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View Full Version : Attention mathematicians, Math's help please :)

selone
22-03-2009, 20:21
Hello warseers I'm trying to figure out the chances of a unit of chaos warriors/chosen (LD 8) passing a break test with the rapturous standard (all rolls of doubles or that contain a one are counted as insane courage) I was wondering whether you could make sure I'm not making schoolboy errors. I am presuming no reroll and not autobroken by fear (although there's a 16/36 in chance of insane courage).

Possible dice results- bold indicates an insane courage.

1+1 1+2 1+3 1+4 1+5 1+6
2+1 2+2 2+3 2+4 2+5 2+6
3+1 3+2 3+3 3+4 3+5 3+6
4+1 4+2 4+3 4+4 4+5 4+6
5+1 5+2 5+3 5+4 5+5 5+6
6+1 6+2 6+3 6+4 6+5 6+6

Unit is beaten by

-6 or more= 16/36 chance of passing 44.4%
-5 or more= 16/36 chance of passing 44.4%
-4 or more= 16/36 chance of passing 44.4%
-3 or more= 18/36 chance of passing 50%
-2 or more= 20/36 chance of passing 55.6%
-1 or more= 24/36 chance of passing 66.6%
Stubborn = 28/36 chance of passing 77.8%

Are these figures right?

As a baseline these are the figures without the rapturous standard. (from avian's website)
-6 2.8%
-5 8.3%
-4 16.7%
-3 27.8%
-2 41.7%
-1 58.3%

O&G'sRule
22-03-2009, 22:17
I hadn't realised just how good an item that is

Kalec
22-03-2009, 22:23
You should try in in a unit with Sigvald and a BSB. Only breaks on a roll of 5 and 6 twice. Only breaks 1/72 of the time.

RCgothic
22-03-2009, 22:29
I make it a 16/36 chance of insane courage.

so beaten by:
0 = 28/36 = 77.8%
1 = 24/36 = 66.7%
2 = 20/36 = 55.6%
3 = 18/36 = 50%
4+ =16/36= 44.4%

Chance of holding.

O&G'sRule
22-03-2009, 22:34
I make it a 16/36 chance of insane courage.

so beaten by:
0 = 28/36 = 77.8%
1 = 24/36 = 66.7%
2 = 20/36 = 55.6%
3 = 18/36 = 50%
4+ =16/36= 44.4%

Chance of holding.

If you're beaten by zero why are you rolling?

RCgothic
22-03-2009, 22:37
When I last played fantasy, musicians carried the combat if it was a draw.
Also maybe other psycology tests, such as terror/panic/shooting casualties?

If not, just ignore that line. I'm not a current fantasy player, just a mathematician. ;)

O&G'sRule
22-03-2009, 22:49
When I last played fantasy, musicians carried the combat if it was a draw.
Also maybe other psycology tests, such as terror/panic/shooting casualties?

If not, just ignore that line. I'm not a current fantasy player, just a mathematician. ;)

Ah ok I was thinking maybe there was an item i hadn't seen. Musicians win drawn combats but still at -1. Insane courage only applies to break tests not other psychology tests:)

22-03-2009, 23:07
Indeed a 16/36 instead of 11/36 chance for insane courage.

And I also come to this:

__________Fail____Pass__% pass
Stubborn: 08/36 _ 28/36 _ 77.8%
-1 modif.: 12/36 _ 24/36 _ 66.7%
-2 modif.: 16/36 _ 20/36 _ 55.6%
-3 modif.: 18/36 _ 18/36 _ 50.0%
-4+ mod.: 20/36 _ 16/36 _ 44.4%

1+1 1+2 1+3 1+4 1+5 1+6
2+1 2+2 2+3 2+4 2+5 2+6
3+1 3+2 3+3 3+4 3+5 3+6
4+1 4+2 4+3 4+4 4+5 4+6
5+1 5+2 5+3 5+4 5+5 5+6
6+1 6+2 6+3 6+4 6+5 6+6

Green is always pass, red is always fail on a unit of stubborn. So the 0 modifier is possible, if you are stubborn.
There are 8 red ones, so a chance of 8/36 to fail when you are stubborn on 8. When you have a -1 modifier, you add 4 options, and on a -2 you add 4 more. On a -3 and -4 modifier you only add 2 options each time, coming to a total of 20/36 combinations of numbers on which you fail if you get massacred. There are 16 green ones (meaning insane courage with the standard) resulting in a chance of 16 to 36 to hold your ground even if you get nearly annihilated.

Right?

Especially if you can make your unit stubborn with a leadership 10 character in it... as close to unbreakable as you can get.

