# Frood AACalc Dicey / Sim / Odds Calculator: Updates and Opinions

• Hello all. I’m starting this new thread as a central place to post updates on my dicey / AAR sim AACalc, aka Frood, found at http://frood.net/aacalc/

First order of business: I’ve added a new feature called “Att. abort threshold”. If you leave this alone, Frood will run as it always has, fighting a battle to the death. However, if you enter a percentage here, the attack will be aborted if the attackers unit count or punch drop below this percentage of the corresponding value for the defender.

Example: If you enter 100%, you’ll keep fighting as long as your force is stronger than the defenders. Suppose 10 Arm attack 8 Arm. The first round goes really badly, with the attacker scoring only one hit and the defender scoring 5. The attacker’s odds of winning have dropped from 88% to just 6%, with the defender likely to survive with 3 Arm or more. Faced with those odds, any sane player would cut their losses and end the attack rather than throw their Armor away. However, until now, Frood would happily keep throwing your precious tanks into the fire.

If you had entered 100%, the battle would end as soon as the odds shifted away from your favour.

When using Frood as an odds calculator, this will eliminate those results that would never occur because the attacker would call off the attack - you get to set your own threshold. Consider this: 20 Arm. v. 19 Arm

If fighting blindly to the death, the attacker has a 66% chance of coming out alive, with an average 3.5 tanks surviving overall - that one extra tank makes a surprising difference to the probability. The defender has a 32% chance of surviving, average 1.5 tanks left.

Now, if an abort threshold of 100% is added, the attacker survives 100% of the time, average 7.3 tanks left. Defender also more likely to survive, but the increase in probability is not as large: 46% survival, with 4.4 tanks left.

At 50 % threshold, the attacker keeps attacking with some disadvantage, with surprising results:
Attacker: 89%, 4.4 tanks
Defender: 33.1%, 1.8 tanks
The attackers results improve significantly from the no threshold result (66% to 89%, and 3.5 to 4.4 tanks left, while the defender’s survival rate does not improve.

At 75%:
Attacker: 96.7%, 5.2 tanks
Defender: 35.3%, 2.5 tanks
Interesting to note that defenders survival rate is almost unchanged, but surviving tanks increases noticeably. Attacker’s survival rate approaches 100%.

Again, at 100%, results were:
Attacker: 100%, 7.3 tanks
Defender: 46%, 4.4 tanks

And at 0% (default)
Attacker: 66%, 3.5 tanks
Defender: 32%, 1.5 tanks

I think this adds a new level of accuracy to AACalc as an odds calculator, because it takes into account that realistically, certain battles would get aborted, and you can specify your own “pain threshold” - how much are you willing to bleed before you decide to live to fight another day?

Also, it could accelerate the use of AACalc as a dicey - you can send the whole battle once, having decided ahead of time that it will be cut short if it gets to a certain point.

• cool idea. so if you went in 75% then you would keep fighting untill you had less than a 25% of succedding? if you do this i think you should have a 60%, because i ussally retreat when i have less than a 40% chance of winning. this sorta reminds me of gambling

• I put this in another thread, but I’ll repeat it here:

It would be nice if you could edit your dicey to handle classic as well.  Should be easy enough since you’re just deleting lines really.  Tanks go from defending at a 3 to a 2.  Infantry do not get boosted by artillery.  Artillery and Destroyers don’t exist.

If you don’t want too that’s fine too, since Classic seems to be dieing off.

Back to Revised:  I recommend putting text on the site (like you do for explaining why Battleships are first in OOL) explaining the 2nd AA Gun option.

Also, is there anyway you could put in a calculator to average the success of multiple attacks?

For instance, if Germany attacks W. Europe, S. Europe, Balkans and E. Europe and has the following chances of success:

77%, 48%, 65% and 90%

They then take those numbers, after determining them, and put them into another form and hit compute to learn they have:

22% Chance of Winning all of them
45% Chance of Winning 3 of them
69% Chance of Winning 2 of them
90% Chance of Winning 1 of them

(Best chances that is.)

• It would be nice if you could edit your dicey to handle classic as well.  Should be easy enough since you’re just deleting lines really.  Tanks go from defending at a 3 to a 2.  Infantry do not get boosted by artillery.  Artillery and Destroyers don’t exist.

all you have to do is to make the defneding tanks artillery and use damged battleships. if you have 5 defending tanks then you just 5 ipc to the ipc colum.

• Yea, that’s a method.

