Handling probabilities - how to make the best of your dice

Discuss the way <b>you</b> play (strategy, etc., etc.)

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Khamul the Easterling
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Handling probabilities - how to make the best of your dice

Post by Khamul the Easterling » Mon Apr 14, 2008 8:25 pm

MECCG-Players often face situations in which proper assessment of probabilities is helpful. As a statistician, I have sometimes asked myself which of two (or more) options is more likely to occur. Due to the numerous situations possible in the game, general guidelines cannot be given, there are lots of further conditions to take into account. However, there are some widely-known situations which are interesting to have a closer look at - in terms of probability:

Thus, I'd like to start this new topic and shed some light on these topics. I plan to make regular contributions, let's see what becomes of my motivation... ;)



# 1: Assassin attacks

This is common : One of your characters is facing an attack from an assassin. How are the odds of defeating the attack / being killed?

Let's say, your wizard (untapped, 6/9) is attacked. You tap him to take the first strike, then being tapped you take the subsequent strikes.

Prob. of defeating (and getting 2 MP): 24.6%.
Prob. of getting killed: 14.7 %
(so it's 60.7 % your wizard survives without defeating the attack)

If you have an "Forewarned is Forearmed" at hand, your chances are:

Prob. of defeating: 72.2 %
Prob. of getting killed: 2.8 %


Btw, "Asssassin-slaying" Annalena is much more challenged: Her prob. of killing an assassin without any means is only 3.2 %

[edit: I've corrected a mistake in my calculations, see also below]
Last edited by Khamul the Easterling on Tue Apr 15, 2008 8:05 pm, edited 1 time in total.

Zarathustra
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Post by Zarathustra » Tue Apr 15, 2008 12:53 am

You seem to have left out the probability that you don't get wounded AND that you don't kill the assassin....

Wacho
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Post by Wacho » Tue Apr 15, 2008 1:32 am

The actual probabilities of this situation are:

Defeating the assassin -- 24.6%
Being wounded at least once -- 56.5%
Attack ineffectual -- 18.9%

These add to 100%

In addition, you have a 14.7% chance of dying, so the complete set of outcomes looks like this:

Assassin defeated -- 24.6%
Attack ineffectual -- 18.9%
Wizard wounded & survives -- 41.8%
Wizard dead -- 14.7%

With Forewarned is Forearmed:

Assassin defeated -- 72.2%
Attack ineffectual -- 11.1%
Wizard wounded & survives -- 13.9%
Wizard dies -- 2.8%

Bandobras Took
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Post by Bandobras Took » Tue Apr 15, 2008 1:39 pm

In my case, the probability of dying is much closer to 89%. :)

Thorsten the Traveller
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Post by Thorsten the Traveller » Tue Apr 15, 2008 10:21 pm

of course what you really need to know is, how much chance do you have to survive/defeat creature after the first attack, and how much after the second? Because you always have to face the first attack, so there is little element of choice, but you can perhaps cancel or tap for 2nd and 3rd...

and then make same calculations for my 5/7 Gloin &nbsp;:wink:

But, great initiative Chistoph, let me thank you on behalf of the mathematically challenged meccg players....
'Elen sila lumenn' omentielvo

Zarathustra
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Post by Zarathustra » Thu Apr 17, 2008 3:36 am

Assuming a tapped wizard who defeated the first attack, with 2 remaining assassin attacks, the probabilities are:

Defeat assassin: 34%
Ineffectual (remain tapped after assassin): 18%
Wounded by not dead: 37%
Dead: 11%

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Sly Southerner
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Post by Sly Southerner » Fri Apr 18, 2008 7:43 am

Personally I dont think the actual probabilities are that important. What is important is to maximise the number times your opponent has to roll the dice during the game and minimise the number that you have to. A 'freak' roll will often tip the game so the more rolls your opponent has to make the better. Likewise if you can minimise the number of rolls you have to make then you are unlikely to have such a "freak" roll.
So that's where that southerner is hiding...He looks more than half like a goblin.