RCgothic
22-03-2009, 23:12
I can't spot the difference between your table and mine.
20/36 to fail on a beaten by 4+ is the same as a 16/36 to pass.

22-03-2009, 23:23
As I said, I also come to that result. Just a confirmation of yours, and a bit more explanation on how we got there, as the OP didn't do that right...

I did edit my post a bit, so you might have seen an unedited version, where I had a bit different wording on that bit...

Anyway, just been skimming through the pages a bit... sigvald has stubborn on leadership 10. Put him in a nice slaanesh unit with the standard and: tadaa! Stubborn on leadership 10, and also insane courage on a 6+6.
Not sure if that is worth the 20 points of the banner, but still...

selone
22-03-2009, 23:53
Ah yeah I'd counted 1 + all other results and all doubles but not all other results +1 hence the missing 5, cheers ! :) For 20 points it's very good imo

Kerill
23-03-2009, 05:33
I also have a 44% chance of getting insane courage (and 69% chance with bsb re-roll), although it's not quite as good as it sounds since some of those values would lead to a passed test anyway (1+2,1+3,1+4,1+5,1+6, 6+1, 5+1, 4+1, 3+1,2+1, 2+2, 3+3). So for losing by one you only have added 4+4,5+5,6+6- an extra 8.3% to the chance of passing normally anyway if you lose by one. Of course in this case if you had bought the warbanner instead you wouldn't even be testing.

It's good, but not good enough to be relied on (unless with bsb present) and when you win, draw, lose by 1 or lose by 2 a warbanner would have been a better buy than the rapturous standard since you would be losing by 1 less or winning by one more.

nosferatu1001
23-03-2009, 12:13
Sigvald and BSB with rapturous only breaks on a 2/36*2/36 roll, or in otherwords 1 time in 324

Until you are outnumbered by fear (easily negated apart from Terror causers by having BSB on something fearcausing, which i presume they can get) you are so damn cloe to unbreakable. and with sigvald having 7 attacks (if memory serves) you shouldchew through opponents.

Avian
23-03-2009, 12:25
Or take the Mark of Slaanesh. ;)

nosferatu1001
23-03-2009, 13:57
Which only protects you from panic, not break tests

23-03-2009, 14:17
But makes you immune to autobreak from fear.

Sigvald is Slaanesh, btw.

But this banner would be the most cost-effective actually on a unit with a lower leadership that is otherwise easily broken. So on chosen are nice to equip with this one.

nosferatu1001
23-03-2009, 15:03
True, forgot the immune to autobreak part. Was more concerned on the value they could break on - stubborn Ld10 with MoS and BSB is pretty much Unbreakable. 1 in 324 chance of breaking from any combat isnt bad!

selone
23-03-2009, 15:30
Whilst yes its funny with Sigvald thats not it's recomended use :p

The banner clearly gets better the worse your ld you'll be testing on. A 44 % chance fo remaining in combat without a reroll when you get hammered in combat is pretty good. Conversely the less you get beat by the worse the less benefit the banner brings. Nevertheless for 20 points I think its excellent given on a unit that takes a nasty charge (I'm thinking being charged by heavy calary here- brettonian lanced in my case)

23-03-2009, 17:35
Have a BSB nearby in addition to the raptorous standard, then calculate the risk of your unit failing its break test... :D

selone
25-03-2009, 17:35
Comparison of rapturous standard vs warbanner

Unit is beaten by (after modifications)
-7 or more 44.4 % vs 2.8 %
-6 44.4% vs 8.3 %
-5 44.4% vs 16.7%
-4 44.4% vs 27.8%
-3 50% vs 41.7%
-2 55.6% vs 58.3%
-1 66.6% vs drawn combat

As a baseline these are the figures without any standard. (from avian's website)
-6 2.8%
-5 8.3%
-4 16.7%
-3 27.8%
-2 41.7%
-1 58.3%

The warbanner is far better ofc if you're going to win or draw. It's much better if you're going to lose by 1, is about the same as rapturous standard if you're going to lose by 2 and is worse by any other result.
It has to be said that ofc the warbanner is slightly better if you have Mark of slaanesh and the rapturous slightly better if you don't (to avoid fear autobreak's)

RaZeR
26-03-2009, 18:00
The warbanner is far better ofc if you're going to win or draw. It's much better if you're going to lose by 1, is about the same as rapturous standard if you're going to lose by 2 and is worse by any other result.
It has to be said that ofc the warbanner is slightly better if you have Mark of slaanesh and the rapturous slightly better if you don't (to avoid fear autobreak's)

And here's the issue...
How often are you likely to see chosen losing combat by more than 2?
It would be much better used on a BSB in a unit of marauders maybe...