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If you're sick of the assault cannon vs. lascannon debate (and who isn't?) go ahead and page off this thread. But this feels like new info to me.

Okay, so in actual gameplay I observe that assault cannons shooting at AR12+ mostly seem to bounce off.

I'm familiar with the well-known numbers and graphs that supposedly show how an assault cannon is better vs. AR12+ than a lascannon, but I understand from math people that those numbers are skewed because the overkill shots (the pen 15 shots and multiple kills) actually pull the average damage rolls of an assault cannon artificially high. A simple average gives the wrong result for comparison

The actual way to compare the assault cannon to the lascannon is to figure out the odds that a given shot will do *nothing*. Whichever weapon bounces off without result less frequently is better at killing heavy armor.

With a lascannon, that's easy.

Vs. AR12, the odds a lascannon hit will bounce off is 33%
Vs AR13 = 50%

With an assault cannon it's more complicated, because of the multiple shots. But rather than going through the overall damage potential of a volley of assault cannons, it's much easier to calculate the odds for each possible number of hits. The assault cannon is going to get 0-4 hits from any given volley, and the odds of doing nothing go down depending how many hits you get.

Vs AR12 or AR13 an assault cannon will bounce off:
0 hits = 100%
1 hit = 5/6 or 83%
2 hits = 25/36 = 69%
3 hits = 125/216 = 58%
4 hits = 625/1296 = 48%

These numbers reflect my tabletop experience much more closely. The odds that an assault cannon volley will bounce off a AR 12-13 vehicle with no effect are *always* higher than the odds that a lascannon hit will bounce no matter how many hits you get, except the case where you manage to get 4 hits with your assault cannon in which case the odds of doing damage are are about the same vs. AR13, but still not as good vs. AR12.

Now for AR14
lascannon hits bounce off AR14 66% of the time.

Chances that assault cannons bounce off of AR 14
0 hits = 100%
1 hit = 83%+ (33% of the remaining 17%) = 89%
2 hits = 79%
3 hits = 72%
4 hits = 64%

So again, the only time the assault cannon is marginally better at damaging AR14 than a lascannon is those rare cases when you get 4 hits. In all other cases, a lascannon is less likely to bounce off of AR 14.

Have I made a mistake in my math or reasoning? Please point it out if I have.

Well I am no statistical genius and I have read several posts on this that go over my head but I will do my best to say why your reasoning may not be 100% on. I like that you are considering the misses or what does "nothing" as it does take out the few dice rolls that are overlap that skew the statistical analyisis. The assault cannon though does not miss as much as the Lascannon. At equal BS's the lascannon will miss some shots and have 0% of doing anything. Those same shots probably some of the Assault Cannon shots will hit and even though the odds are low, there is a chance for a 6 as opposed to the Lascannon that missed.

I guess
100 Lascannon shots at AV 12. Say BS 4. Roughly 66 hit and half will do something so 33. 33 lascannon shots out of 100 will result in some sort of roll.

Assault cannon same BS would be 400 to hit rolls with Aprox. 266 hits. Out of the 266 1/6 will do something, granted they are auto pens but besides the point. So 1/6 of 266 is 44 roughly. Now because of the overlap of the few times you roll a pair of 6's you cant say 44 shots produce results. On average though you will hit with 2.5 out of the 4 shots aprox. The odds that 2 dice are both 6's on the pen rolls is 1/30 maybe 1/25 (roughly 1/36 but a bit better due to sometimes there being 3 or 4 hits and not just 2) So lets say 1/25 shots have overlapping 6's. That is 4 shots out of the 100. I would then take that out of the 44 rolls that do something leaving you with aprox. 40/100 shots do something.

Now Im sure a math whizz could tear my theory up but thats how I look at it. Yes the overlapping 6's skew the results, but multiple 6's are not common. Some people may argue that 3 or even 5% is a big deal but when its just a couple dice rolls any result is possible and you just have to make a call on the spot and you cant rely on the math always working out.