• cool idea. so if you went in 75% then you would keep fighting untill you had less than a 25% of succedding? if you do this i think you should have a 60%, because i ussally retreat when i have less than a 40% chance of winning. this sorta reminds me of gamblingÂ

No, the percentage is a percentage of either unit count of your opponent, or punch of the opponent, so eg. if you put in 75% and then you drop to having only 3 Arm while the defender has 4 Arm. Since you have 75% of the unit count of the defender, the battle gets aborted. The percentage is not a chance of winning, it it a ratio of the strengths of each side.

• I put this in another thread, but I’ll repeat it here:

It would be nice if you could edit your dicey to handle classic as well.Â  Should be easy enough since you’re just deleting lines really.Â  Tanks go from defending at a 3 to a 2.Â  Infantry do not get boosted by artillery.Â  Artillery and Destroyers don’t exist.

If you don’t want too that’s fine too, since Classic seems to be dieing off.

I’ve actually been thinking about adding a dropdown for differen variant rulesets, I just don’t know the differences, If someone who knows could explain them all to me it shouldn’t take me too long.

I could do Europe, Pacific, Classic - are there others? I REALLY don’t want to mess with subs.

Back to Revised:Â  I recommend putting text on the site (like you do for explaining why Battleships are first in OOL) explaining the 2nd AA Gun option.

There’s an explanation on the readme page, but honestly I think I should just drop that option. Who ever flies over 2 AA Guns? With ALL of their aircraft for a battle?

Also, is there anyway you could put in a calculator to average the success of multiple attacks?Â

For instance, if Germany attacks W. Europe, S. Europe, Balkans and E. Europe and has the following chances of success:

77%, 48%, 65% and 90%

They then take those numbers, after determining them, and put them into another form and hit compute to learn they have:

22% Chance of Winning all of them
45% Chance of Winning 3 of them
69% Chance of Winning 2 of them
90% Chance of Winning 1 of them

(Best chances that is.)

That’s a different app altogether, but it would be a simple one. I could make one on a subpage.

However, I think you’d have a higher than 90% chance of winning one. That’s the chance you have of just winning the one 90% odds battle, but if that fails there’s still some chance that you’ll win one of the other three.

• I don’t know the other flavors, just Classic, LHTR and Revised.

But here’s some of the differences between Revised and Classic, and I think I have them all, just don’t quote me:

1)  Armor defends at a 2, not a 3.
2)  No destroyers, thus submarine sneak shots always work when they hit
3)  No Artillery, so infantry always attack at a 1
4)  Battleships take 1 hit to sink. (optional rule to make them 2 hit BBs)
5)  Heavy Bombers do 3d6 damage on SBR
6)  Heavy Bombers get 3 attacks in combat
7)  Fighters cost 12, not 10
Aircraft Carriers cost 18 not 16.

I think that is all of the changes.

• Alright, now you can select which ruleset you want AACalc to use - Classic or Revised.

I don’t really know anything about LHTR, does it have different unit values?

• i think just price changes but i’m not sure.

• The only difference I can think of in LHTR over the OM rules relate to Heavy Bombers.

In LHTR, it is the better of 2 dice rolled instead of 2 dice added.

All of the other units stay the same.

Also, you may want to consider a “Consolidated Bombardment” check box option that will allow DST’s to fire a support shot of 3 in addition to Battleships during an amphib assault (like BB’s the casualties are taken before the defenders can return fire, they only fire once, and they cannot be taken as losses).

• Also your list of results is great, Dan.  However, could you also offer an option of numbers of units lost?

For isntance, if you attack with 2 infantry vs 1 infantry you could say:

Most likely outcome 1 Attacking Unit Lost, 1 Defending Unit Lost.

Etc.

That would be especially helpful in very large battles when you want to compare damage dealt in units to damage received. (For instance if Russia attacks iwth 30 infantry, 10 artillery, 5 armor and 2 fighters vs 40 infantry, 10 armor, 3 fighters and an AA gun, you might want to know how many units you destroyed in X number of rounds to determine if you can weaken Germany enough for England to finish her off.)

• Agreed, a 50% result highlight would be great.

A result entry that follows the various percentage breakdowns that shows the result that is exactly in the percetnage middle that says:
“Most Likely Results:  Attacker: X, Y, Z units left, Defender destroyed”

Would be great (and would be a great time saver for many of us)

• @ncscswitch:

The only difference I can think of in LHTR over the OM rules relate to Heavy Bombers.

In LHTR, it is the better of 2 dice rolled instead of 2 dice added.

All of the other units stay the same.

