attack, you should expect 0. And if it's an important roll, always boost. I touched on it in my article, but this depends on the definition of “expect” and what your goal is. Warmachine players often “expect” “average dice” and then wonder why they get disappointed 50% of the time. Expected Value, however, is a defined term in probability theory Anyways, if you’re swinging 2d6-7 against single wound models, then you need an 8 or better to kill, which is something like a 40% chance. That’s not great, but also not terrible. Especially when we’re talking about an entire unit going in on another unit — the in-game difference between wiping out 40% of a unit and doing nothing can be huge. If you simply say “well, dice minis seven means I do nothing so I will tell these guys to run over here instead,” you may be making a sub-optimal tactical decision based on bad math causing you to underestimate a unit’s potential. If you’re trying to damage a multi-wound model, then you could do anything from nothing to boxcars. As an example, a couple months ago I was shooting at a Greylord Forge Seer with a unit of Widowmakers and a Marksman. “Average dice = 7” theory gives me an expected output of 7 damage, while doing the math properly gives me an expected output of about 9 damage. Since the Forge Seer has 8 boxes, and whether it is dead or not is a big deal, this small difference means a lot in game — It could dictate whether I go after the Forge Seer or shoot something else. Because I know actual math rather than “average dice” bad math, I chose to go after the Forge Seer (who was marshalling a Behemoth) and killed it, which had a big impact on the game.
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Post by welshhoppo on Dec 20, 2017 22:27:54 GMT
I'm pretty sure that every failed assassination plan starts with the words "I only need a 6 to hit, I don't need to boost to hit that." And in that case it is still correct to buy instead of boosting (leaving aside factors like Dodge). It gives you the highest odds of success. Those odds can still fail, but that's just how chance works. I am now bitter and angry because in tonight's game of warmachine. I failed to roll 5 7s in a row.
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regleant
Junior Strategist
Sometimes things go right
Posts: 267
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Post by regleant on Dec 21, 2017 0:25:05 GMT
And if it's an important roll, always boost. That is also a pretty common misconception. Don't always boost. Do the thing that gives you the highest chance at achieving your goal. Okay. You just need a 5 to hit to to win the game. You can either make 2 separate attacks, or boost the first attack. Which do you do and why? What if it's a 4? What if it's a 7?
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