I really like this. I really hope this info spreads and spreads and spreads even more, so more people waste their shots with lascannons and assault cannons on my Land Raider.... I really like this

The math error is 1 lascannon hit = max assault cannon hits. You can not apply a to hit roll to the asscannon and not the las. When you compare a multi shot weapon to a single shot weapon of the same bs you have to multiply the multi shot weapon by its number of shots. That and you missed the big picture.

General_Chaos wrote:I really like this. I really hope this info spreads and spreads and spreads even more, so more people waste their shots with lascannons and assault cannons on my Land Raider.... I really like this

The big picture is shooting land raiders with asscannons or lascannons is a waste of firepower. Against mech meq its better to use high str weapons to pick off low av transports early in the game, and late in the game melta weaponas are in range.

The odds of doing nothing are certainly worth knowing, but they're also not the most salient piece of information.

It's more useful to know the odds of getting a given result, most often a "destroyed" result.

Against AV12, the Assault Cannon can ONLY Penetrate, making the odds very "polarized." It's both more likely to kill the vehicle AND more likely to do nothing at all, when compared to a Lascannon.

This might give you some impression when watching the game that the Assault Cannon doesn't do anything. Quite often, it doesn't.

The other issue schadenfreude explained, but perhaps it could be clearer... What it comes down to is that you're cancelling out the odds of hitting, on the side of the Lascannon, but not on the side of the Assault Cannon.

The equation

1 * (2/3) * (Lascannon odds) <> 4 * (2/3) * (Assault Cannon odds)

Correctly you assume that you can factor out the (2/3) and the equation remains intact...

However, at that point, you have to assume that all 4 Assault Cannon shots have hit, the same as the 1 Lascannon shot.

Given that, you use the value next to 4, not some weighted average of 1-4.

Also, your math is a little confusing on the Assault Cannon. If we assume that the Assault Cannon hits, then the odds of getting any result are (1/6) * (5/6), ie. rolling a 6+ and then a 2+, which is .139. Conversely, the odds of no result would then be .861, and .861 ^ 4 is .550, pretty significanly better than the .667 of the Lascannon.

When running numbers you need to assume all hits. As schadenfreude mentioned, comparing a 100% ratio for LC to a roll for AC is not a equal comparison. If you fire the LC and AC 100 times each the total percentage of hits begin to average out.

The challenge comes from the multiple shots from the AC. While each shot has a 1/9 chance to effect AV14, it does not mean there is a 4/9 chance of that happening due to multiple hits. That's why the TL AC (which has a 8/9 chance of hitting per shot) only has a ~35% of effecting AV 14. Were it a simple 4/9th chance, it would be closer to ~41%

35% are not betting odds. Its not surprising that you don't see much result on AV 14. When melta-guns up close effect AV 14 on a 6+ on two dice (or 72.2%) its easy to see why AC's are not the tools for the job. The numbers get even in more favor of the melta if your talking about actual penetrating hits.

The takeaway of the AC vs. LC debate is this -- AC's are multi-purpose and can effect armor as well as infantry
On AV 12, the AC has 4 shots each at 1/6 chance to penetrate per hit. It also wounds MEQ on a 2+ with rending. That's not a pile of suck, and makes Baal Predators worth a second look.

IMO Baal Predators don't need a second look, the first look should have convinced you.

Lascannon v. AV12

100 Shots at BS4 = 67 hits (rounding up)

34 Pen hits (rounding up)

11 Glancing hits

26 Weapon destroyed or > result
11 Wrecked or destroyed

Assault Cannon v. AV12

400 Shots at BS4 = 267 hits (rounding up)

44 Pen hits

29 Weapon destroyed or > result
15 Wrecked or destroyed (rounding up)

Lascannon v AV14

100 Shots at BS4 = 67 hits (rounding up)

11 Pen hits

11 Glancing hits

11 Weapon destroyed or > result
4 Wrecked or destroyed (rounding up)

Assault Cannon v AV14

400 Shots at BS4 = 267 hits (rounding up)

14 Pen hits

15 Glancing hits (rounding up)

14 Weapon destroyed or > result
5 Wrecked or destroyed (rounding up)

Conclusion: The Assault Cannon on average is always greater than the Lascannon at 24" or less.

