VANN FORMULAS

Is anybody aware why the aatoolkit is down?

I’m getting the following message:

This site can’t be reached.
www.aatoolkit.com’s server IP address could not be found.

Building analytic tools for Axis and Allies type games, and a game similar to Axis and Allies.

I’m building in what I want. But I want to hear what other players want too.

Particularly, I have three questions.

How important is the setting of the game to you? How would you feel about playing a game themed, not around armed combat, but cute animals doing pizza delivery, supposing the gameplay were identical?

Name some specific data visualizations you’d like to see, including specific examples of actual usage and/or screenshot so I can look them up. E.g. David Skelly’s tool has a visualization of expected unit count surviving over multiple rounds of combat.

How to handle asynchronous play. (more below)

If this sounds familiar, I wrote parts of it up on different forums at different times.

This is a pretty specific case, and I know a lot of players don’t play like this. But nevertheless, just bear with me.

Suppose Japan hits the Hawaiian Islands fleet; Japan has up to submarine, cruiser, two fighters, bomber; US has submarine, destroyer, carrier, one fighter.

Scenario A: Suppose Japan wants to play it risky and only sends 1 sub 2 fighters. Then maybe the US wants to have the US submarine fight.

Scenario B: Suppose Japan hits with the kitchen sink. Then maybe the US wants to have the US submarine submerge.

1942 Online handles this with “defensive profiles”, but defending players can’t switch up their actions depending on what the attacker does. And not to get into the use case too deeply, but digging a bit deeper shows defender may want to change decisions depending on composition of attacking force (not just the count of units), dice roll results from earlier rounds, the outcomes of battles in different territories/seazones conducted earlier (and not just loss/win, but again, the composition.

So this is where I sort of shrugged and said, well, 1942 Online’s implementation, sort of is where it is. It’s not the same as the boardgame, but that’s just how it is.

But suppose it were “fixed”? The way it’s handled in TripleA last I heard, you sort of agree on OOL and conditions before the game, and if someone does a bad OOL for the defender, then the game gets rewound and the “correct” decision made, which can get messy (lot of complications I won’t get into but been there a few times.). Or in TripleA, if a game gets to that point where you know there’s sort of a weird OOL coming up, the upcoming defender could send sealed instructions, or unsealed directions, or even the game could be paused until both players could go live. You get the idea. It’s messy.

So I wrote elsewhere, you CAN make a really detailed UI where the defender can pre-specify exhaustive conditions, but that’s super cumbersome.

The idea I’m working with right now is, instead of having a static “defensive profile” like 1942 Online, instead have an AI that makes decisions round to round, with some additional input decisions by defender.

So for example, if UK hit a German fleet in the Baltic, the AI might by default land a fighter on Berlin. But a human player COULD specify that the fighter land on Norway or Finland instead (because maybe US / USSR didn’t have a followthrough to destroy the German fighter cheaply), and the German fighter range has better to some targets. Etc.

@Panther

I came up with this before I used TripleA. TripleA is still vastly superior, but I wanted to share this anyway. It’s still somewhat useful for playing house rules that you cannot otherwise edit easily on TripleA.

As I said, you send the emails to yourself to keep track of it.

As for why do I not do Google Docs instead, I just didn’t do it and didn’t think of it.

I only used the Notes app on the Ipad, which doesn’t really work, and emails.

So perhaps Microsoft Word might be better.

It is very complicated. I do not recommend playing Global 1940 using this. Anything less complicated is manageable, but best to stick with the more simple side.

Thanks for moving it.

Hi guys,

Do you want to play Axis and Allies online?
The game was already heavily scripted.
However, the new update 4.0.0 to the scripted Axis & Allies 1940 brings big new improvements!
New key features:

Try it out!
https://steamcommunity.com/sharedfiles/filedetails/?id=2290267328

Wait. Vann made a mistake? What?

@Imperious:

The globe rejoices in Larry- Marx since it is the only formula that offers the true combat picture. VANN shoes was a failure. Nobody even knows about enigma except during WW2. Even Trump tweets about Larry-Marx…

No, no, no…
:-) :cry: :cry: :cry: :-D

The Stack formula coming from Kreuzfeld, Ozymandiac and Vann has been modified to take accounts of 2 hits units.

@Baron:

@Kreuzfeld:

@Ozymandiac:

@Kreuzfeld:

Ususally, subs is the most costeffective unit to buy for defence.

I’m not following this. Suppose I have 48 IPCs and want to buy a defensive fleet.
-I buy 8 subs, receive metapower=881=64.
-I buy 6 destroyers, receive metapower=662=72.

Aren’t destroyers the units with a higher metapower and as such better as defensive units?

I think I also said that it was dependent on what other ships you had available. Subs isn’t best if you only have subs. I would expect the optimal ratio for subs vs other ships would be between 40 and 60 % of your fleet.

if you have no fleet, then you would be correct.

lets ssume you have 2 CV + 4 ftr, + 2 DDs + 2 subs.   I will count the CV as 2 units.  For your fleet so far, you have 26 pips and 12 hp. if you buy 6 subs, you will have 38 pips and 18 hp. if you buy 10 subs, you will have 34 pips hand 20 hp.

with sub
342020 = 13600
with DD
381818 = 12312

So, as you can see, the sub will be better for your metapower. It will also give you a better lossdistribution.