Hmm… that could take some work. No other units hit in that manner, so the logic of my dice rolling routine might have to be slightly disassembled. I have some ideas though. Also, how would this work for Low Luck? I wonder if simply having Heavy Bombers attack on a 5 would approximate the odds of scoring a hit on the better of two dice hitting on 4 or less?
@ncscswitch:

Also, you may want to consider a “Consolidated Bombardment” check box option that will allow DST’s to fire a support shot of 3 in addition to Battleships during an amphib assault (like BB’s the casualties are taken before the defenders can return fire, they only fire once, and they cannot be taken as losses).

No checkbox needed. At present you should be able to add Destroyers to a land battle just like Battleships and they take a shot in opening fire of the first round.

• Yep, I just checked, DST’s are able to bombard in the current format if they are entered in the battle sim

• Also your list of results is great, Dan.  However, could you also offer an option of numbers of units lost?

For isntance, if you attack with 2 infantry vs 1 infantry you could say:

Most likely outcome 1 Attacking Unit Lost, 1 Defending Unit Lost.

Etc.

That would be especially helpful in very large battles when you want to compare damage dealt in units to damage received. (For instance if Russia attacks iwth 30 infantry, 10 artillery, 5 armor and 2 fighters vs 40 infantry, 10 armor, 3 fighters and an AA gun, you might want to know how many units you destroyed in X number of rounds to determine if you can weaken Germany enough for England to finish her off.)

There’s a considerable difficulty in displaying most likely COMBINED results as you are suggesting, especially in a large battle such as you describe. Each side has about 50 units, and it is reasonable that each side might survive with as many as 25 units … wait - I was going to say that you then have a possibility of 25*25 total possible outcomes, but that’s not the case if you  fight to the death, because each of the set of 25 results has the other side with 0 units, not with any number from 0-25. So really that means only about 50 different possible results, and of course even many of those will be highly unlikely. With 50 results, the average likelihood of each would be 2%, but obviously a few would be much more likely and many would be below 1%.

However, the number of results is still compounded by the presence of the AA gun (or any battle with subs) because you could have the same number of units surviving with different amounts of air units left.

Sorry, I’m just thinking out loud, as it were. This has been a major shift in my thoughts about how the outcome can break down. I can see that this would be much more intuitive, to see the combined results, not just separate for each side, and now also that it might be doable.

• If you just highlight the 50% line, the exact percentage middle, that would be great

• Actually, I was thinking since you give the amount of money lost, it might be possible to just say:  If you attack with 9 Infantry you’ll probably kill 2 infantry and loose 1 infantry to return fire.

(LL would say 1.5 kills, rounded up to 2 hits; 0.67 kills, rounded up to 1 hits.)

Also, I noticed that if you hit a 1 round only 5000 attempt simulation (you attack for 1 round, but it computes 5000 attempts at the same round) it doesn’t give you even an average monetary loss.  Maybe I’m just blind.  /shrug.

Heard a complaint that it’s not emailing results anymore.  Tested a couple of tries to my own inbox, havn’t gotten results yet.  Maybe just a slow server?

• There’s a considerable difficulty in displaying most likely COMBINED results as you are suggesting, especially in a large battle such as you describe. Each side has about 50 units, and it is reasonable that each side might survive with as many as 25 units … wait - I was going to say that you then have a possibility of 25*25 total possible outcomes,

Haha!  I wrote an analytic calculator once that DID break down the values.  But it always crashed my browser whenever I used it for more than fifteen units because it had to do so many calculations!  Although I think I know a way to fix that nowadays.

It isn’t 25*25 total possible outcomes with a 50 on 50 battle.  Depending on attack or retreat, it’s clearly 2^100, even if the odds for either extreme are astronomically low.  25 * 25 is only 625 outcomes.  2^100 is 1,267,650,600,228,229,401,496,703,205,376 outcomes.

I have to wonder just what sort of “logic” your dice roller program uses . . . maybe you should stick the code on here and let us have a look-see.

Whadjoo use to make that webpage anyways?  Quark or somethin?  All that funny formatting in the HTML . . .

• BTW, confirmed that FROODs isn’t mailing results anymore.  Just did a few trials with both my comcast, yahoo, hotmail and gmail accounts listed individually and as multiple addresses.  been 10 hours, no results in my boxes yet.

• Well, FROOD’s sending emails again.  Just hit submit 14 times and got 14 submissions to both of my inboxes. (Not good for JSP, all of them were 12-18 hits, with 4 of them at 17 hits!)

• There’s a considerable difficulty in displaying most likely COMBINED results as you are suggesting, especially in a large battle such as you describe. Each side has about 50 units, and it is reasonable that each side might survive with as many as 25 units … wait - I was going to say that you then have a possibility of 25*25 total possible outcomes,

Haha!  I wrote an analytic calculator once that DID break down the values.  But it always crashed my browser whenever I used it for more than fifteen units because it had to do so many calculations!  Although I think I know a way to fix that nowadays.