Why do people do math in such stupid ways? Why describe things in terms of "bouncing off" or "what if you fired 342 shots?" Can't we just use statistics?

E: And yes, the Assault Cannon is good. And usually expensive.

Hi. I'm new to Dakka and interested in Mathhammer so I guess this is a good place to start posting.

After reading this and other threads, I decided to run the numbers on this myself. I agree with others that the best way to proceed is to compare an act of shooting a lascannon to an act of shooting an assault cannon, and in doing so, make sure to account for the possibility for overkill that others have mentioned.

So, what I did is calculate the probability of acheiving different levels of damage, or better. That is, what is the probability of doing something, the probability of immobilizing or wrecking or exploding, etc. I'd like to put these numbers in a table, but I haven't figured out how to do that yet.

Starting with AV 10 up to 14, a lascannon has the following probabilities of doing something: 67%/56%/44%/33%/22%
While an assault cannon has: 80%/63%/38%/38%/26%

Same format, but weapon destroyed or better:
L: 41%/33%/26%/19%/11%
A: 56%/38%/26%/22%/14%

Immobilized or better:
L: 30%/24%/19%/13%/7%
A: 43%/26%/20%/16%/10%

Destroying:
L: 19%/15%/11%/7%/4%
A: 26%/14%/14%/10%/5%

I think this shows that the assault cannon is a clear winner as long as it can fire. Note that I'm assuming no cover saves or rerolls of any sort here, and that both cases have a BS 4 firer. The cover saves should hurt the lascannon more, though, since cover saves should diminish the wastage from overkill. If there's interest, I can run numbers on that too. I'm also not accounting for cost, and the fact that it seems generally easier to get lascannons into one's army than assault cannons.

I can provide more details on how I did this if there's interest.

One last thing: The OP noted that his assault cannon shots at AV 12+ always seem to bounce off. That makes sense, since both weapons are going to do nothing 3 times out of 4 against AV 12, and will do even worse against AV 13 or 14. I think this is one of the benefits of doing a little mathhammer: It keeps you from making judgements based on small samples, and can also point you to small advantages that will build up over time but be hard to spot just by playing.

schadenfreude wrote:The math error is 1 lascannon hit = max assault cannon hits.

Ooops, yeah, that's the error. A lascannon does nothing 33% of the time because of missing (at BS4 without twin-linking) whereas the assault cannon very seldom misses all four shots. So the hit roll has to be taken into account.

I don't think that comparing max hits gives a completely accurate picture either, though. Maybe my die rolling is unusually bad, but even with twin-linking, I seldom get 4 hits.

There are 1296 possible permutations of 4 dice, and to really factor in the odds of hitting with assault cannons I'd need to figure out which of those instances have 1s and/or 2s and how many 1s and or 2s.

I guess I'll have to go review permutations to get the number I'm looking for.

Mr. Economics: I'm interested in how you got your results.

I'm also a firm believer the MEQ armies (excluding chaos who can't buy asscannons) should always take an asscannon over a lascannon.

Schadenfreude's quick and easy mathhammer.

Step 1 if it's always BS4 versus BS4 or TL BS4 versus TL BS4 there is no reason to add To hit into the equation.
Just compare 1 lascannon hit to 4 AC hits.

AV10
LC= 1/6 glance 5/6 Pen
AC=4/6 glance 8/6 Pen

AV11
LC=1/6 glance 4/6 Pen
AC=4/6 glance 4/6 Pen

AV12
LC=1/6 glance 3/6 Pen
AC=4/6 Pen

The AC is clearly superior when shooting AV10 to AV12 vehicles

AV13
LC=Shoot a softer AV target, or use melta for this job. You're wasting firepower without melta.
AC=Shoot a softer AV target, or use melta for this job. You're wasting firepower without melta.