But, I think your point is interessting. I think this formula can be used to figure out what you want to buy. Just calculate your metapower and hp, and figure out what units  you should add. This can be extremely nice russia, germany, japan and USA.

This need a few Edits to be correct:
lets assume you have 2 CV + 4 ftr, + 2 DDs + 2 subs.   I will count the CV as 2 units.
For your fleet so far, you have 26 pips and 12 hp.
If you buy 6 Destroyers (D2= +12Def pips), you will have 38 pips and 18 hp.
If you buy 8 subs (D1= +8Def pips), you will have 34 pips hand 20 hp.

with Submarines:
342020 = 13600

with Destroyers:
381818 = 12312

But applying avg pips of stack to follow the formula almost to the letter, this give:

with Submarines:
(34/20)2020 = 34*20 = 680

with Destroyers:
(38/18)1818 = 38*18 = 684

And, considering Carrier being 1 unit for 2 hits, to apply this stack formula to the letter:
with Submarines:
(34/18)2020 = 755.6

with Destroyers:
(38/16)1818 = 769.5

So, in lasts 2 cases, you get a better defense with Destroyers compared to Subs purchase.
This contradict your initial thesis.

This rise a question: how consider the number of units compared to hits in this formula?

75 Cruisers Attack 3 vs 40 Battleships D4, 2 hits

Cruisers 225 pips, 75 hits vs BBs 160 pips and 80 hits

Cruisers
3* 75^2= 16875

Battleships
4* 80^2 = 25600,  too high!!!
Or
4* 40^2 = 6400,  too low!!!

But AACalc gives a pretty even match still win by Cruisers:
Overall %*: A. survives: 53.4% D. survives: 46.2% No one survives: 0.4%

Maybe the formula need this addition (1.618034) on hits or rolls for all 2 hits units
Battleships
*4 [(401.618034)^2] = 16755**
So, this seems to work.
However, IDK the derivative formula…

So, the complete Stack formula would be :
**Metapower = units^2 * power

N1 is nb of 1 hit units
N2 is nb of 2 hits units
(N1+ N2*1.618034)^2 * avg power [total power/(N1+N2 units)] = Metapower**

For instance, comparing these 2 fleets on defense:
2 CV + 4 ftr, + 2 DDs + 10 subs
(16 hits + 2*1.618034)^2 * 34 pips/18 units = 698.9

2 CV + 4 ftr, + 8 DDs + 2 subs
(14 hits + 2*1.618034)^2 * 38 pips/16 units = 705.6

And this confirmed that adding DDs brings more defense metapower.

But not that much.
And this returns to the tricky Subs, DDs and planes triangle.
If attacker brings a lot of planes, Subs but no DDs, defending Subs will not protect the fleet core from air attack.

ENIGMA_Vann formula_Cost vs Odds_Roster charts_D6_D8_D12_D10.xls

This is a different derivation from Stack formula and it probably allows to get the derivative formula for Enigma.
Indeed, all 50% vs 50% comparison always requires like x Cruiser A3 = y Fighter D4 meaning that Cruiser should cost y while Fighter cost x.

Assuming Kreuzfeld is a mathematician, I’m pretty sure he can be able to derive Enigma formula (former Baron-Larrymarx) from his formula.

@Kreuzfeld:

Yes.

TLDR Version: (number Attacker units needed for 50% chance) = (Number of Defender units) * SQRT ( ( Average Defender Strength) / (Average Attacker Strength))

My formula is exact and easy to prove correct when you attack with only units of one type, against only units of a different type ( like inf v inf, inf v tanks, inf v ftrs, etc). I am a mathematician, I can send you the proof if you don’t trust me.

If average Defence  power is 2, and average attack power is 1, then  you need Sqrt(2) (1.141 number of units to win the attack 50%

I have made some calculations. If you assume you attack with only units with strength 1, and the defenders have only units of strength 2,3,4, then the number of units needed to have 50% chance of taking the terr is as follows;
1 v2 -> (sqrt(2)  =) 1,41… This means that 141 infs will have less than 50%, while 142 has more than 50% against 100 infs defenders.
1v3 -> (sqrt(3) = )1.73…  This means that 173 infs will have less than 50%, while 174 has more than 50% against 100 tanks defenders
1v4 -> (sqrt(4) =) 2 . So 200 infs have exactly 50% chance of winning against 100 planes.
2v4- > (sqrt(2)  =) 1,41… This means that 141 art will have less than 50%, while 142 has more than 50% against 100 ftr defenders.

The main advantage of the attacking infs is that they lose less of their combatstrenght when taking losses, than defenders does. This is why they need fewer dice than the defendes.

Lets assume that the defender has the highest average strength (it the attacker has the highest, just switch it around)
The quick and dirty formula will then be :
strenghtratio = (Defenders Average Strength) / (attackers average strength)
Number of units needed for 50% to win for the attackers will then be:
#Numbers needed = SQRT(Strength Ratio) * (#Number of Defender units)

This will change depending on the “structure” of the strength, however it will not be a Huge change. The more diverse, the better the force is.  A force defening force of 50% inf and 50% FTRs  is better than a defending force of 100% tanks.  So depending on Who I judge to have the better designed force, I add some Strength to that side when I calculate the average strength