New odds calc for AAAE

[Uberlager]

I think the sim may be correct, but the reason it is is not intuitive.  In order to capture the territory, you must have one of the 4 land units survive.  These units are the first to go without the “Must Take Territory” option checked, therefore the probability of capturing the territory is quite low.  Click on the “Details” and you will see the histogram only gives you those 4 units’ survival probabilities.  Once you lose those 4 units, the sim must consider the battle over.

Now with the “Must Take Territory” box checked, it will allow the battle go on longer due to retention of at least 1 land unit, having taken air units as casualties.

[Jennifer]

I think Uber might be on to something.

note:  Your armor and fighters attack at the same strength, so theoretically, your odds of success should not be affected at all if you lose fighters before armor or armor before fighters.  Thus, the only affect on your win/loss would be the loss of the bomber before the armor and that would happen just before the last armored unit dies.  Therefore, that should also have a minimal impact (on a larger battle) than if it died after the armor. (If we’re talking 3-5 rounds with only the last round changing to 1@3 instead of 1@4 you’d imagine it would have next to no serious impact.)

[Unknown Soldier]

No, something is definitely not right.

Run the battle that DY gave in his post, making sure to select “Must take territory” under “Set unit loss order” on the attacker side. You should get a 65.439% chance of attacker victory. Looking at the battle itself, anyone with a decent amount of A&A experience should realize right away that this has to be wrong.

Now, click on “Details”. Then make sure the “Exactly” button is pressed.

There are a few problems here. First, notice that there is no probability listed for 0 units surviving on the attacking side, even though the main interface of the program says the defender wins over a third of the time. How can the defender win if the attacker has units remaining (including land units) every time?

Second, look at the column for 3 units remaining. The probability is listed as 67.51%, higher than the combined probability of the attacker winning! This obviously does not add up.

Finally, if you look at the distribution for surviving defenders, you’ll see that you get an approximately normal looking distribution for 2-8 units, but for 0 units, it spikes to 65.62%. The probability of 1 unit remaining is not even listed.

So something is definitely not right here. I think its only a bug with the “Must take territory” setting thouigh, as it appears to run fine when this isn’t selected.

[atarihuana]

the subs screw up too

4 ftr attacking any small fleet like ac 2 ftr. add 2 subs and it shouldnt change but it does significantly

[Unknown Soldier]

@atarihuana:

the subs screw up too

4 ftr attacking any small fleet like ac 2 ftr. add 2 subs and it shouldnt change but it does significantly

Actually, this is not a screw up. What’s happening is that the fighters cannot kill the subs, so the attacker can only “draw”, since there will be surviving defenders every time when the subs are added.

So while 4 fighters vs. 1 CV, 2 fighters is ~73% for the attacker to win and ~7% to draw, if you add 1 or more subs to the defender side you’ll instead get 0% win for the attacker and 73% draw.

I made a post about this earlier in the thread in response to someone else complaining about the sub battles. I guess you missed it.  :-P

[Uberlager]

@Unknown:

There are a few problems here. First, notice that there is no probability listed for 0 units surviving on the attacking side, even though the main interface of the program says the defender wins over a third of the time. How can the defender win if the attacker has units remaining (including land units) every time?

Second, look at the column for 3 units remaining. The probability is listed as 67.51%, higher than the combined probability of the attacker winning! This obviously does not add up.

Finally, if you look at the distribution for surviving defenders, you’ll see that you get an approximately normal looking distribution for 2-8 units, but for 0 units, it spikes to 65.62%. The probability of 1 unit remaining is not even listed.

So something is definitely not right here. I think its only a bug with the “Must take territory” setting thouigh, as it appears to run fine when this isn’t selected.

I agree that, in your first two points, there would appear to be an error.  Your last point, though, is affected by the “Details Cutoff” slider, whatever that does.  Move the slider to 0.0% and look at the details again.  It paints a more comprehensive picture of the possible battle outcomes.  For the defender, there are now probabilities for survival of 0 units to all 10 units.

The skewed distribution is correct, I believe.  I have seen this shape many times before when using the sim during previous games and in battles with several different unit types (when not using “Must Take Territory”).  The chance of 0 units surviving (losing the battle) coincides with the chance of victory for the attacker - with some small apparent error.  The number of units remaining if the defender wins the battle then takes a normal-looking distribution.  So you have to first separate winning and losing the battle, then think of how many units you have left.

[Uberlager]

Ah-ha!  The Details Cutoff merely allows you to remove probabilities that fall below what you select.  If, for example, you have the slider set to 1%, it will not display results that have a probability of occurring of < 1%

[Unknown Soldier]

I agree that, in your first two points, there would appear to be an error.  Your last point, though, is affected by the “Details Cutoff” slider, whatever that does.  Move the slider to 0.0% and look at the details again.

D’oh! I didn’t even notice that slider, thanks for the info. That would explain why some probabilities are not listed. As you say, though, there are still some errors.

The skewed distribution is correct, I believe.  I have seen this shape many times before when using the sim during previous games and in battles with several different unit types (when not using “Must Take Territory”).

I don’t think it is correct. Usually with these sims, the “meat of the curve” is clustered around the most likely result. A normal-ish looking distribution, in other words. In this case, the most likely result (at least the one this program says is the most likely) is 0 units remaining for the defender. So, we would expect the probabilities for various other results to cluster around this point. Obviously since the defender can’t have negative units, we only see the tail-end of the distribution, with the result for 0 units spiking up since it represents the “rest of the curve” crammed into one result.

However, looking at the actual distribution of results for surviving defenders, we see that the high point occurs in the 5-7% range around 5 units remaining, and actually declines for fewer units remaining. I think this is probably what the actual distribution should look like, but somehow the result for 0 units is messed up. It would be correct I think if the results for 0 units remaining were fixed so that it’s less than the result for 1 unit remaining, and the probabilities were all increased proportionally so that they equal 100% again.