AV14
LC=Shoot a softer AV target, or use melta for this job. Anything besides melta is a gross mismanagement of your own firepower. It's either a monolith which you can ignore in favor of going for phase out, or a Land Raider/Battlewagon (you should have maneuvered to get a side shot on a battle wagon) which isn't much of a threat if it's too far away to move a melta weapon within melting range (Threat range of a mechanized melta is 20", threat range a fast multimelta is 24").
AC=Shoot a softer AV target, or use melta for this job. Anything besides melta is a gross mismanagement of your own firepower. It's either a monolith which you can ignore in favor of going for phase out, or a Land Raider/Battle wagon (you should have maneuvered to get a side shot on a battle wagon) which isn't much of a threat if it's too far away to move a melta weapon within melting range(Threat range of a mechanized melta is 20", threat range a fast multimelta is 24") .

Since the AC is superior when shooting AV12 or less, and av 13+ is a job for melta the AC is clearly the superior weapon which is why it costs more points.

Guys who are reiterating the chance of "success" please recall my original post where I said:

Flavius Infernus wrote:I'm familiar with the well-known numbers and graphs that supposedly show how an assault cannon is better vs. AR12+ than a lascannon, but I understand from math people that those numbers are skewed because the overkill shots (the pen 15 shots and multiple kills) actually pull the average damage rolls of an assault cannon artificially high. A simple average gives the wrong result for comparison .

New information would be the chances of having *no effect* for a 4-shot AC volley, rather than the skewed values of success.

So the hit roll has to be taken into account.

No, it doesn't.

If you want to know the true probabilities, then sure, you need it. But if you merely want to know their proportional weight (i.e. an Assault Cannon is x% better), then the to hit roll isn't relevant. Recall the equation I wrote above.

Maybe my die rolling is unusually bad, but even with twin-linking, I seldom get 4 hits.

Right, and you also don't hit every time with a Lascannon. Nobody is suggesting you often get 4 hits with an Assault Cannon. However, if you factor the impact of BS out of the equation, which you can certainly do, then you're assuming that the Lascannon hits once, and the Assault Cannon hits four times.

That said, the odds of hitting with all 4 BS4 shots is about .198 (.667 ^ 4). So, if you don't hit with all four about one time in five, then yes, your die rolling is unusually bad.

Phryxis wrote:

If you want to know the true probabilities, then sure, you need it. But if you merely want to know their proportional weight (i.e. an Assault Cannon is x% better), then the to hit roll isn't relevant.

Exactly--I want to know the true probabilites.

Exactly--I want to know the true probabilites.

You can calcluate that in much the same way you calculated what you've already done. It will show a uniform reduction in the efficacy of both weapons.

So, to be clear, factoring in BS is not going to show that the Assault Cannon is overrated. It's still better than the Lascannon.

Phryxis wrote:

Exactly--I want to know the true probabilites.

You can calcluate that in much the same way you calculated what you've already done. It will show a uniform reduction in the efficacy of both weapons.

So, to be clear, factoring in BS is not going to show that the Assault Cannon is overrated. It's still better than the Lascannon.

I don't think it will be as uniform for the assault cannon because of the break point caused by the extra die roll. That's the whole gist of my argument. By my estimate, the assault cannon should bounce off AR 12 and 13 significantly more often than a lascannon does.

I need a few days to work out the math to back it up, though.

I don't think it will be as uniform for the assault cannon because of the break point caused by the extra die roll.

It'll be exactly uniform... Both weapons will get 33% more likely to "fail," but they remain in the same proportion to each other.

By my estimate, the assault cannon should bounce off AR 12 and 13 significantly more often than a lascannon does.

Honestly, I think you'd be best served by trying to examine why your perceptions are not in line with the actual probabilities, because those just don't change. It'd be useful for any player to know how to correct for in game perceptions, that'd help them make better informed adjustments to list and strategy.

I need a few days to work out the math to back it up, though.

