Forum adverts like this one are shown to any user who is not logged in. Join us by filling out a tiny 3 field form and you will get your own, free, dakka user account which gives a good range of benefits to you: No adverts like this in the forums anymore. Times and dates in your local timezone. Full tracking of what you have read so you can skip to your first unread post, easily see what has changed since you last logged in, and easily see what is new at a glance. Email notifications for threads you want to watch closely. Being a part of the oldest wargaming community on the net. If you are already a member then feel free to login now.

Rather than continue to clog up the chaos rumor thread with falcon discussion I thought I'd follow a hint and move here. Warning: Nerdy maths and figures follow.

In that thread there was some discussion on how many SM lascanons to kill a tricked out falcon.  Not surprisingly most people just take the chance of an outright 1 shot kill and say 81 on average.  Some recognise that cumulatively it will be less than that due to earlier immobilses, weapon destroyed etc.

Following that there was also a discussion somewhere - I forget the thread - on multi-shot S6 weapons being better/worse. Again most logic is based on say eldar Scattler laser, 4 shots = 1/81 chance outright kill = 81 average attempts, and declare it as equal to a lascannon against Falcons.

In the chaos thread I provided some figures for killing falcons over many shots accounting for the cumulative damage, as follows:

chance to have killed after x shots

1    1.23%
5    8.38%
10    20.46%
20    48.4%
30    71.11%
40    85.19%


As you can see you need less than 81 shots to reliably take one down (not that needing 30 odd is exactly great news).

Being into figures like I am, I was interested in breaking that down into how much of each percentage was due to outright kill against a mobile target,how much was due to kill vs immobile (ie penetrable) and how much from weapons destroyed accumulating. I came up with the following (decimals don't all add up due to rounding):

<table rules="groups" frame="void" cols="6" cellspacing="0" border="1"> <colgroup><col width="249"></col><col width="46"></col><col width="47"></col><col width="55"></col><col width="56"></col><col width="61"></col></colgroup> <tbody> <tr> <td width="249" height="17" align="left">
</td> <td width="46" align="left">
</td> <td width="47" align="left">
</td> <td width="55" align="left">Shots</td> <td width="56" align="left">
</td> <td width="61" align="left">
</td> </tr> <tr> <td height="17" align="left">
</td> <td bgcolor="#999999" align="right" sdval="1" sdnum="2057;">1</td> <td bgcolor="#999999" align="right" sdval="5" sdnum="2057;">5</td> <td bgcolor="#999999" align="right" sdval="10" sdnum="2057;">10</td> <td bgcolor="#999999" align="right" sdval="20" sdnum="2057;">20</td> <td bgcolor="#999999" align="right" sdval="30" sdnum="2057;">30</td> </tr> <tr> <td height="17" align="right">Overall chance</td> <td align="right" sdval="1.23" sdnum="2057;">1.23</td> <td align="right" sdval="8.38" sdnum="2057;">8.38</td> <td align="right" sdval="20.46" sdnum="2057;">20.46</td> <td align="right" sdval="48.4" sdnum="2057;">48.4</td> <td align="right" sdval="71.11" sdnum="2057;">71.11</td> </tr> <tr> <td height="17" align="right">outright death</td> <td align="right" sdval="1.23" sdnum="2057;">1.23</td> <td align="right" sdval="5.59" sdnum="2057;">5.59</td> <td align="right" sdval="9.93" sdnum="2057;">9.93</td> <td align="right" sdval="15.84" sdnum="2057;">15.84</td> <td align="right" sdval="19.19" sdnum="2057;">19.19</td> </tr> <tr> <td height="17" align="right">outright death from immobilized</td> <td align="right" sdval="0" sdnum="2057;">0</td> <td align="right" sdval="2.78" sdnum="2057;">2.78</td> <td align="right" sdval="10.01" sdnum="2057;">10.01</td> <td align="right" sdval="26.5" sdnum="2057;">26.5</td> <td align="right" sdval="38.14" sdnum="2057;">38.14</td> </tr> <tr> <td height="18" align="right">death from cumulative weapons/immob</td> <td align="right" sdval="0" sdnum="2057;">0</td> <td align="right" sdval="0" sdnum="2057;">0</td> <td align="right" sdval="0.52" sdnum="2057;">0.52</td> <td align="right" sdval="6.05" sdnum="2057;">6.05</td> <td align="right" sdval="13.76" sdnum="2057;">13.76</td> </tr> </tbody> </table>

as you can see once you have taken 10 seperate shots it is really the ability to pentrate an immobile target that is becoming the dominant way to kill the falcon.

Following that I got intrigued in the supposedly roughly equal scatter laser. In theory it has a better chance of accumulating results due to effect of potential multi hits each round which over time should build up, on the other hand on seeing the above I also realised it would drop of rapidly as it can never penetrate the immobile falcon which seems to be the key. I reran the maths  for a scatter laser and got the following (table only went to 15, as the number crunching beyind that was going to take a looong time) [Edit: computer finally finished crunching 20 volleys]

