Hey all

i was reading a thread on Warseer that talked about preventing units from Regrouping after they were forced to Fall Back from CC, by Consolidating to within 6" of them, and it prompted me to work out the odds of this happening.

for the sake of argument, lets make some assumptions:
- the Fall Back move being made is the normal 2D6", the Consolidation move is the normal D6", and there are no obstructions to worry about
- at least one of the survivors in the losing unit starts his Fall Back move in B2B contact with one of the enemy models
- the winning side is in front of their opponents (they have not attacked from the side or rear, or lapped around them)
- the Consolidation move and the Fall Back move are made in exactly the same direction, and it is the losing side's turn next
- we will use theoretical distances between models to determine whether Regrouping is allowed (we wont worry about inacuracies in measurements etc, for example, a 7" Fall Back and a 1" Consolidate = no Regrouping, since you are within 6")



so, what do you think the chance is that the unit will end up too close to Regroup?

i make it .

here's how i got my answer:
the first thing i did was work out the chance of scoring a particular distance on the 2D6 roll.
then i worked out the furthest distance the losing unit could Fall Back, and still be within 6", for each of the 6 possible Consolidation distances.
for each of these Fall Back distances, i added the chances of scoring each number equal to or less than that distance together, to get the chance of the unit being unable to regroup for each Consolidation distance.
i divided each of these chances by 6, and added them all together to get the overall chance of the unit being unable to regroup.

so, did i get it right?

if i did, the result is quite suprising, IMO...

cheers

~ Tim
EDIT: looking at the numbers again, it seems that the chance of the unit being unable to regroup in 5th ed is almost exactly the same as it would have been under 4th (when Consolidation under such circumstances would have been fixed at 3"). wow...

One thing you are assuming here is that your combative units are similarly placed. If I were smart enough to do a drawing like you did, I would do so, but I'll have to rely on ascii.

...xo
..xooo
.xo
xo

When the o troop falls back, you measure from the closest o to the nearest x chasing which may NOT be the one they were fighting.

...x....o
..x....ooo
.x....o
x....o

in my example, the bottom o is 4 dots away from the x it was fighting, but only about 3 away from the top x it wasn't fighting.

I think you'd have to do some kind of graphical analysis assuming some kind of typical combat topographical arrangment along with using standard deviation to determine start and end conditions.

Now, having SAID all that stuff, going from apocryphal instances, it doesn't seem like recovery is EVER hindered in a real game.

It is very easy to "chase" long term but sometimes not economical or tactical.. say you have a heavy weapon you want to fire and your just chasing a squad that can't regroup (or has little chance/offensive capability left).Or say they have good assualt weaponry (they can fire as they fall back..it might be better to let them fall out of range) Or they run (and you do not wish too).
your looking for "and" results in probability (linky to good thread )
I might give the maths some time..when I have some time



GAAHHHH, right EDIT 4
Take all the possible results of 2d6, x by the number of the second variable possible results (the other dice)=bottom of fraction.. then work out how many of those events allow your situation to occur=the number on the top of the fraction..you have all the maths just insert them in that method.

Gymbol wrote:One thing you are assuming here is that your combative units are similarly placed.

yep - would get far too complicated otherwise.
(too many "what if"'s)

Gymbol wrote:If I were smart enough to do a drawing like you did, I would do so, but I'll have to rely on ascii.

its just a simple diagram drawn in Paint and uploaded to my Photobucket.

Gymbol wrote:Now, having SAID all that stuff, going from apocryphal instances, it doesn't seem like recovery is EVER hindered in a real game.

but... is my answer correct?

~ Tim

Yeah, it probably is correct.

If consolidate = 1, then flee has to = 7, or 58%.
If consolidate = 2, then flee has to = 8, or 42%
If consolidate = 3, then flee has to = 9, or 18%
If consolidate = 4, then flee has to = 10, or 8%
If consolidate = 5, then flee has to equal 12, or 3%
If consolidate = 6, then flee = fail.

I think you can average these numbers, with rounding = 21% get away chance.

So why does it NEVER work for me then?

Gymbol wrote:If consolidate = 1, then flee has to = 7, or 58%.

if you flee 7" and i consolidate 1", you cant regroup (you took that into consideration, right?).

Gymbol wrote:I think you can average these numbers, with rounding = 21% get away chance.

So why does it NEVER work for me then?

actually, i get the chance of being able to regroup as less than that...