I'm not exactly sure what you think you're going to uncover... Can you try to describe the logic you're using? I can give you the math if you can give the logic.

Phryxis wrote:
I'm not exactly sure what you think you're going to uncover... Can you try to describe the logic you're using? I can give you the math if you can give the logic.

Let me try to describe the logic and see if it makes sense.

If you hit a vehicle with a lascannon, the odds of damaging the target are pretty consistent, statistically. In the AR12-13 range that means rolling a 3 or 4 on your next die to at least shake the thing--a relatively flat probability curve.

If you hit with one or more assault cannon shots, now you're in a situation that's different from the lascannon. You pick up your 2 or 3 dice that hit, and you need to roll a 6 to do *anything*. Yes, there are more hits, but the way that anything but a six drops you out of a kind of statistical trapdoor makes it feel to me like you have a large percentage to get no effect at all, and then another largish (?) percentage to get multiple damaging hits or significant overkill, with a probabilistic trench in the middle. Especially at AR12 where glancing hits are basically impossible.

So, based on things dakka posters have said in other threads about the distribution of hits and how the average damage of the assault cannon is skewed high by the overkill results, the question becomes whether the odds of getting multiple damaging hits from a volley of AC fire offsets the "spread" of results that gives a largeish chance of doing nothing, versus a lascannon which may be more likely to do *something* every time it hits against AR 12-13.

Also based on what dakka posters have said, I believe that calculating the chances that an autocannon volley will bounce off will show more accurately that a lascannon is more likely overall to have *some* effect on a vehicle target than an assault cannon at the same BS value.

If the math shows I'm wrong, I'll be the first to admit it.

Flavius, I believe your fault in numbers lies in the fact that you always assume the Lascannon is going to hit and that 1 or 2 of the Assault Cannon shots are misses. This is why previous posters in this thread have pointed out that you can exclude hit all together but then you have to assume that all 4 shots from the Assault cannon are going to hit.

The reason why averages work is because in a real scenario, the lascannon is going to miss 1/3 of the time from a BS4 unit, whereas the 4 shots with the assault cannon will usually guarantee that 1 or more shots will probably hit the target, and although it'll now require a 6 inorder to pen AV12, at least you now have that probability of rolling a 6 in this situation instead of not having the opportunity 1/3 of the time with the lascannon.

The maths has already been done correctly above.

Your problem is that you are working wth the assumption that the Lascannon will always hit.

What you need to do is compare 0.67 Lascannon hits with 2.67 assault cannon hits. Be a remarkable coincidence 0.67:2.67 is the same ratio as 1:4

If the math shows I'm wrong, I'll be the first to admit it.

Well, I suppose nothing is certain, but if we're talking probabilities, I'm about 99.9% sure you're wrong on this one...

The reason the "overkill" argument isn't of merit here, is because we can calculate the "odds to get at least one Destroyed result." If that's better for an Assault Cannon than for a Lascannon (and it is), then that's your answer. We can do the same for "any result," etc. etc.

To be clear, what you're talking about is "the average number of Destroyed results generated by an Assault Cannon." That, indeed, would be skewed by the rate of fire, and would over emphasize the value of an Assault Cannon, since, as we have said, multiple Destroyed results are unhelpful against single vehicles.

Consider "the odds to not get a destroyed result vs AV12." How do we calculate that for a single shot?

1 - (Odds To Hit * Odds to Pen * Odds to Roll Destroy Result) = Odds to Not Destroy

So...

Lascannon: 1 - (.667 * .5 * .333) = .889

Assault Cannon: 1 - (.667 * .167 * .333) = .963

Clearly, the Assault Cannon has a much worse chance with one shot.

However, what are the odds of all four of its shots failing to get the result?

.963 ^ 4 = .860

That's a better chance to Destroy.

Now consider the converse perspective, which overemphasizes the Assault Cannon. In that case, people tend to calculate the odds to get a Destroyed result, then multiply that by the number of shots, and then call that the "average number of Destroyed results" (or whatever result they're interested in).