<table rules="groups" frame="void" cols="6" cellspacing="0" border="1"> <colgroup><col width="249"></col><col width="46"></col><col width="47"></col><col width="55"></col><col width="56"></col><col width="61"></col></colgroup> <tbody> <tr> <td width="249" height="17" align="left">
</td> <td width="46" align="left">
</td> <td width="47" align="left">
</td> <td width="55" align="left">Shots</td> <td width="56" align="left">
</td> <td width="61" align="left">
</td> </tr> <tr> <td height="17" align="left">
</td> <td bgcolor="#999999" align="right" sdnum="2057;" sdval="1">1</td> <td bgcolor="#999999" align="right" sdnum="2057;" sdval="5">5</td> <td bgcolor="#999999" align="right" sdnum="2057;" sdval="10">10</td> <td bgcolor="#999999" align="right" sdnum="2057;" sdval="15">15</td> <td bgcolor="#999999" align="right" sdnum="2057;" sdval="20">20</td> </tr> <tr> <td height="17" align="right">Overall chance</td> <td align="right" sdnum="2057;" sdval="1.22">1.22</td> <td align="right" sdnum="2057;" sdval="6">6</td> <td align="right" sdnum="2057;" sdval="11.89">11.89</td> <td align="right" sdnum="2057;" sdval="18.29">18.29</td> <td align="right" sdnum="2057;" sdval="25.71">25.71</td> </tr> <tr> <td height="17" align="right">outright death</td> <td align="right" sdnum="2057;" sdval="1.21">1.21</td> <td align="right" sdnum="2057;" sdval="5.49">5.49</td> <td align="right" sdnum="2057;" sdval="9.78">9.78</td> <td align="right" sdnum="2057;" sdval="13.1">13.1</td> <td align="right" sdnum="2057;" sdval="15.65">15.65</td> </tr> <tr> <td height="17" align="right">outright death from immobilized</td> <td align="right" sdnum="2057;" sdval="0.01">0.01</td> <td align="right" sdnum="2057;" sdval="0.49">0.49</td> <td align="right" sdnum="2057;" sdval="1.84">1.84</td> <td align="right" sdnum="2057;" sdval="3.77">3.77</td> <td align="right" sdnum="2057;" sdval="6.05">6.05</td> </tr> <tr> <td height="18" align="right">death from cumulative weapons/immob</td> <td align="right" sdnum="2057;" sdval="0">0</td> <td align="right" sdnum="2057;" sdval="0.01">0.01</td> <td align="right" sdnum="2057;" sdval="0.26">0.26</td> <td align="right" sdnum="2057;" sdval="1.41">1.41</td> <td align="right" sdnum="2057;" sdval="4">4</td> </tr> </tbody> </table>




As you can see whilst they start fairly even at 1 shot, the lascannon rapidly takes a huge lead as more shots are taken. at 10 volleys the scatter laser has only just over half the chance of killing a falcon.

Anyway I found it interetsing :S

Ps I can't absolutely guarantee those figures, though I'm pretty sure they are accurate. If anyone can demonstrate they are inaccurate Id be interested in knowing so I can revisit the calculations.

I am not interested in checking his figures. But I have on a few other of Puree's posts; and he has been spot on each time. (Unfortunately, most of them involve finding my mistakes.)

It appears that you are counting 1 scatter laser shot as one round of shooting (iow, 4 shots) is that correct?

Also, Did you calculate the next step as 5 rounds of shots, or 20 single shots?

Posted By coredump on 07/26/2007 4:17 PM
I am not interested in checking his figures. But I have on a few other of Puree's posts; and he has been spot on each time. (Unfortunately, most of them involve finding my mistakes.)

It appears that you are counting 1 scatter laser shot as one round of shooting (iow, 4 shots) is that correct?

Also, Did you calculate the next step as 5 rounds of shots, or 20 single shots?

Yes 1 sl 'shot' = 4 shots.

Edit:
each Scatter laser shot is a volley of 4 shots, so 5 rounds = 5 volleys of 4 (a total of 20 shots).  The model used accounts for not being able to immobilise and then penetrate in the same single volley (not that it effects a scatter laser). That is also of note on the lascannons, which assumes each lascannon shot is 1 seperate volley.  4 devs taking 20 lascannon shots would not come up with as good figures as the 20 column as they have less chance to benefit from hitting an already immobile target. NB - Unless I'm getting that rule wrong, I've assumed that you roll the Penetration for all shots in a volley before rolling the damage for any of them, so all shots will count as glancing (vs fast skimmer) even if the first one then immobilises.

I trust your figures, but not your conclusions. Scatters will obviously drop off in effectiveness once they've immobilised a Falcon and are trying to pen it, but I've never (well, rarely) seen a single Falcon fielded before. There will likely still be another Falcon/Prism that needs the attentions of the multishot weapons, leaving the immobilised tank to be finished off by more conventional weaponry (EMLs, melta weapons).

Posted By tegeus-Cromis on 07/27/2007 12:41 AM
I trust your figures, but not your conclusions. Scatters will obviously drop off in effectiveness once they've immobilised a Falcon and are trying to pen it, but I've never (well, rarely) seen a single Falcon fielded before. There will likely still be another Falcon/Prism that needs the attentions of the multishot weapons, leaving the immobilised tank to be finished off by more conventional weaponry (EMLs, melta weapons).

You are jumping to conclusions about my conclusions (did I even state a conclusion beyond point out the difference in the figures!). The only conclusion I would come to is that you need far fewer lascannon shots to reliably kill a falcon than scatter lasers volleys, although both have the same initial average chance of an outright kill - which is the oft quoted statistic on dakka (mean avergaes for x ,y or z is about the only statistic used by dakkites).

Of course there are other ways of finishing of the falcon, I never claimed there wasn't. please don't put words in my mouth.

