Has anyone figured out hit probabilities?

[MarcusAurelius]

I'd like to create a table listing the probabilities of achieving X number of hits with Y attack dice in War at Sea. But beyond 3 dice, the calculations exceed my limited statistical abilities. Has anyone else figured out a way to do this?

Here's what I've got so far by simply counting hits manually (6 possible outcomes with 1 die, 36 with 2 dice, 216 with 3 dice).

1 ATTACK DIE
1+ hits 3/6 .500
2+ hits 1/6 .167

2 ATTACK DICE
1+ hits 27/36 .750
2+ hits 15/36 .417
3+ hits 5/36 .139
4+ hits 1/36 .028

3 ATTACK DICE
1+ hits 189/216 .875
2+ hits 135/216 .625
3+ hits 72/216 .333
4+ hits 28/216 .130
5+ hits 7/216 .032
6+ hits 1/216 .005

Ideally, the table would extend out to 18 attack dice (assuming that the Iowa has the highest attack value in the game).

[polar]

The 'average' number of 'hits' per die is 2/3.

To get a feel of how 'difficult' it is to hit a curten armor multiply the number of dies by 2/3. For example 12dice: 12*2/3=8. You get you AVERAGE result. Then just compere what need to get and the average (for example 10)

This is not binomial distrubution I know, but you can then take
12*2/3*1/3
and take the squar root. This is know the standar deviation. Add some to compensate for that the standar deviation is somewhat larger than in a normal binomial distrubution. But the result will be about 1 or maybe closer too 2 for all cases.

Then here is the clue: given that you can approximate it to a normal distrubution
2/3 of all results will be :
<average> +/- standar deviation.
Lets for simplicity say that standar deviation=2.

If you need 8, thats about 50/50 or somewhat higher.

If you need 10 hits to score. Following my example, that is 2 above the average
of 8 (or 1 standar deviation). So you got to be lucky, but is by far not impossible.

If you need 12 is about two standar-deviations (4) higher than the average so it starts to become very unlikely.

To acieve 14 you can simply forget!

Looking at the average is much simpler than looking at the probabilities.

[XAos]

Probabilities as Accumulative percentages;
copy & load as a CSV file...