So, for our case, the odds to Destroy:

Lascannon: (.667 * .5 * .333) = .111

Assault Cannon: (.667 * .167 * .333) = .037

And then...

.037 * 4 = .148

As you can see, the difference between .148 and .111 is much more than the more useful/accurate difference of .860 vs .889.

But, in either case, the Assault Cannon is still more effective.

Just to clarify my methodology:

I calculated the odds of not achieving each result just like Phryxis did. The only trick is that for the immobilized or better and the weapon destroyed or better results, you need to be careful in calculating the probability of not getting the result because both glancing and penetrating hits can cause the result. I set up an Excel spreadsheet to do most of the calculations quickly.

I should point out that calculating the effect per shot and then scaling up by the number of shots, while a reasonable approximation in some circumstances, can be dangerous here. The intuition is that the sum of a bunch of random outcomes behaves very differently, probabilisticaly, than taking the result of one random outcome and multiplying. In D&D terms, there is a huge difference between, say 10d10, and 1d10 x 10. The probability of getting a result of 100 on 10d10 is essentially zero, while the probability of getting 100 on 1d10 x 10 is 0.1.

For a 40k example, consider a unit of 10 Ork Lootas that shoots at an AV 10 vehicle. One way to do the analysis is to say, ok, each loota gets an average of 1.5 shots, of which on average 0.5 will hit, and you need a 4 to penetrate, so that's 0.25 penetrating hits per loota, and then there's a 1 in 3 chance to destroy, so each loota has an average number of destructions of 0.25*0.33 = 0.0825, so 10 lootas have about an 82.5% chance to destroy the vehicle, if it has no cover save.

The correct way to do it is this: Start by making assumptions about the number of shots. Each shot has a 1/3 chance to hit, a 1/2 chance to penetrate, and a 1/3 chance to destroy, so that's a 1/18 = .056 chance to destroy per shot. So, assume you get 10 shots. That's 10 chances to roll an 18 on a 18 sided die, or a binomial distribution with success probability of .056. This has a .565 probability getting no successes, so you will get at least 1 destroy result with probability 1 - .565 = .435. Doing the same for when you get 2 or three shots gives destruction probabilities of .681 and .82. Then, since each of these results is equally likely, you take the average to get the "average" probability of getting a destroyed result, which is about .645. So, the quick way gives you a probability of 82.5%, while the correct way gives 64.5%, a huge difference.

Apologies to anyone bored by math, but I think the real takeaway is that you have to be careful with your Mathhammer in situations where there can be lots of overkill, like the lootas example. The example I always keep in mind is the difference between 2d6 and 1d12. Years ago I played a game of tabletop Battletech and used a d12 instead of 2d6, and wondered why there were so many head shots, which happen when you rolled a 12.

Fractions are your friends people. Mathhammer is easier to see and takes less work with fractions.
Against Vehicles mathhammer can stop at calculating the chance to glance/pen unless dealing with meltas. When comparing 2 non AP1 weapons there is no reason to calculate past the chance to glance or pen because there are too many possibilities for what the situation needs. If it's a vindicator or Medusa anything besides an immobilized will stop if from shooting next turn, if it's a land raider the goal is probably to immobilize it, and if it's a rhino the goal is probably to force the troops to disembark. When comparing AC to LC there is just no reason to add the effect of the glance/pen in, just compare the ratio of glance/pen and let the players decide what they need.

Start with the # of shots.
LC 1/1
AC 4/1

Then chance to hit.
Normal 2/3
or TL 8/9

Then work out chance to glance/ pen.

The first #is the # of shots, 2nd is chance to hit, and 3rd is the chance of a glance/pen=the chance of a single shot/volley of 4 shots resulting in a glance/pen.