Well, you attributed these claims to the proponents of SLs:





You then state a conclusion that seem to debunk these claims:



The strong implication is that these pro-SL claims are in some sense mistaken, since the two weapons are not in fact equal. My point is that when people say that SLs are as good as lascannons, they do not, in fact, mean that there are equal in the way that you are assessing for, but only that they are equal, and more cost-effective, in getting the hard part done--that is to say, immobilising or destroying mobile Falcons.

im curious to see what the numbers would look like shooting against a tau hammerhead with disruption pods(at more than and less than 12" to get the hull down roll), and decoy launchers,

Posted By tegeus-Cromis on 07/27/2007 1:52 AM
Well, you attributed these claims to the proponents of SLs:

Following that there was also a discussion somewhere - I forget the thread - on multi-shot S6 weapons being better/worse. Again most logic is based on say eldar Scattler laser, 4 shots = 1/81 chance outright kill = 81 average attempts, and declare it as equal to a lascannon against Falcons.

Following that I got intrigued in the supposedly roughly equal scatter laser.

You then state a conclusion that seem to debunk these claims:

As you can see whilst they start fairly even at 1 shot, the lascannon rapidly takes a huge lead as more shots are taken.

The strong implication is that these pro-SL claims are in some sense mistaken, since the two weapons are not in fact equal. My point is that when people say that SLs are as good as lascannons, they do not, in fact, mean that there are equal in the way that you are assessing for, but only that they are equal, and more cost-effective, in getting the hard part done--that is to say, immobilising or destroying mobile Falcons.

Maybe I didn't word it as well as I could, or you are jumping to conclusions about my intent, but for the avoidance of doubt:

I'm not of the , nor started on the basis of the, opinion there was a pro or anti SL group that I was either finding in favor of or against. My only interest was the maths (and the programming). At least as far as I was concerned my only conclusions were A) that it takes considerably less than 81 lascannons to 'reliably' take down a falcon (read 'reliable' as you like, it is subjective but I used the column that had over 70% chance for no specific reason) and B) that the Scatter laser falls quite a long way behind quite quickly in the same scenario.

I realise that if you have other waepons better suited to finishing off an immobile falcon then you'd use it, but that gets into the realm of something not easily calculable - what did you bring, is it alive still when you get the opportunity etc. The figures are I believe accurate, but as I noted in another thread, what you read such stats them is entirely up to you, I try not lead anyone down subjective paths.

You are hugely jumping to conclusions, this was just an example of how a lascannon and a SL are not equal in their ability to destroy a Falcon, and that is it. He never says anything about the relative use of each weapon, only that a las cannon is better at killing a falcon.



But thanks for that info Puree, that is very informative. I am curious to compare the relative survivability of the different vehicles in the game. For instance, what the same odds are of a las cannon dropping an av14 vehicle for example, or a hull down av14 vehicle. 

The odds of a one shot one kill with a BS4 las cannon against a kitted falcon are 1.23%.  The odds of the same result against an av14 tank are about 7.5%. That means that a falcon is 6 times less likely to be destroyed in one shot than a land raider, for example. The LR is much more expensive as well, and serves am identical function but is inferior in nearly every respect.

Also, because the LR (or any av14 vehicle) can be penned, the odds of something worse than a stun result occuring are far higher. with a pen, the LR has a 5/6 of something worse than a stun happening. On a glance a 1/2 chance of something worse than a glance. So a 2/3 chance for something worse than a stun with any succesful shot.

Whereas with a falcon, the odds of anything worse than a stun occuring are only 1/4. So, not only is the Falcon 6 times harder to kill with one shot, it is also far less likely to have and real damage done to it.

Really, holo fields should have been like the venerable upgrade for a dread, that would have made a lot more sense and made the vehicle less rediculously resiliant.

Some one needs to mail these results to the GW Dev team. They need to understand how ridiculous Falcons are to kill.

Maybe they should hire puree to test any codex before they release it...

Ozymandias, King of Kings

Yeah but don't forget that AV14 is immune to S6 and S7 (well except for rending and possible tank hunter). So while the falcon is harder to kill with a lascannon, it is vulnerable to a much greater variety of weapons, leading to more total volleys being sent at the falcon over the course of a game (or tournament). Not saying that makes them equals, but it is something that has to be considered. Of course, the falcon has a greater chance of avoiding fire all together by using terrain and speed, something that gets lost on the one guy that thinks Falcons are worse then land raiders and monoliths.


Agree 100%.

I put these numbers together really fast to compare the one shot one kill with a BS4 las cannon against of the vaious types of vehicles in the game. I will finish it when i have the chance, but i have actual work to do at work right now =0



Non Skimming

AV10

2/3 to hit x 1/6 to glance = 1/9 x 1/6 to destroy = 1/54

2/3 to hit x 5/6 to pen = 5/9 to pen x 1/2 to destroy = 5/18

about a 30% chance to destroy your target.

AV11

Same odds to destroy with a glance = 1/54

2/3 to hit x 4/6 to pen = 4/9 to pen x 1/2 to destroy = 2/9

about a 25% chance.

AV12

glance = 1/54

pen = 1/6

about 19%

AV13

glance= 1/54

pen = 1/9

13%

AV14

glance = 1/54

Pen = 1/18

7.5%

Open Topped

AV10

40% to destroy

AV11

33% to destroy

AV12

26% to destroy

AV13

19% to destroy

AV14

11.14% to destroy

Good work, puree. This looks like good math, and I would be willing to thoroughly peer-review the results and methods.