It isn’t 25*25 total possible outcomes with a 50 on 50 battle.  Depending on attack or retreat, it’s clearly 2^100, even if the odds for either extreme are astronomically low.  25 * 25 is only 625 outcomes.  2^100 is 1,267,650,600,228,229,401,496,703,205,376 outcomes.

I have to wonder just what sort of “logic” your dice roller program uses . . . maybe you should stick the code on here and let us have a look-see.

Whadjoo use to make that webpage anyways?  Quark or somethin?  All that funny formatting in the HTML . . .

I have to say I don’t much care for your tone. It sounds like you’re slagging my math, my logic, and my HTML code. But because I’m the patient sort, I’ll respond politely, even if my flame finger is feeling itchy. I want this thread to be for improving the sim, not for flame wars.

In terms of “logic” that my dice roller uses: it rolls the results of a battle thousands of times and tracks how often each side survives with a different number of units. It is not an analytic calculator. It gets used about 10,000 times a month and only very occasionally do I get an e-mail from someone saying the results don’t seem right. That hasn’t happened in a while. So no, you don’t get to see my source code, at least not if you can’t ask nicely.

I think you might be stretching it with 2^100, and saying that this is “clearly” so just sounds pretentious. It sounds like anyone who can’t see that must be a cretin.

At least without retreats, there is a range of results of maximum 100 possible outcomes, where one or both players by definition will have 0 units surviving. Allowing for retreats probably increases this by a few orders of magnitude, but not to 2^100. The possible results are limited by the order of loss and other aspects of the game mechanics. In any case, since the sim works by actually rolling the results randomly many times over, I only care about the results that happen at least once every 10,000 battles, and I can limit the display to only show results that have a significant probability. No one needs to know about a possible outcome that only happens once in 2^100 or whatever, or even only 1 in 10,000.

As for the HTML source, I am not some quarkhead or frontpage newbie. It’s all hand-coded, and the “funny formatting” you refer to is called inline styles. Usually I control all the style with a separate stylesheet, but because the results also get e-mailed, I have to stick them in-line. Since the source is generated by a PHP script, inline styles are less of a disadvantage, because there is still a single point of control in the PHP script. Or if you mean the way the HTML itself is formatted, that’s because it is generated by a PHP script and indentation etc. is not an issue for me in the final page that is built, since I do my debugging at the PHP level.

If you weren’t being rude, sorry if I misunderstood. You have to be careful online

• Actually, I was thinking since you give the amount of money lost, it might be possible to just say:  If you attack with 9 Infantry you’ll probably kill 2 infantry and loose 1 infantry to return fire.

(LL would say 1.5 kills, rounded up to 2 hits; 0.67 kills, rounded up to 1 hits.)

Also, I noticed that if you hit a 1 round only 5000 attempt simulation (you attack for 1 round, but it computes 5000 attempts at the same round) it doesn’t give you even an average monetary loss.  Maybe I’m just blind.  /shrug.

Heard a complaint that it’s not emailing results anymore.  Tested a couple of tries to my own inbox, havn’t gotten results yet.  Maybe just a slow server?

Must have been a slow server - I didn’t fix anything.

Did you do the 5000x simulation with “No Luck” mode? Because it should show the averages just as normal.

Switch and Jennifer, are you suggesting just stating in one line what the most likely result for the attacker is, the most likely result for the defender, and the amount they survive with and lose in that case?

• It’s okay, Dan.  It was a very touchy battle that could have gone either way on round 1 and then suddenly we had no email confirmations!  Luckily I had the page still up to save time so I got a screenshot of it for confirmation, whew…

Yes, what I am asking for is:

Attacker attacked with X units
Attacker remains with Y units

Defender started with X units
Defender remains with Y units

Currently you show a bar graph of IPC value in attack and what’s left after the battle.  Instead of the IPC value (I think it’s IPC, maybe it’s punch, didn’t really look at it very hard) a graph for each unit and how many are left would be better, IMHO.  (Light gray for starting overlaid by dark grey for remaining would be fine.)

After all, from that, we can determine the cash lost. (Your program rounds to the nearest decimal anyway, and since you can’t have 0.8 IPCs, you have to round anyway.  And what if that’s 0.8 of 1 infantry?  that’s really 3 IPC since you either have it or you don’t, right?)

• Switch and Jennifer, are you suggesting just stating in one line what the most likely result for the attacker is, the most likely result for the defender, and the amount they survive with and lose in that case?

Just a seperate line as “Median Result” with the pecentage center result from the detailed breakdown of potential results.

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