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Ringbearer
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Post by Ringbearer » Fri Apr 18, 2008 7:59 am

Makes we wonder what the odds are for radagast to survive 4 assassins, kill 2 and not even be wounded....

I pulled it off once vs Mikko.
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Post by Jambo » Fri Apr 18, 2008 8:40 am

Mikko, must have left his "I win" cards at home that day. &nbsp;:)

I'd imagine the odds of that happening are staggeringly low however!
Visit the Optional Rules forum and try out the community accepted Unofficial Errata.

Zarathustra
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Post by Zarathustra » Sat Apr 19, 2008 1:36 pm

less than 1 percent....

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Konrad Klar
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Post by Konrad Klar » Sat Apr 19, 2008 10:36 pm

CRF and Lidless Eye wrote:Excess strikes applied as -1 modifiers do not have to have their body defeated.
And this lead to some strange consequences.

1st example:
Elladan (5/8) and Elrohir (5/8) vs Scorba (3x 12/8). Prowess and body of characters and creature are normal.
Probability of defeating of prowess of Scorba is 5./12 * 5/18 = 25/216
and now two rolls on Scorba's body 5/18 x 5/18 = 25/324
Total probability defeating of attack = 625/69984 = 0,0089306127114769090077732053040695

2nd example:
Elladan (5/8) vs Scorba (3x 12/8). Prowess and body of character and creature are normal.
Probability defeating of prowess of Scorba is 1/6
and one roll on body 5/18.
Total probability defeating of attack 5/108 = 0,046296296296296296296296296296296

that is 5,184 times higher than in 1st example.

Third example:
Elladan (5/8), Elrohir (5/8) and Gimli (5/8) vs Scorba (3x 12/8). Prowess and body of characters and creature are normal.

Probability of defeating of prowess of Scorba is 5/12 * 5/12 * 5/12 = 125/1728
and three rolls on body 5/18^3 = 125/5832 = 15625/2985984 = 0,0015504535957425189249606259208454.

This means that in many cases small companies have significantly bigger chance of defeating creature than big ones.
We will not speak of such things even in the morning of the Shire.

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Ringbearer
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Post by Ringbearer » Sun Apr 20, 2008 7:51 am

Which is perfectly logical with body checks. The more body checks you make, the more chance you fail one.
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Konrad Klar
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Post by Konrad Klar » Sun Apr 20, 2008 9:48 am

...and which is not achieved by boosting of creature (increasing number of strikes), but by attacking more numerous (theoretically stronger) companies.
All thanks: "Excess strikes applied as -1 modifiers do not have to have their body defeated.".

I'm not surprised by logic of probabilistic itself.
We will not speak of such things even in the morning of the Shire.

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Post by Wacho » Sun Apr 20, 2008 12:12 pm

Konrad Klar wrote:1st example:
Elladan (5/8) and Elrohir (5/8) vs Scorba (3x 12/8). Prowess and body of characters and creature are normal.
Probability of defeating of prowess of Scorba is 5./12 * 5/18 = 25/216
and now two rolls on Scorba's body 5/18 x 5/18 = 25/324
Total probability defeating of attack = 625/69984 = 0,0089306127114769090077732053040695
You made an minor error in this, probably a typo. &nbsp;The probability of defeating the prowess should be 5/12*5/12 = 25/144. &nbsp;This leads to a total probability of 625/46656 = .0134

It is interesting that small companies normally have a better chance at defeating bodied attacks. &nbsp;Maybe the creatures get overconfident facing only one guy :)

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Konrad Klar
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Post by Konrad Klar » Sun Apr 20, 2008 1:08 pm

Wacho wrote:The probability of defeating the prowess should be...
Take into account fact that prowess of one of characters is modified by -1 due to excess strike allocated to him. So he makes roll 4 vs 12, hence probability of defeating the prowess of this strike is 5/18.

EDIT:
Thematical explanation of this paradox may be that characters are bashing against other companions during combat. &nbsp;:wink:
We will not speak of such things even in the morning of the Shire.

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