The chance of 0 units surviving (losing the battle) coincides with the chance of victory for the attacker - with some small apparent error.

If I’m not mistaken, the difference arises because the chance of 0 units surviving for the defender equals the sum of victory for the attacker and and the chance of a draw (both sides destroyed). If you add up those 2 numbers it should be the same as the probability of the defender having 0 units remaining.

The number of units remaining if the defender wins the battle then takes a normal-looking distribution.  So you have to first separate winning and losing the battle, then think of how many units you have left.

Yes, this has to do with only getting the “tail-end” of the curve if you are favored to lose the battle, as I mentioned.

[Uberlager]

I have looked into the issue more, and I believe with relative certainty that it is correct (the defender stats that is).  Here’s my proof:

Let’s take a relatively easy scenario:
Attacker - 3 inf, 3 art, 3 tk
Defender - 8 inf, 1 art, 1 tk

With Detail Cutoff @ 1.0%, this is what you get:

Notice the odd shape similar to what we have been talking about.

Now go to this odds calc: http://www.dskelly.com/misc/aa/aasim.html
Type in the same number of units and run the sim.  The win/loss/draw percentages are the same, so these two methods agree in that regard.  Look at the average IPC loss (25).  Now calculate the average IPC loss from the results in the image.  You do that by multiplying the IPCs lost by the percentage chance of that happening.  So you end up with:
(6)(.0133) + (9)(.0346) + (12)(.0641) + …. etc.
The result is ~25.

I will reiterate that you need to look at the probability of 0 units remaining as not being part of the distribution.  It is merely the chance of losing the battle.  The chance of winning the battle is actually greater, but is distributed over the number of units you can expect to survive.  Therefore, each row will individually be less than the ‘0 units’ line.

[TimTheEnchanter]

That 60+ percent survival rate makes no sense whatsoever.  Something is very wrong.

I did a little experiment that should prove something isn’t quite right with the “must take territory” option.

I ran a test of the same units, but changed the order so the armor were killed last.  This predictably lowered the success rate from 13 to 12 percent and change because the armors (@3) are kept instead of the bom(@4).  Killing the armor last should fit any criteria of “must take territory”

I then turned on the flag for “must take territory” and reran it, and the the chances of success went up to over 15%.  If the armors were already dying last, what in the world would have changed to allow it to take the territory more often?  Then, to make it even worse, when I look at the details it says there is a 69% chance that I end with 1 unit (the arm + it gives me the AA), and no chance (even with the slider set to the lowest setting) that I end with 0 units.

[Unknown Soldier]

Uberlager, yes, that example is clearly correct. Not sure what your point is though, because the issue with the program is with the “Must take territory” button, which is not needed for that particular battle you just gave. I’m pretty sure that the prog works fine if you don’t use that button.

@Uberlager:

I will reiterate that you need to look at the probability of 0 units remaining as not being part of the distribution.  It is merely the chance of losing the battle.  The chance of winning the battle is actually greater, but is distributed over the number of units you can expect to survive.  Therefore, each row will individually be less than the ‘0 units’ line.

Yeah, I basically agree with this, I think I just worded my previous post poorly. So I’ll try again.  :-)

I understand that the 0 units result will often have a higher probability than each of the other individual rows. I’m saying in the particular battle DY gave, the 0 unit result should be much, much lower, since it’s at the extremity of the curve. It should not have a big spike because the probability of getting 9 or more hits as the attacker (i.e. 0 defending units left) is very low.

What I was trying to point out though, is that 0 unit result is not “merely” the chance of losing the battle and should be ignored as part of the distribution. It has meaning if you realize that the probability distribution for the surviving defenders is really just a reflection of the probability distribution of the number of hits the attacker rolls.

Specifically, the 0 units remaining result is the chance that the opposing side rolls a number of hits equal to or greater than the number of units you have. So, if the attacker rolls 10 hits and you only have 9 units, its counted under the 0 unit result (since you can’t have -1 units), just as if he had rolled only 9 hits. Thus, the 0 unit result is the sum of multiple probability events for the attacker, all of which have the same meaning in game terms: 0 units surviving. This is in contrast to the other results, which represent only one specific number of hits rolled.

That’s basically all I was getting at when I said the 0 units result was the rest of the distribution curve crammed into one category.

[DY]

Well other than the one bug, this sim appears to be a really good application  :roll:

[Dash_Riprock]

Uhh sorry I haven’t been back here in a while, I’ll look into that bug and try to fix whatever other bugs people have been mentioning and post an updated version whenever I get a chance.

[Unknown Soldier]

@Dash_Riprock:

Uhh sorry I haven’t been back here in a while, I’ll look into that bug and try to fix whatever other bugs people have been mentioning and post an updated version whenever I get a chance.

Hey, that’s awesome. Didn’t think we would hear from you again.  :-D

[Dash_Riprock]

That bug should be fixed now.  I also made it so you can now use any number of defending fighters in a naval battle, since as someone pointed out the calc could be used half way into a battle once the carriers are already sunk.

[Unknown Soldier]

Thanks, d/l’ing now.

[Merlin]

I was able to download it…. very nice!

[DakotaYoda]

@Adlertag:

only whimps use odds calculators  :wink:

real men gamble  8-)

Well said!

[Uberlager]

@Dash_Riprock:

That bug should be fixed now.  I also made it so you can now use any number of defending fighters in a naval battle, since as someone pointed out the calc could be used half way into a battle once the carriers are already sunk.

Sweet, thanks.  This is - by far - the best odds calc I’ve used.

[DY]

Thanks for the fix.

On the quality of the final product – I’m with Uberlagger  :-)