Battling the Woodland Alliance - Should you? - Can you?

[Thimple ThighMan]

*** Feel free to skip the TLDR, done that, worn the T-shirt. :) ***

These are some observations I made after playing against the Woodland Alliance (WA) recently. Why are they apparently so difficult to get rid of when they establish bases etc. So, I decided to try and quantify things a bit, and hopefully this helps someone else too.

But, before discussing that, let's discuss battling in general where the attacker gets the high roll, and before even doing that, let's establish some basic understanding of probability. It gets more interesting later, I promise. :)

Probability is expressed as either a figure between 0 and 1, or as a percentage chance. I'll use percent chance here, mostly. To convert probability to percent chance, just multiply by 100. Divide percent chance by 100 to get back to probability again.

A probability of 0 means the event is impossible i.e. Can not happen, whereas a probability of 1, means the event is certain and definitely will happen. All other probabilities fall somewhere in-between.

Personally, I think 'probability' is a misnomer. In English, it implies 'likely' to happen. Think of it as 'possibility' instead. A probability of 0.001 doesn't sound very 'probable' does it? ;)

Some Civ players who seem to think that a 90% chance to hit means it will hit, come unstuck when they miss three times in a row, complaining about the game being broken. :)

This is because, a 90% chance to hit means a 10% chance not to hit. When you expand this to say a 900,000 out of 1,000,000 chance to hit - which is still exactly the same 90% chance - the mental illustration should make it abundantly clear that there are 100,000 possibilities out of that 1 million to miss. Does it still look so 'certain'?

This last point is useful for some calculations of probability which would be difficult otherwise. You can always say, that if a probability of an event occuring is 'x', then the probability of it NOT occurring is simply 1 - x (1 minus x). 25% chance to occur is same as (100 - 25)% = 75% of it NOT occurring.

Take the Civ example above. To score at least one hit in 3 attempts, can be expressed as 1 - (Try 1 doesn't hit AND Try 2 also doesn't AND try 3 doesn't either). So, we get 1-(0.1 x 0.1 x 0.1) = 1 - .001 = .999 or 99.99%. Pretty good odds eh. But remember, the 2nd roll has no 'memory' of the first, the 3rd has no 'memory' of the first two. It's a 10% chance EACH time you roll NOT to hit. The player ALWAYS remembers the bad beats though, and forgets the other 100's of times it 'worked as expected'. :)

That said, it's important to bear in mind when dealing with probabilities, that they only apply in the 'long term' i.e. after hundreds, thousands, or millions of outcomes. They are not predictors of when an event will occur, just their likelihood of occurring if the event was repeated many, many times.

For example, it's a probability of 1 that we will die. We just don't know when. If you toss a coin it will definitely be either a head or a tail, and the two possible outcomes are equally likely (0.5 or 50%), and the two possible outcomes add up to certainty i.e. 1. We just don't know 'when' a head or tail is going to occur. If you toss a coin a thousand times, you would expect roughly 500 occurences of each. Each run would be different and it's not certain to be 'exactly' 500 of each by any means, but extremely unlikely to be significantly divergent e.g. 800 heads vs 200 tails.

So, ROOT! We have two dice. In the physical game, each die is 12 sided and has the numbers 0-3, 3 times on it. So, each number has a 3 in 12 chance of occurring. 3 in 12 is the same as 1 in 4. The digital versions just produce a pseudo random digit from 0-3 twice.

So, fundamentally, we have 16 possible 'outcomes' after 'rolling the two dice'.

0,0
0,1
1,0
0,2
2,0
0,3
3,0
1,1
1,2
2,1
1,3
3,1
2,2
2,3
3,2
3,3

All of these outcomes are equally likely, which is a 1 in 16 chance for each, 1/16 = a probability of 0.0625 = 6.25%.

Note, however, that ALL rolls that are NOT pairs (0,0 - 1,1 - 2,2 - 3,3) such as for examples 0,1 and 1,0, or 2,3 and 3,2 are regarded by the game as the same outcome. The attacker just takes the highest roll of the two numbers. So, all these non-pair rolls have a 2/16 chance of occurring = 0.125 or 12.5%.