One question (which probably comes down to significant digits, or my misunderstanding of your row labels and terminology): For 5 shots with the lascannon, you indicate 0 possibility of kills due to cumulative WD/Immo results. Now, as I see it, this is a non-zero number. It is small, no doubt.

One way to model the analysis is via damage point equivalences, call them WP (for Weapon Points, because that doesn't get used elsewhere and we're counting Weapons). A Falcon has 3 WPs - three weapons that can/will be destroyed by WD results before those results roll over into Immo or Destroyed.

A vehicle under fire - particularly a falcon, as here - has two states with which we concern ourselves when calculating the impact of an incoming hit on future states. These are:
WP (3-0)
Mobile (1 or 0)

If (Mobile = 1) then
all hits glance;
else use glance/pen stats AND if (result=immo) then (result=WD)

...because this effect happens immediately, even if a prior shot in the same turn immos a vehicle.
Looking farther down the charts once we have identified the proper odds of chart outcomes (which isn't all that hard, even with holofields), we come to:

if (result=WD) then
if (WP=0) then
(result=immo)
else (WP=WP-1)
if (result=immo) then
if (Mobile=1) then
(Mobile=0)
else if (WP>0) then
(WP=WP-1)
else (result=destroyed)

Right?

So given this, then let's say we've got the LEAST desirable set of durable results from a set 5 lascannon shots:
1) Weap Dest
2) Weap Dest
3) Weap Dest
4) Immo or Weap Dest (which becomes immo)
5) Immo (which becomes Destroyed) or Weap Dest (which becomes immo, which becomes Destroyed)

Before to-hit and to-glance/pen numbers, just looking at effect percentages:
1-3)Weap Destroyed onna WP>0 Falcon: 5/36
4) Immo or WD onna WP=0 Falcon: 8/36
...now it's immobilized, so our Effect percentages go up...
5) Immo or WD or Destroyed onna WP=0, Mobile=0 Falcon = %Glance*1/4 + %Pen*25/36

Multiply all those up, and we've got a non-zero chance of a lascannon shot accumulating results over 5 shots to down a Falcon... and that's the HARDEST possible path. It gets easier if you include the 1/12 to immobilize it on an earlier shot, and the subsequent effect on future shots.

Whew... Math time. Each lascannon shot has 2/3*2/3*1/4 or 1/9 chance of creating a durable result when Mobile=1. If Mobile=0, then 2/3*1/6*1/4 + 2/3*1/2*25/36 are durable results: 1/36 + 25/108 = 28/108 = 7/27 of a durable result.

LC shot 1
20/324 WP=2, (6.173%)
12/324 Immo, (3.704%)
4/324 Destroyed (1.235%)
...which we double check by adding percentages to make sure we equal 1/9 durable result, or 11%. Which we do. On to the next shot:

LC Shot 2 :
LC1=Noeffect class:
(8/9*12/324) Immo@WP=3 (3.292%)
(8/9*20/324) WP=2 (5.487%)
(8/9*4/324) Destroyed (1.097%)
LC1=WD Class:
(20/324*20/324) WP=1 (.381%)
(20/324*12/324) Immo@WP=2 (.229%)
(20/324*4/324) DESTROYED (.076%)
(20/324*8/9) WP=2 (5.487%)
LC1=Immo Class
(12/324*(5/324+3/324+9/108+7/108)) Immo@WP=2 (1.920%)
(12/324*(1/324+9/108)) DESTROYED (.320%)
(12/324*(1/3+1/3+1/36+11/324)) Immo@WP=3 (2.743%)
This all results in the following probabilities of each of the following states after 2 Lascannon Shots:
Immo@WP=3 (6.035%)
Immo@WP=2 (2.149%)
WP=2 (10.974%)
WP=1 (.381%)
DESTROYED (1.493%) (which should also add in the 1.235 from first shot, to make 2.728% Destroyed cumulative.)

This nested list gets even deeper at LC Shot 3 because we, at that point, have to add together the cumulative probablilites of the states from prior turns (including misses in subsequent turns, etc) and also keep track of the probability of the Falcon being in any one of the following states before and after the turn:
WP=3
WP=2
WP=1
WP=0
Immo@WP=3
Immo@WP=2
Immo@WP=1
and of course, Destroyed.

All of this math gets simplified when looking at ScatterLasers, because I don't have to do the second set of fractions to figure the change in effect once the vehicle is immobilized - in that case, all my hits are glancing anyway.

puree, do you follow and agree with my approach here? I'd love to see what language you used attack the problem. So far to me, this is all pencil and paper fractions - I haven't formulated it algorithmically and would be interested to see how you handled the nesting/iteration.

===

to mughi3: I'm kinder and gentler now. Back when, I'da suggested you use my example math to find out on your own. Now I'll do half the math for you and point out that the AV on a Hammerhead is 13, so your chance with a ScatterLaser is 0.

-JT

EDIT:


More correctly I should have said:
"A vehicle under fire - particularly a falcon, as here - has three variables and thus 9 possible states with which we concern ourselves when calculating the impact of an incoming hit on future states. These variables are:
WP(3-0)
Mobile(1 or 0)
Destroyed(1 or 0)"

Posted By JTS1486 on 07/27/2007 10:47 AM
Good work, puree. This looks like good math, and I would be willing to thoroughly peer-review the results and methods.

One question (which probably comes down to significant digits, or my misunderstanding of your row labels and terminology): For 5 shots with the lascannon, you indicate 0 possibility of kills due to cumulative WD/Immo results. Now, as I see it, this is a non-zero number. It is small, no doubt.