,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1
0,100.00%,100.00%,100.00%,100.00%,100.00%,100.00%, 100.00%,100.00%,100.00%,100.00%,100.00%,100.00%,10 0.00%,100.00%,100.00%,100.00%,100.00%,100.00%
1,100.00%,100.00%,100.00%,100.00%,99.99%,99.99%,99 .98%,99.95%,99.90%,99.80%,99.61%,99.22%,98.44%,96. 88%,93.75%,87.50%,75.00%,50.00%
2,100.00%,99.99%,99.98%,99.97%,99.94%,99.88%,99.78 %,99.59%,99.25%,98.63%,97.53%,95.57%,92.19%,86.46% ,77.08%,62.50%,41.67%,16.67%
3,99.97%,99.94%,99.89%,99.81%,99.66%,99.41%,98.97% ,98.22%,96.97%,94.92%,91.62%,86.46%,78.65%,67.36%, 52.08%,33.33%,13.89%,
4,99.85%,99.74%,99.56%,99.25%,98.76%,97.95%,96.66% ,94.64%,91.55%,86.94%,80.28%,71.06%,58.97%,44.21%, 28.01%,12.96%,2.78%,
5,99.47%,99.14%,98.61%,97.78%,96.50%,94.57%,91.71% ,87.58%,81.80%,74.00%,63.94%,51.69%,37.85%,23.77%, 11.50%,3.24%,,
6,98.51%,97.69%,96.44%,94.62%,91.98%,88.27%,83.19% ,76.45%,67.85%,57.39%,45.40%,32.65%,20.41%,10.24%, 3.47%,0.46%,,
7,96.46%,94.74%,92.32%,88.97%,84.46%,78.55%,71.07% ,61.97%,51.44%,39.95%,28.32%,17.65%,9.08%,3.42%,0. 69%,,,
8,92.69%,89.66%,85.61%,80.37%,73.78%,65.77%,56.43% ,46.07%,35.23%,24.69%,15.36%,8.06%,3.27%,0.85%,0.0 8%,,,
9,86.67%,81.98%,76.12%,69.00%,60.65%,51.28%,41.24% ,31.11%,21.60%,13.42%,7.16%,3.07%,0.92%,0.14%,,,,
10,78.16%,71.78%,64.28%,55.77%,46.51%,36.92%,27.53 %,18.96%,11.77%,6.37%,2.84%,0.95%,0.20%,0.01%,,,,
11,67.44%,59.69%,51.16%,42.14%,33.05%,24.39%,16.68 %,10.36%,5.67%,2.61%,0.94%,0.23%,0.03%,,,,,
12,55.28%,46.83%,38.13%,29.59%,21.64%,14.72%,9.13% ,5.05%,2.39%,0.92%,0.26%,0.04%,0.00%,,,,,
13,42.80%,34.49%,26.50%,19.23%,13.01%,8.07%,4.50%, 2.18%,0.88%,0.27%,0.06%,0.01%,,,,,,
14,31.17%,23.74%,17.10%,11.52%,7.15%,4.01%,1.98%,0 .83%,0.28%,0.07%,0.01%,0.00%,,,,,,
15,21.27%,15.22%,10.22%,6.34%,3.58%,1.80%,0.78%,0. 28%,0.07%,0.01%,0.00%,,,,,,,
16,13.57%,9.07%,5.63%,3.20%,1.63%,0.72%,0.27%,0.08 %,0.02%,0.00%,0.00%,,,,,,,
17,8.07%,5.01%,2.86%,1.48%,0.67%,0.26%,0.08%,0.02% ,0.00%,0.00%,,,,,,,,
18,4.46%,2.56%,1.34%,0.62%,0.25%,0.08%,0.02%,0.00% ,0.00%,0.00%,,,,,,,,
19,2.29%,1.21%,0.57%,0.24%,0.08%,0.02%,0.00%,0.00% ,0.00%,,,,,,,,,
20,1.09%,0.52%,0.22%,0.08%,0.02%,0.01%,0.00%,0.00% ,0.00%,,,,,,,,,
21,0.48%,0.21%,0.08%,0.03%,0.01%,0.00%,0.00%,0.00% ,,,,,,,,,,
22,0.19%,0.08%,0.03%,0.01%,0.00%,0.00%,0.00%,0.00% ,,,,,,,,,,
23,0.07%,0.03%,0.01%,0.00%,0.00%,0.00%,0.00%,,,,,, ,,,,,
24,0.02%,0.01%,0.00%,0.00%,0.00%,0.00%,0.00%,,,,,, ,,,,,
25,0.01%,0.00%,0.00%,0.00%,0.00%,0.00%,,,,,,,,,,,,
26,0.00%,0.00%,0.00%,0.00%,0.00%,0.00%,,,,,,,,,,,,
27,0.00%,0.00%,0.00%,0.00%,0.00%,,,,,,,,,,,,,
28,0.00%,0.00%,0.00%,0.00%,0.00%,,,,,,,,,,,,,
29,0.00%,0.00%,0.00%,0.00%,,,,,,,,,,,,,,
30,0.00%,0.00%,0.00%,0.00%,,,,,,,,,,,,,,
31,0.00%,0.00%,0.00%,,,,,,,,,,,,,,,
32,0.00%,0.00%,0.00%,,,,,,,,,,,,,,,
33,0.00%,0.00%,,,,,,,,,,,,,,,,
34,0.00%,0.00%,,,,,,,,,,,,,,,,
35,0.00%,,,,,,,,,,,,,,,,,
36,0.00%,,,,,,,,,,,,,,,,,

[MarcusAurelius]

XAos,

Many, many, many thanks. That's exactly what I was looking for.

I plan on reformatting your data into a simple hit probabilities table for quick reference. Having seen what others on the boards have done with AAM stat cards, I'm sure someone else will be able to create a more interesting layout in keeping with War at Sea style. But I'll post it anyway when I've got it ready as a start.

[MarcusAurelius]

I've created a simple attack probabilities table in Word, but apparently the file is too large to attach. I haven't had any more luck converting this to a .pdf that's small enough, either. Hmm...

I'm thinking about making a laminated, two-sided reference card — ideally the same dimensions as an AAM stat card. Have to see if legibility holds up at that size.

Perhaps WotC would consider producing something like this as a player aid.