In all, this will give us - as the game sees it - 10 unique roll possibilities (high number first):

*** Table 1 ***
Roll - Probability
3,3 1/16
3,2 2/16
3,1 2/16
3,0 2/16
2,2 1/16
2,1 2/16
2,0 2/16
1,1 1/16
1,0 2/16
0,0 1/16

We can now use the above table to calculate 'some' probabilities. We'll assume, base game, 3 warriors battling and taking the high rolled dice on the left hand side. We'll also disregard any abilities (e.g Eyrie's Commander for +1 hits), and cards such as Ambushes, Armourers, Sappers etc. Just stick to generalities for now.

You can see, that there's a (1+2+2+2)/16 chance = 7/16 = 43.75% to inflict 3 hits on the defender!

We can also see, that to inflict at least 2 hits, there's a 12/16 = 75% chance!

To inflict at least 1 hit, there's a 15/16 = 93.75% chance!

There's only a 1/16 = 6.25% chance to score no hits at all.

In other words, we can say, that all rolls except 0,0 inflict at least 1 hit on the defender.

What else can we say? There are 3 ways to inflict hits without taking damage AT ALL i.e 3,0 2,0 1,0 = 6/16 = 37.5% chance.

*** Now then, the Woodland Alliance. Oh boy. :)

Let's re-arrange the table from worst to 'best' (for the attacker). Remember, the WA take the high roll and the attacker takes the low roll. (In other words, the WA always takes the high roll). We also disregard 'defenceless' battles of course. In that case...go for it. :)

*** Table 2 ***
Roll - Probability
0,3 2/16
0,2 2/16
0,1 2/16
0,0 1/16
1,3 2/16
1,2 2/16
1,1 1/16
2,2 1/16
2,1 2/16
3,3 1/16

What can we see here?:

There's a (2+2+2+1)/16 chance = 7/16 = 43.75% to score no hits whatsoever against the WA! In addition to that particular line (throwing a roll involving a 0), there's a 6/16 chance = 37.5% chance of taking at least one hit yourself!

We can also see, that to score x hits against the WA, YOU will take at least x hits yourself (depending on the number of defending warriors of course)! Ouch

So, when attacking 3 WA warriors with 3 of your own, your 'best' outcome is 3,3 which wipes you out in the process, and you only have a 1/16 chance 6.25% to do so!

We can also see, there is NO roll where you get out 'Scot free' and take no hits, other than 0,0 which is a redundant roll!

To inflict at least 1 hit on the WA is now only a 9/16 = 56.25% chance. Much lower than the 93.75% chance when you take the high roll, AND notwithstanding hits you take yourself.


In summary, this explains why even battling one WA warrior can be such a PITA.

For example, just one warrior with a sympathy token and base on the same clearing. There's only ONE roll (with a 6.25% chance of getting it) to achieve this i.e. 3,3, and you take a hit too.

A 2,2 or 2,3 roll will most likely not get the base removed. (Defender chooses the token / building to remove), and you take a hit too.

In addition to all that, if you now take into account possible ambushes, and mitigating cards that allow the defender to disregard hits or deal you extra hits, you have a bit of a nightmare on your hands.

I found that (especially with Marquise), battling the WA loses you so much momentum and is (as the intuitive 'feeling' that something is 'off' tries to tell you and hence this post) very unsatisfying.

Hope this is of some use to someone.

[MarleyTown]

Nice calculations.

Yeah Cats should very rarely battle the WA. The main exception to this is removing 1-2 undefended sympathy tokens in the early game to prevent them getting a base for the first few turns.

Birds, ideally with Commander, or crafting the relevant partisan card, or using false orders, or Lizard acolytes are all very good options in helping take down a WA base.

[Sakarov]

Well, yeah it's rarely a good idea to straight up attack WA warriors. Duh. Fortunately there are many other ways to slow them down.

Originally posted by MarleyTown:

Birds, ideally with Commander, or crafting the relevant partisan card, or using false orders, or Lizard acolytes are all very good options in helping take down a WA base.

Also any vagabond with a crossbow, an allied vagabond, scoundrel's torch, brutal tactics, favors...

You can go to their base and build next to it (as cats or birds).

You can (and really should whenever possible) put martial law around their territory.

And of course you can destroy undefended sympathy tokens if you're scared of a revolt, want the free point or just to annoy them.