<snip brevity="" for="">[snip for brevity]

puree, do you follow and agree with my approach here? I'd love to see what language you used attack the problem. So far to me, this is all pencil and paper fractions - I haven't formulated it algorithmically and would be interested to see how you handled the nesting/iteration.

===

to mughi3: I'm kinder and gentler now. Back when, I'da suggested you use my example math to find out on your own. Now I'll do half the math for you and point out that the AV on a Hammerhead is 13, so your chance with a ScatterLaser is 0.

-JT</snip>

Yes, the 5 shots = 0 is merely me simply pasting the first 2 decimals on to the forum, I doubt most readers are that bothered with even that degree of precision, never mind the other dozen odd digits sitting in my output. I actually got 0.00530884562700%

Your basic description of the problem does fairly closey resemble my approach in concept, Its a Java program (what I'm most comfortable with), there's a basic state pattern representing the falcon that transitions to each of the next approiate states with each hit. Mobile -> immobile or dead, Immobile -> dead. Theres also an additional state for handling the transition between mobile->immobilised state during the course of a volley, as until the volley is over I think all hits will have already been resolved as glance only (though I started to wonder whether that was true afterwards). weapons are tracked with a simple number (0 1 2 or 3 destroyed)

The processing is a fairly simple brute force approach of building up a tree, where each node represents the state of the falcon for a given possiblity. So it starts with 1 node (mobile) and then adds child nodes for each of the possibilites underneath from 1 shot, (mobile, immobile, dead, mobile+1WD). It then does the same for each of those children recursing down to however many shots are taken. Whenever we transition to dead, the Dead state chucks the cumulative probabilty of having arrived at that node and the reason (weapon, kill, etc) into a 'bucket' to be analysed after the tree building.

Its hardly well optimised after just a couple hours work, even more so as I wasn't initially thinking of going as far as I did with it. I've a far more optimised probability tree builder for squad vs squad calcuations, but I spent quite a while optimising that for memory vs speed - memory became the limiting factor there, million plus nodes get a little heavy and I hate having to increase the heap size beyond the default.

I'd be interested in seeing if you can verify some of the numbers - I could only work out some of the top nodes on paper, otherwise I just stepped through the code in debug makng sure it was doing what it was supposed to, the weapon accumulation in particular doesn't really start kicking until well beyond the point I could confirm on paper the results.

The first cut to simplifying this state sounds like making sure there is a state for "unaffected", and then at each stage consolidate the tree so that identical states are lumped as sums to pass on for the next event, in the same way that you toss things into the same "destroyed" bucket. You can doublecheck the progress working properly by making sure your states count up to 100% at each stage.

It's been about a decade since I actually coded up anything useful. Props to you for banging this out. I'd have to really crack open the texts to make something like this work... lemme see what i can do in an hour.

-JT

damn, you guys know your stuff.

Would it be possible to make a chart of the effectiveness of X strength weapons at BS X against X armor, with and without hull down, skimming or open topped?

that is a lot of variables, but something like that would be really useful in game to determine what the most effective way to utilize your weapons was. You could look at a chart and quickly determine what the odds of taking a vehicle down would be with x amount of shots.

Plus, it would just be interesting to read, too.

I took a look at that - and it IS a lot of variables, since you have such a broad set of states to manage with different vehicle types and especially with various wargear effects. I'm making a modular sheet for Falcon work that could be modified for different classes of vehicles, based on plugging in fractions for each event (hit, effect, damage result, etc) - so a user could in fact plug in all their variables and get valid answers IF they were able to do the first-stage math manually to figure out the single-event probabilities... which is something most hardcore Dakka types can do.

-JTS

This is real great stuff, as it is both interesting, and necissary for the competitive gamer.  I doubt GW ever put this much effort into balancing/testing their lists.  

and i am sure the dice gods haven't either

 

theres stats on probability, and then there is dice.....i played a game against IG where out of 15 ordinance shots in a 6 turn game between his demolisher, rus and basalisk he only scattered 3 times. :|

Stats and probabilities won't win you a game, they will however help win you games, and over a period of time give you a better win record.

That is the basis of the whole gambling industry, the casino doesn't know when you roll whether you will win or lose, but they know the probabilities of each event. From that they can adjust the odds for each game so that over many bets they come out tops. Even sports gambling is the essentially same, I used to work with someone who left to live quite comfortably (from what I hear every now and again) on betting, at its simplest he was tracking the odds being offered by different bookies and seeing if any seem to have their odds out of kilter with the majority of others and more in favor of the punter, if they do then place a bet- the sport or event wasn't important.  On an individual bet he may well lose, but over many such bets he wins as many such bets are usually the bookie mispricing the bet or calculating his odds wrong.

Understanding the probabilities in a game like 40k possibly won't overcome someone who is just a much better player, or has a list that seems to be the perfect counter to yours etc, but in the grand scheme of things it is another little weight on your side of the scales - as the chinese bod said, if you wanna win then stack every advantage you can to yourself.

For Myself - I just like stats and maths and programming.

Thanks for sharing your odds. It seems like one should do best with a mix of high strength and multi shot weapons, to begin shooting with multishot and use high strength on immobilized targets, right?

An unanswered question by now is how essential vectored engines are. Some People me included claim that the chance to get a use of VEs doesn justefy the price. It would be very helpful if you ran your numbers without VEs. That should be rather simple. One could compare odds with and without VEs then and see if the price increase warrents the resiliance increase.

