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Post by snarlyyow on Dec 28, 2017 19:53:19 GMT
TL; DR: Know the math or you will end up blaming the dice and no good plays come off that. I do think you can overdo the math, though. But you can also just totally misunderstand it. When I started playing I heard, frequently, "7's are average". It was a mantra at my LGS. Players not only thought they were average, but that 7's were expected. So we'd be playing games and my opponents would go for these assassinations and stuff needing 7 after 7 and start cursing their dice. It was a real problem. And I didn't know anyone else in the game at the time and I hate math generally, so I got home and started rolling 2d6 again and again and again putting the results in a spreadhsheet. What did I find? That all of my LGS' perceptions on dice were totally wrong. Basically, if you are trying to kill a single wound trooper, if you want to reliably do it, you need a 5 and a 7. Either a 5 to hit and a 7 to kill or the other way around. I think this is a good rule to keep in your head when trying to kill single wound troopers. If you need two 6s in a row or two 7s the odds aren't super that you'll do it. The easiest way to get math to swing in your favor is to eliminate either roll. Abilities like Sniper only require one positive dice outcome. Knocking down targets takes away the hitting problem. That's why those abilities are so strong, it's not necessarily that they do an auto-point, it's that they are eliminating an entire dice roll. Hell, I had a game this year where an electroleap failed to kill a whelp...and it mattered. Like, really helped decide the outcome of a very real tournament game. With all that said I think there's one very real dice math problem that I see again and again and again: Assassinations. If I want to get it done I always look for the slam angle. I had an opponent recently forgo slamming something into my caster with his jack. If he had slammed one of his own models he would have hit more of those desperate assassinations shots and almost certainly have killed me. That's where power attacks really started screwing with math. |
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Post by NephMakes on Dec 28, 2017 21:53:30 GMT
My sanctifier rolls up to an ironclad. it's gotten battle, charged, and has a full load of focus (that's one PS 16, one charging PS 18, MAT 6 onto DEF 12, ARM 18, 2 focus remaining). [...] What are my chances of [killing the ironclad], and how do I maximize them? I've been working through the boost/buy possibilities on damage rolls and seeing which do the highest mean damage under different conditions. For a single focus: And for 2+ focus: These results mostly match up with the advice i've read/heard, but working through the math and having an image to attach it to helps me remember it all. These could work together as the front and back of a quick-reference card for damage rolls. But since the choice matters less near the boundaries where the damage difference between options is not so great, I think eventually I'm just going to remember some simplified rule-of-thumb so I don't have to look at the card all the time. Now to your example: You need sixes to hit the ironclad and your attacks do dice -2 or straight dice. To maximize your chances you want to buy unboosted attacks. I haven't worked out any quick-reference plots for the probability of downing it, but we can do some "back of the envelope" math. Calculating your expected damage if all the attacks hit: - Charge attack: 3d6 + 0 = 10.5
- 2nd initial attack: 2d6 - 2 = 5
- 1st bought attack: 2d6 + 0 = 7
- 2nd bought attack: 2d6 + 0 = 7
That's 29.5 damage on average against the ironclad's 30 boxes, so something like a 50% chance at the damage stage. Needing to roll sixes, though, and looking at the to-hit graph earlier, it's likely one of your four attacks will miss. What's the chance you get lucky and hit all four attacks? It's harder to do in your head, but it's around (0.75)^4 = 0.32. So all together something like a 16% (1 in 6) chance of downing the ironclad. But if you only missed one attack it likely has a couple crippled systems. As for the ironclad into your sanctifier: MAT 7 P+S 14/18 against DEF 10 ARM 19 means it needs threes to hit and damages dice -5/-1. It also wants to buy unboosted attacks. If it's at full focus, fully functioning, and all its attacks hit: - 1st initial: 2d6 - 5 = 2
- 2nd initial: 2d6 - 1 = 6
- 3 more bought attacks: 3x (2d6 - 1) = 18
That's 26 damage on average against your 32 boxes, not counting any of the systems you probably crippled on it. Your sanctifier's probably not going down, especially if you got the ironclad's cortex or its good melee arm, but it's not impossible. Most game decisions revolve around "can i kill that thing in one round?" I suppose I could plot the probability of doing a certain amount of damage for a given average, since averages are easier to calculate on the fly. It'll depend on how much of your expected damage is dice (and the variance that comes along with them) or damage modifiers (which don't increase the variance). |
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Post by NephMakes on Dec 28, 2017 22:31:34 GMT
Players not only thought they were average, but that 7's were expected. So we'd be playing games and my opponents would go for these assassinations and stuff needing 7 after 7 and start cursing their dice. That sounds like a misinterpretation of the statistical term "expected value", which basically just means average. Sometimes jargon gets in the way. George Carlin understood averages: "Think of how stupid the average person is, and realize half of them are stupider than that." — George Carlin |
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regleant
Junior Strategist
Sometimes things go right
Posts: 267
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Post by regleant on Dec 29, 2017 7:21:35 GMT
So, per the above math, it is "on average" always better to boost if the attack absolutely needs to hit? That was my initial point.  I don't know how many times I've seen the Angelius go in with it's Armor Piercing attack, my opponent saying "okay just need a 5 to hit, and.... *&$&^%" yeah, but what about when it's more than one roll, in a scenario with more outcomes? Consider the following:
My sanctifier rolls up to an ironclad. it's gotten battle, charged, and has a full load of focus (that's one PS 16, one charging PS 18, MAT 6 onto DEF 12, ARM 18, 2 focus remaining). Killing the ironclad doesn't end the game, but the rest of the table is such that it allows a win this turn. If the ironclad lives and is capable of destroying the sanctifier alone, I'll probably lose. If neither can kill the other alone, play will continue further. Ironclad does not have any buffs.
What are my chances of winning this turn, and how do I maximize them? If those rolls go wrong, does that increase my chances of losing?
This is the real test for that card.
Right. But that was not my point at all. My point is that you don’t always get multiple rolls. And if it is important, you boost. If you have the luxury of multiple attacks, then that’s a different situation. We can both be right. |
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Haight
Junior Strategist
Posts: 396 
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Post by Haight on Dec 29, 2017 13:27:05 GMT
A lot of you are far superior mathematicians than I am. It's always interesting to see these conversations and analyze the pure number theory vs. the in practice (despite the fact that i'm personally against odds programs being legal for use in play as my take is that is a couple of steps further down the simulation role as opposed to abstraction, and i think wargaming is at its best when those two things are in balance). I think one of the largest dis-services the greater internet community around Warmachine ever did was the myth conflating the "average" of 7 on 2d6 with "expected" result on 2d6, and then translating that conflation into a yardstick by which in game decisions are made by new and mid-level skill players. The math experts in this thread have spelt out why far better than i ever could, and i'm thankful that i don't even have to clumsily attempt it ! I know early on I was guilty of not doing a better job of spelling out that average != expected and / or reliable expectation of result. |
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mazog
Junior Strategist
Walking and talking
Posts: 748
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Post by mazog on Dec 29, 2017 17:49:10 GMT
I almost think we should have a couple threads for discussion of numbers, one for buying versus boosting and a separate one for considering the effects of many attacks. The discussion started out talking about how dice off X resulted in higher average damage than taking average dice off X, and then the whole boosting vs buying thing came in and now we have multiple conversations about very distinct cases that are overlapping. Both conversations have value, but the overlap seems very confusing.
I am very glad that somebody posted the dice minus X averages, as I've been wondering about them for some time but to lazy to do them on paper.
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