AV10
LC 1/1*2/3*1/6glance=2/18 Glance or 11.1%
LC 1/1*2/3*5/6 Pen=10/18 Pen or 55.5%
AC 4/1*2/3*1/6glance=8/18 glance or 44.4%
AC 4/1*2/3*2/6 pen=16/18 Pen or 88.8%

TL LC 1/1*8/9*1/6glance=8/54 Glance or 14.8%
TL LC 1/1*8/9*5/6 Pen=40/54 Pen or 74.1%
TL AC 4/1*8/9*1/6glance=32/54 glance or 59.3%
TL AC 4/1*8/9*2/6 pen=64/54 Pen or 118.5%

AV11
LC 1/1*2/3*1/6glance=2/18 Glance or 11.1%
LC 1/1*2/3*4/6 Pen=8/18 Pen or 44.4%
AC 4/1*2/3*1/6glance=8/18 glance or 44.4%
AC 4/1*2/3*1/6 pen=8/18 Pen or 44.4%

TL LC 1/1*8/9*1/6glance=8/54 Glance or 14.8%
TL LC 1/1*8/9*4/6 Pen=32/54 Pen or 59.3%
TL AC 4/1*8/9*1/6glance=32/54 glance or 59.3%
TL AC 4/1*8/9*1/6 pen=32/54 Pen or 59.3%

AV12
LC 1/1*2/3*1/6glance=2/18 Glance or 11.1%
LC 1/1*2/3*3/6 Pen=6/18 Pen or 33.3%
AC 4/1*2/3*0glance=0 glance
AC 4/1*2/3*1/6 pen=8/18 Pen or 44.4%

TL LC 1/1*8/9*1/6glance=8/54 Glance or 14.8%
TL LC 1/1*8/9*3/6 Pen=24/54 Pen or 44.4%
TL AC 4/1*8/9*0glance=0 glance
TL AC 4/1*8/9*1/6 pen=32/54 Pen or 59.3%

Once we hit AV 13 a simple glance/pen is replaced with a chance to rend, then the chance the rend will be a glance/pen

AV13
LC 1/1*2/3*1/6glance=2/18 Glance or 6/54 Glance or 11.1%
LC 1/1*2/3*2/6 Pen=4/18 Glance or 12/54 Pen or 22.2%
AC 4/1*2/3*1/6 rend*1/3 glance= 8/54 glance or 14.8%
AC 4/1*2/3*1/6 rend *2/3 pen=16/54 Pen or 29.6%

TL LC 1/1*8/9*1/6glance=8/54 Glance or 24/164 or 14.8%
TL LC 1/1*8/9*2/6 Pen=16/54 Pen or 48/164 or 29.6%
TL AC 4/1*8/9*1/6 rend*1/3 glance=32/164 glance or 19.5%
TL AC 4/1*8/9*1/6 rend*2/3 pen=64/164 Pen or 39%

AV14
LC 1/1*2/3*1/6glance=2/18 Glance or 6/54 Glance or 11.1%
LC 1/1*2/3*1/6 Pen=2/18 Glance or 6/54 Pen or 11.1%
AC 4/1*2/3*1/6 rend*1/3 glance= 8/54 glance or 14.8%
AC 4/1*2/3*1/6 rend *1/3 pen=8/54 Pen or 14.8%

TL LC 1/1*8/9*1/6glance=8/54 Glance or 24/164 or 14.8%
TL LC 1/1*8/9*1/6 Pen=8/54 Pen or 24/164 or 14.8%
TL AC 4/1*8/9*1/6 rend*1/3 glance=32/164 glance or 19.5%
TL AC 4/1*8/9*1/6 rend*1/3 pen=32/164 Pen or 19.5%

Your method is incorrect Shadenfreude - for reasons pointed out above. The AV10 calculations show this explicitly: The TL assault cannon has over 100% chance to penetrate. Since you know chance can't go over 100%, and that you will occasionally roll all 1s and thus fail to do something, you know that it has to be <100%.

MrEconomics has the method right I think.

The AV10 calculations show this explicitly: The TL assault cannon has over 100% chance to penetrate.

He's just misrepresented what the percentage is. It's not the percentage, it's the average number of results, so the 118% is acually 1.18 expected Pens.