Posted By Raider on 07/28/2007 4:01 AM

An unanswered question by now is how essential vectored engines are. Some People me included claim that the chance to get a use of VEs doesn justefy the price. It would be very helpful if you ran your numbers without VEs. That should be rather simple. One could compare odds with and without VEs then and see if the price increase warrents the resiliance increase.

Assuming you are always moving fast and would crash without them:

<table rules="groups" frame="void" cols="6" cellspacing="0" border="1"> <colgroup><col width="86"></col><col width="86"></col><col width="86"></col><col width="86"></col><col width="86"></col><col width="86"></col></colgroup> <tbody> <tr> <td width="86" height="18" align="left">
</td> <td width="86" align="left">
</td> <td width="86" align="left">lascannon shots
</td> <td width="86" align="left">
</td> <td width="86" align="left">
</td> <td width="86" align="left">
</td> </tr> <tr> <td height="17" align="left">
</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="1">1</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="5">5</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="10">10</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="15">15</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="20">20</td> </tr> <tr> <td height="17" align="left">death</td> <td align="right" sdnum="2057;" sdval="4.93827161">4.94</td> <td align="right" sdnum="2057;" sdval="22.376731116687">22.38</td> <td align="right" sdnum="2057;" sdval="39.899810556787">39.9</td> <td align="right" sdnum="2057;" sdval="53.8531534763164">53.85</td> <td align="right" sdnum="2057;" sdval="65.0363146463712">65.04</td> </tr> <tr> <td height="17" align="left">outright</td> <td align="right" sdnum="2057;" sdval="1.2345679">1.23</td> <td align="right" sdnum="2057;" sdval="5.592529203937">5.59</td> <td align="right" sdnum="2057;" sdval="9.931081507757">9.93</td> <td align="right" sdnum="2057;" sdval="13.2811770768794">13.28</td> <td align="right" sdnum="2057;" sdval="15.8413252816242">15.84</td> </tr> <tr> <td height="17" align="left">skimmer crash</td> <td align="right" sdnum="2057;" sdval="3.70370371">3.7</td> <td align="right" sdnum="2057;" sdval="16.78420191275">16.78</td> <td align="right" sdnum="2057;" sdval="29.96872904903">29.97</td> <td align="right" sdnum="2057;" sdval="40.571976399437">40.57</td> <td align="right" sdnum="2057;" sdval="49.194989364747">49.19</td> </tr> </tbody> </table>

Again - until I can get some verification from a second source, take them with a slight pinch of salt.

Hey, no need to react so strongly to my comments. I'm just saying that the statements you're referring to regarding the rough equivalence of SLs and lascannons are, on closer examination, usually not making the same claims that you are testing here, that's all. I don't mean to discredit your project or anything.

So, the next step is what about strength 8 (missile launchers and bright lances) and strength 7 heavy 2 (auto cannons)?

Posted By Phoenix on 07/29/2007 1:55 PM
So, the next step is what about strength 8 (missile launchers and bright lances) and strength 7 heavy 2 (auto cannons)?

I've re-written it, now much more optimised and vastly faster than my first cut.  Also still gives the same results, so I'm a bit more confident that they are probably accurate. Also modeled it in a way which should handle calculating things that the first version wouldn't have, e.g being stunned (extra armor) as and when I get round to them.

The weapns above (ML and AC), plus broad-side rail guns, and twin linked VCs on a fex (I havn't got multi weapon volleys in yet for the VC/BS version).

