A Rush Calculator

[VoiceOfUnreason]

Edit: Oops, I get it now; you'd look for the odds that one of your first two axemen win, but that the other two fail. So, you would have to look at the odds that:

1. both of the first two axemen win
2. both of the first two axemen lose
3. the third axemen loses

Since your first two axemen will be fighting different archers, you'd look at the odds of winning, times two. One is the inverse of the other. Ok, got that far. What about the odds of the third axeman? Man, that seems like a pain to figure out, am I right? Then again, you must've already done that to make this calculator

Close - you've got the right idea in your head, but your vocabulary is a little bit off.

If I want the odds that the first two axemen win, then I take the probability that one axe kills an archer X(1) and square it - so the answer is X(1) * X(1). You should see that relationship in the first two rows of every table.

The odds that a single axeman loses is the complement of the odds that he wins. !X(1), if you like, which is 1 - X(1). So if I want the odds that both of the first two axes lose, I can take advantage of the fact that we know both axes fight a healthy archer, and the probability is
!X(1) * !X(1)
= ( 1 - X(1) ) * (1 - X(1))
= ...

Now, if the first two axes die, can we predict the odds that the third will face? Yes - given the information in the spreadsheet; you just have to figure out how likely it is that the stronger of the surviving archers has 100, 73, 66 etc hit points remaining. Tedious, but not difficult.


Oddly enough, it's NOT something I actually solved along the way though. Given that the case I was interested in was "kill ALL the archers", I didn't have to look at cases where I didn't have enough axes. That allows me to take a short cut.

Essentially, because I'm going for a kill in each case, I can pretend that I'm fighting the archers in order. What are the odds of killing 2 with 3: P(2,3)?

A kills #1, B kills #2, C naps. That's X(1) * X(1)
A kills #1, B dies, C kills #2. That's X(1) * X(2)
A dies, B kills #2, C kills #1. Thats ? * X(1) * ?? - but multiplication commutes, so we can write that as X(1) * ? * ??, and it's clear that we have X(1) * X(2) again. To make it clearer that this isn't the same case as above, I order the terms to match the archers. X(2) * X(1)

So you see, I can get the answer to all of the successful outcomes by computing X(n) -- it turns out that X(8) was as high as I needed to go for these cases -- and then jumbling things around.

In other words, I can calculate the odds that two axes out of four survive against two archers without needing the result that one axe survives out of three against two archers.

 

[coanda]

I've been meaning to get around to installing Excel, but don't feel like doing that now just so I can check this myself. Any chance of getting a comparison look at just C1 vs. C1 and CR1? The barracks discount for AGG leaders means I can't imagine rushing without a barracks, but it would be nice to have an idea of how many hammers AGG saves in a rush.

 

[VoiceOfUnreason]

Any chance of getting a comparison look at just C1 vs. C1 and CR1?

You over looked it.

Which is to say, it never makes sense to call out City Raider by itself - it's always precisely equivalent to the corresponding attack without city raider against a target with 20% less defense. 95% and (115% - 20%) give precisely the same results.

 

[VoiceOfUnreason]

Promoted Chariots

I realized a short time back that I hadn't provided any numbers for promoted chariots, without which it's difficult to argue the utility of constructing a barracks.

The good news is that Flanking doesn't actually change the combat odds, just the survival odds. So you can use the previous calculation to determine your odds of success - you only need to revise your estimates of how many chariots survive.

When we consider combat promoted Chariots, I get a bit of a surprise - it looks like the barracks pays for itself when there are three or more more archers defending, and with two archers defending it's too close to call.

Remember, the calculator is designed for Archers, not Spears.

Combat Chariots vs Archers at 115% Defense.

           1       2       3       4       5       6
 1        7.87%
 2       66.50%   0.62%
 3       93.20%   9.84%   0.05%
 4       [color=blue][b]98.97%[/b][/color]  48.43%   1.14%   0.00%
 5       99.86%  80.65%   9.75%   0.12%   0.00%
 6       99.98%  94.67%  37.40%   1.45%   0.01%
 7      100.00%  [color=blue][b]98.82%[/b][/color]  68.24%   8.96%   0.18%   0.00%
 8      100.00%  99.78%  87.70%  29.97%   1.58%   0.02%
 9      100.00%  99.96%  [color=blue][b]96.17%[/b][/color]  57.47%   8.01%   0.24%
10      100.00%  99.99%  99.00%  79.45%  24.57%   1.61%
11      100.00% 100.00%  99.77%  91.87%  48.48%   7.06%
12      100.00% 100.00%  99.95%  [color=blue][b]97.29%[/b][/color]  70.97%  20.45%
13      100.00% 100.00%  99.99%  99.21%  86.33%  41.05%
14      100.00% 100.00% 100.00%  99.80%  94.51%  62.84%
15      100.00% 100.00% 100.00%  99.95%  [color=blue][b]98.08% [/b][/color] 80.03%
16      100.00% 100.00% 100.00%  99.99%  99.41%  90.74%
17      100.00% 100.00% 100.00% 100.00%  99.83%  [color=blue][b]96.24%[/b][/color]
18      100.00% 100.00% 100.00% 100.00%  99.96%  98.64%
19      100.00% 100.00% 100.00% 100.00%  99.99%  99.56%
20      100.00% 100.00% 100.00% 100.00% 100.00%  99.87%