~ Tim

Gymbol wrote:If consolidate = 4, then flee has to = 10, or 8%
If consolidate = 5, then flee has to equal 12, or 3%

Why the extra inch? (ok so i'm sitting working out the fractions now so you can contrast em)

So correcting
if consolidate =1 then flee must be 8 or greater=5 possible escapes.
if consolidate =2 then flee must be 9 or greater=4 possible escapes.
if consolidate =3 then flee must be 10 or greater=3 possible escapes.
if consolidate =4 then flee must be 11 or greater=2 possible escapes.
if consolidate =5 then flee must be 12 or greater=1 possible escape
so 15 possible combinations of events can lead to you escaping..(top number of your fraction)
Am I right about timesing the multiple event denominators?(not sure about that bit) If so isn't it 15 over 216
or around 6.94% chance of escaping (based on changing the fractions by timsing the numerator by 100 and diving by the set denominator)

killmaimburn wrote:if consolidate =1 then flee must be 8 or greater=5 possible escapes.
if consolidate =2 then flee must be 9 or greater=4 possible escapes.
if consolidate =3 then flee must be 10 or greater=3 possible escapes.
if consolidate =4 then flee must be 11 or greater=2 possible escapes.
if consolidate =5 then flee must be 12 or greater=1 possible escape
so 15 possible combinations of events can lead to you escaping..(top number of your fraction)

but each of those escapes arent equally as likely (because there are more ways to make certain distances on 2D6 than others).

take:
"if consolidate =1 then flee must be 8 or greater=5 possible escapes."
yes, there are 5 scores that can lead to an escape, but the chance of each is different.
you need to add the chance of getting and 8 on 2D6 to the chance of getting a 9, plus the chance of getting a 10, plus the chance of getting an 11 plus the chance of getting a 12. that will give you your chance of scoring high enough to get away when i roll a 1 for Consolidation.

that chance will apply in 1/6 of all cases (since there are 6 different and equally likely consolidation distances), so divide it by 6.

then repeat for all the consolidation distances (inc. dividing the chance by 6) and add them together.

isnt that right?

cheers

~ Tim

yeah.. thats true.. so get that number and stick it over 216
Anyone have that picture that lists results of 2d6 for easy counting, in case tim didn't keep that number?
15,10,6,3,1
3rd edit so is 35 about right?-- if so thats 16.203703703703703703703703703704% chance of escaping

killmaimburn wrote:if so thats 16.203703703703703703703703703704%

your 16.2% chance of getting away + my 83.8% chance of not getting away = 100%, so that looks right.

can someone else check our maths?

cheers!

~ Tim

Sorry, earlier I messed up my numbers. Since measurement isn't an exact science (g) I always assume if someone is 6" away, they are really 6.01" and by golly I just can't reach them.

One way I look at dice probability that makes it easier for me to quickly figure is I set up a square

.1.2.3.4.5.6
.2.x.x.x.x.x
.3.x.x.x.x.x
.4.x.x.x.x.x
.5.x.x.x.x.x
.6.x.x.x.x.x

I plug one die in on the axis, and the other on the vertical, then I can rapidly count how many squares out of 36 give the result I want. When the consolidate roll is 1, then for all the rolls where the minimum requirement is 8, so you get 6,2 5,3 4,4 3,5 2,6 and everything outside that diagonal line that runs from 6,2 to 2,6, or 15 events out of 36 give you a chance of getting away.

There are more elegant functions than this, but my mind is capable of remembering this one. And I still mess it up don't I?

Gymbol wrote:Since measurement isn't an exact science (g) I always assume if someone is 6" away, they are really 6.01" and by golly I just can't reach them.

ahem:

LordMalekTheRedKnight wrote:for the sake of argument, lets make some assumptions:
- we will use theoretical distances between models to determine whether Regrouping is allowed (we wont worry about inacuracies in measurements etc, for example, a 7" Fall Back and a 1" Consolidate = no Regrouping, since you are within 6")

besides, if you move 7" away from me and i chase after you 1", how can you claim you have enough movement to get more than 6" from me, ruleswise? (inaccurate measurements dont change the math)

just like if a mission says you must be more than 18" away from me - you cant move 12" and assault 6" in the first turn, no matter what the tape measure says.

Gymbol wrote:When the consolidate roll is 1, then for all the rolls where the minimum requirement is 8, so you get 6,2 5,3 4,4 3,5 2,6 and everything outside that diagonal line that runs from 6,2 to 2,6, or 15 events out of 36 give you a chance of getting away. ... And I still mess it up don't I?

actually, 15/36 = 41.7 chance of getting away when the winner Consolidates 1", which matches with my 58.3% of them not getting away (adds up to 100%). so that looks right IMO.

just need to repeat for all the other possible Consolidation distances now.

cheers!

~ Tim

Man! You're harshing my mellow. I NEVER read past the 3rd assumption! It's too difficult for my attention deficiency.

NEWay, the (CORRECTED) numbers from my cludge are:
(15/36 + 10/36 + 6/36 + 3/26 + 1/36 + 0/36)/6
(35/36)/6

to which I get 16.2% for getting away, which matches your number 84% for getting caught.

====

Want to see a real head buster? figure the likelyhood of a winning toss for all the dice configurations in a Risk combat.

lol u geeks - get a life!!

obviously being a house husband affords u guys far too much time... are you one of those too Gymbol ?

Nah.
I foreclose on other people's houses. You guys that really irritate me need to be glad you live in England.

By the way, does anyone know what the average distance traveled through cover for Monstrous Creatures is? Compared to the normal 2d6 troopers?