<table rules="groups" frame="void" cols="7" cellspacing="0" border="1"> <colgroup><col width="189"></col><col width="53"></col><col width="58"></col><col width="53"></col><col width="65"></col><col width="64"></col><col width="55"></col></colgroup> <tbody> <tr> <td width="189" height="17" bgcolor="#999999" align="left" sdnum="2057;0;0">
</td> <td width="53" bgcolor="#999999" align="left" sdnum="2057;0;0">
</td> <td width="58" bgcolor="#999999" align="left" sdnum="2057;0;0">
</td> <td width="53" bgcolor="#999999" align="left" sdnum="2057;0;0">
</td> <td width="65" bgcolor="#999999" align="left" sdnum="2057;0;0">ML</td> <td width="64" bgcolor="#999999" align="left" sdnum="2057;0;0">
</td> <td width="55" bgcolor="#999999" align="left" sdnum="2057;0;0">
</td> </tr> <tr> <td height="17" bgcolor="#c0c0c0" align="left" sdnum="2057;0;0">
</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;0;0" sdval="1">1</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;0;0" sdval="5">5</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;0;0" sdval="10">10</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;0;0" sdval="15">15</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;0;0" sdval="20">20</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;0;0" sdval="25">25</td> </tr> <tr> <td height="17" bgcolor="#00ae00" align="left" sdnum="2057;0;0.00000">death</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="0.925925925">0.93</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="5.77895353679">5.78</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="13.675888971659">13.68</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="22.989013096349">22.99</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="33.139471133649">33.14</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="43.416726956049">43.42</td> </tr> <tr> <td height="17" align="left" sdnum="2057;0;0.00000">outright</td> <td align="right" sdnum="2057;" sdval="0.925925925">0.93</td> <td align="right" sdnum="2057;" sdval="4.2991576901535">4.3</td> <td align="right" sdnum="2057;" sdval="7.8582313287465">7.86</td> <td align="right" sdnum="2057;" sdval="10.7998797645465">10.8</td> <td align="right" sdnum="2057;" sdval="13.2216287808465">13.22</td> <td align="right" sdnum="2057;" sdval="15.2031297416465">15.2</td> </tr> <tr> <td height="18" align="left" sdnum="2057;0;0.00000">from immobillsed</td> <td align="right" sdnum="2057;" sdval="0">0</td> <td align="right" sdnum="2057;" sdval="1.478727078951">1.48</td> <td align="right" sdnum="2057;" sdval="5.677509120891">5.68</td> <td align="right" sdnum="2057;" sdval="11.293050497791">11.29</td> <td align="right" sdnum="2057;" sdval="17.356749152791">17.36</td> <td align="right" sdnum="2057;" sdval="23.200687112791">23.2</td> </tr> <tr> <td height="18" align="left" sdnum="2057;0;0.00000">cumulative weapons/immob</td> <td align="right" sdnum="2057;" sdval="0">0</td> <td align="right" sdnum="2057;" sdval="0.0010687676855">0</td> <td align="right" sdnum="2057;" sdval="0.1401485220215">0.14</td> <td align="right" sdnum="2057;" sdval="0.8960828340115">0.9</td> <td align="right" sdnum="2057;" sdval="2.5610932000115">2.56</td> <td align="right" sdnum="2057;" sdval="5.0129101016115">5.01</td> </tr> <tr> <td height="17" align="left" sdnum="2057;0;0.00000">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> </tr> <tr> <td height="17" align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> </tr> <tr> <td height="17" bgcolor="#999999" align="left">
</td> <td bgcolor="#999999" align="left">
</td> <td bgcolor="#999999" align="left">
</td> <td bgcolor="#999999" align="left">
</td> <td bgcolor="#999999" align="left">AC (BS4)</td> <td bgcolor="#999999" align="left">
</td> <td bgcolor="#999999" align="left">
</td> </tr> <tr> <td height="17" bgcolor="#c0c0c0" align="left">
</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="1">1</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="5">5</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="10">10</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="15">15</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="20">20</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="25">25</td> </tr> <tr> <td height="17" bgcolor="#00ae00" align="left">death</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="1.230757505">1.23</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="7.58100908481464">7.58</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="17.8423450830148">17.84</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="29.9293268470548">29.93</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="42.7461762683308">42.75</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="55.0182625244328">55.02</td> </tr> <tr> <td height="17" align="left">outright</td> <td align="right" sdnum="2057;" sdval="1.2193263208">1.22</td> <td align="right" sdnum="2057;" sdval="5.5301194635793">5.53</td> <td align="right" sdnum="2057;" sdval="9.8324685429933">9.83</td> <td align="right" sdnum="2057;" sdval="13.1627405493333">13.16</td> <td align="right" sdnum="2057;" sdval="15.7148544734133">15.71</td> <td align="right" sdnum="2057;" sdval="17.6443293745633">17.64</td> </tr> <tr> <td height="18" align="left">from immobillsed</td> <td align="right" sdnum="2057;" sdval="0.0114311842">0.01</td> <td align="right" sdnum="2057;" sdval="2.03513536164309">2.04</td> <td align="right" sdnum="2057;" sdval="7.51260728877529">7.51</td> <td align="right" sdnum="2057;" sdval="14.4405674256453">14.44</td> <td align="right" sdnum="2057;" sdval="21.4192175628713">21.42</td> <td align="right" sdnum="2057;" sdval="27.6218504925633">27.62</td> </tr> <tr> <td height="18" align="left">cumulative weapons/immob</td> <td align="right" sdnum="2057;" sdval="0">0</td> <td align="right" sdnum="2057;" sdval="0.01575425959225">0.02</td> <td align="right" sdnum="2057;" sdval="0.49726925124625">0.5</td> <td align="right" sdnum="2057;" sdval="2.32601887207625">2.33</td> <td align="right" sdnum="2057;" sdval="5.61210423204625">5.61</td> <td align="right" sdnum="2057;" sdval="9.75208265730625">9.75</td> </tr> <tr> <td height="17" align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> </tr> <tr> <td height="17" align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> <td align="left">
</td> </tr> <tr> <td height="17" bgcolor="#999999" align="left">
</td> <td bgcolor="#999999" align="left">
</td> <td bgcolor="#999999" align="left">
</td> <td bgcolor="#999999" align="left">
</td> <td bgcolor="#999999" align="left">Broadside</td> <td bgcolor="#999999" align="left">