As has been said, this method of calculation isn't entirely wrong, it's useful to know how many Pens you'll get on average, but it will skew things as you may get overkill against single vehicles.

And, honestly, fractions are not easier to work with or look at. It's why God invented people, who invented calculators.

How to work out the odds ... First list all the fraction (try to keep them as fractions it keeps out errors)

LC vs AV 10 = 4/6 (to hit) 1/6 (to glance) 1/6(then you're odds for rolling enough ... I want at least Immoblised)
+ 4/6 (BS) 5/6 (Pen) 3/6 (D-I&gt
Next lets start to merge them ...
LC vs AV 10 = 4/216 + 60/216 = 64/216 = 29.6%
Working out TL is easiest to work out the odds of missing twice then take that from one ... 1- (2/6*2/6) = 1-(4/36) = 32/36
TL LC Vs AV10 = 32/1296 + 480/1296 = 512/1296 = 39.5%
...Now Assault cannons throw a spanner in the works by having 4 shots what you need to do is work out the odds of hit once inverting that (as above) then raising that figure to the power of X (number of shots) then inverting again ... ^_^ ... oh and it has an extra D3 which needs to roll be rolled (that's the D3 that pops up later)

AC VS AV10 = 1- (1 - (4/6 (hit) 1/6 (G) 1/6 (D-I&gt + 4/6 (hit) 2/6 (note that At AV12 we roll an extra D3 so this changes to 1/6 3/3) (P) 3/6 (D-I&gt))^4(number of shots)
... sorry but I'm not simplifying...

AV 10-14 ...
AC = 42.61%, 26.50%, 20.44%, 16.20%, 9.52%
LC = 29.63%, 24.07%, 18.52%, 12.96%, 7.41%
TL AC = 53.19%, 34.03%, 26.50%, 21.13%, 12.53%
TL LC = 39.51%, 32.10%, 24.69%, 17.28%, 9.88%

That is the odds that you will Pen/glance and get an immobilised or better result.

To calculate the odds of a multiple shot weapon getting a certain result (for example 'destroyed' or 'explodes'), you have to calculate the chance that the weapon does not achieve that result, and substract those odds from 1. For example:

The chance of a single Assault Cannon shot hitting, penetrating, and destroying (or exploding) an AV14 vehicle are:
(2/3)*(1/6)*(1/3)*(1/3) = 1/81.
The chances of that single shot not destroying the AV14 vehicle are:
1 - (1/81) = 80/81.
The chances to destroy an AV14 vehicle with AT LEAST one of the 4 shots the Assault Cannon has are:
1 - (80/81)^4 = 0.0485.

For a lascannon, it is easier as it has only a single shot. The chances of a Lascannon destroying (or exploding) an AV14 vehicle are:
(2/3)*(1/6)*(1/3) = 1/27 = 0.0370.

As you can see, the Assault Cannon (4.85%) has a greater chance to destroy or explode an AV14 vehicle than a Lascannon (3.7%).


The chances to do either glance or penetrate an AV14 vehicle are also better with an Assault Cannon (26.50%) than with a Lascannon (22.22%).

Phryxis wrote:

The AV10 calculations show this explicitly: The TL assault cannon has over 100% chance to penetrate.

He's just misrepresented what the percentage is. It's not the percentage, it's the average number of results, so the 118% is acually 1.18 expected Pens.

As has been said, this method of calculation isn't entirely wrong, it's useful to know how many Pens you'll get on average, but it will skew things as you may get overkill against single vehicles.

And, honestly, fractions are not easier to work with or look at. It's why God invented people, who invented calculators.

Six of one or a half dozen of another. 118 pennies or 118% of a dollar

All that really matters is the final numbers which say ac>lc

hamsterwheel wrote:
Conclusion: The Assault Cannon on average is always greater than the Lascannon at 24" or less.

I think this is the salient point. There are other costs/benefits to the weapons not reflected in the math, such as range, AP and maneuverability. Each weapon is situationally better than the other but deciding which one you need for your army depends on the rest of the army composition.