</td> <td bgcolor="#999999" align="left">
</td> </tr> <tr> <td height="17" bgcolor="#c0c0c0" align="left">
</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="1">1</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="5">5</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="10">10</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="15">15</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="20">20</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="25">25</td> </tr> <tr> <td height="17" bgcolor="#00ae00" align="left">death</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="2.08333333">2.08</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="16.68294019927">16.68</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="41.29648668574">41.3</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="63.65019559864">63.65</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="79.10516971584">79.11</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="88.60446956144">88.6</td> </tr> <tr> <td height="17" align="left">outright</td> <td align="right" sdnum="2057;" sdval="2.08333333">2.08</td> <td align="right" sdnum="2057;" sdval="8.81905853231">8.82</td> <td align="right" sdnum="2057;" sdval="14.49783030631">14.5</td> <td align="right" sdnum="2057;" sdval="18.04855684091">18.05</td> <td align="right" sdnum="2057;" sdval="20.15983937251">20.16</td> <td align="right" sdnum="2057;" sdval="21.34885771071">21.35</td> </tr> <tr> <td height="18" align="left">from immobillsed</td> <td align="right" sdnum="2057;" sdval="0">0</td> <td align="right" sdnum="2057;" sdval="7.7787406005">7.78</td> <td align="right" sdnum="2057;" sdval="23.1042745735">23.1</td> <td align="right" sdnum="2057;" sdval="35.2244995805">35.22</td> <td align="right" sdnum="2057;" sdval="42.6919881411">42.69</td> <td align="right" sdnum="2057;" sdval="46.910143583">46.91</td> </tr> <tr> <td height="18" align="left">cumulative weapons/immob</td> <td align="right" sdnum="2057;" sdval="0">0</td> <td align="right" sdnum="2057;" sdval="0.08514106646">0.09</td> <td align="right" sdnum="2057;" sdval="3.69438180593">3.69</td> <td align="right" sdnum="2057;" sdval="10.37713917723">10.38</td> <td align="right" sdnum="2057;" sdval="16.25334220223">16.25</td> <td align="right" sdnum="2057;" sdval="20.34546826773">20.35</td> </tr> <tr> <td height="17" align="left" sdnum="2057;0;0.00000">
</td> <td align="left" sdnum="2057;0;0.00000">
</td> <td align="left" sdnum="2057;0;0.00000">
</td> <td align="left" sdnum="2057;0;0.00000">
</td> <td align="left" sdnum="2057;0;0.00000">
</td> <td align="left">
</td> <td align="left">
</td> </tr> <tr> <td height="17" align="left" sdnum="2057;0;0.00000">
</td> <td align="left" sdnum="2057;0;0.00000">
</td> <td align="left" sdnum="2057;0;0.00000">
</td> <td align="left" sdnum="2057;0;0.00000">
</td> <td align="left" sdnum="2057;0;0.00000">
</td> <td align="left">
</td> <td align="left">
</td> </tr> <tr> <td height="18" bgcolor="#999999" align="left" sdnum="2057;0;0.00000">
</td> <td bgcolor="#999999" align="left" sdnum="2057;0;0.00000">
</td> <td bgcolor="#999999" align="left" sdnum="2057;0;0.00000">
</td> <td bgcolor="#999999" align="left" sdnum="2057;0;0.00000">
</td> <td bgcolor="#999999" align="left" sdnum="2057;0;0.00000">Fex(TLVC)</td> <td bgcolor="#999999" align="left">
</td> <td bgcolor="#999999" align="left">
</td> </tr> <tr> <td height="17" bgcolor="#c0c0c0" align="left">
</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="1">1</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="5">5</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="10">10</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="15">15</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="20">20</td> <td bgcolor="#c0c0c0" align="right" sdnum="2057;" sdval="25">25</td> </tr> <tr> <td height="17" bgcolor="#00ae00" align="left">death</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="3.4420814026">3.44</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="16.706681081412">16.71</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="39.531277667372">39.53</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="65.782437557107">65.78</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="84.356861962615">84.36</td> <td bgcolor="#00ae00" align="right" sdnum="2057;" sdval="93.8869205282768">93.89</td> </tr> <tr> <td height="17" align="left">outright</td> <td align="right" sdnum="2057;" sdval="3.351658949">3.35</td> <td align="right" sdnum="2057;" sdval="12.81444666568">12.81</td> <td align="right" sdnum="2057;" sdval="18.81327060424">18.81</td> <td align="right" sdnum="2057;" sdval="21.30219375063">21.3</td> <td align="right" sdnum="2057;" sdval="22.204635208222">22.2</td> <td align="right" sdnum="2057;" sdval="22.4977645280388">22.5</td> </tr> <tr> <td height="18" align="left">from immobillsed</td> <td align="right" sdnum="2057;" sdval="0.0904224536">0.09</td> <td align="right" sdnum="2057;" sdval="3.239595974852">3.24</td> <td align="right" sdnum="2057;" sdval="10.054141350852">10.05</td> <td align="right" sdnum="2057;" sdval="15.961288172397">15.96</td> <td align="right" sdnum="2057;" sdval="19.404531967913">19.4</td> <td align="right" sdnum="2057;" sdval="20.975545640968">20.98</td> </tr> <tr> <td height="18" align="left">cumulative weapons/immob</td> <td align="right" sdnum="2057;" sdval="0">0</td> <td align="right" sdnum="2057;" sdval="0.65263844088">0.65</td> <td align="right" sdnum="2057;" sdval="10.66386571228">10.66</td> <td align="right" sdnum="2057;" sdval="28.51895563408">28.52</td> <td align="right" sdnum="2057;" sdval="42.74769478648">42.75</td> <td align="right" sdnum="2057;" sdval="50.41361035927">50.41</td> </tr> </tbody> </table>

Rail gun is pretty nice, and it gets even nicer if you paint your target with markerlights, A few  markerlights and 3 full squads of broadsides is looking like one of the few things able to down a falcon over 50% of the time in 1 turn .

This Pic best describes it

http://tsoalr.com/comic.php?id=449&save-as=09_Dehne02_Holofalcon.gif

Started adding some more things in, but just need to check something.

Am I right in assuming that hull down is like fast skimmer in always affecting any penetrate irrespective of source (e.g it overrides the wraithcannon/ap1 etc rules).

No not any more.

It gives you the possibility of downgrading any pen roll on a 4 - 6.

Sorry just re read your post and yes it affects all weapons downgrading pen to glances on a 4 - 6.