THE VANN FORMULA IS BROKEN/OBSOLETE

@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

For house rules, this is a good way to price your units, and to give them a proper attack, and defense for your dice.

It’s good for tweaking your game. 8-)

@Dauvio:

Great news, we had a huge response for the VANN FORMULAS!!! So with a select few we gave them the formulas. They were sworn to secrecy to not to tell anyone that they have them. They have been winning just about every game against there friends, and their friends can’t figure out how they are doing it!!! Hence they became Grand Masters of the game.

Now you are saying when are we going to get the VANN FORMULAS ourselves, you’re not. That’s right, you’re not going to get the VANN FORMULAS.

LARRY HARRIS the creator of the A&A games will get them instead.

However we will keep bring you news, and game results on the VANN FORMULAS.

HAPPY HUNTING EVERYONE!!!  8-) 8-) 8-)

I shared some of my formulas a week ago. The VANN FORMULAS win not make you a good players. If you are not a good player, it doesn’t matter what aids you have, you will probably will lose. I talk to some of the A&A dot org members, and we will not name the formulas, and equations after ourselves.  We will probably use the word ENIGMA in some form, or fashion to the formulas, and equations.

Thank you.

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

Here is a longer thread about Tank cost in Axis & Allies Global 1940 forum:
Tank Purchases R.I.P.
@allweneedislove:

_My tank was a unit that was strong and fast
it loved threatening all with such joy and pride
that it lit up every time we were together.

There was never a time that I could not attack with it.
Some of you may not have known my tank the way that I did,
but for those who did not get to see this side of him
missed out on knowing a great unit.

A unit that made sure that its power was taken care of
even if it meant it had to sacrifice itself.*_

*i ripped this of eulogyspeech.net and replaced the words father with tank, man with unit, he with it, talk with attack, family with power, kind and generous with strong and fast. i also added the words threatening

The title is self explaining about this topic in  Axis & Allies Global 1940 forum:
Are Mechs Too Strong?
@Zhukov44:

Pondering the reason why Axis strategies seem to be improving faster than Allied strategies (resulting in escalating bids for Allies), I keep coming back to the mobility of mechanized infantry on a map where Eurasia is a huge, contiguous continent, where it is possible to blitz inaccessible places like China, Africa, Siberia, etc.

The main weakness of AA50 was that tanks (at $5) were way too strong.  The increased map size of AA50 relative to Revised made them even stronger than in Revised (where they had been improved to 3/3 to make for more dynamic offensive play and less defensive stacking).

So the decision to increase tanks to $6 was well-grounded.  However, mechs may be too cheap at $4.  Even though a mech attacks at only 1 (w/o artillery support), the defensive capacity of the mech is just too much.  If Germany and Japan had only tanks at their disposal, then it would be easier for Allies to counterattack tank stacks driving into Eurasia.  However, when Axis powers can buy mechs at 4$, defensive stacks deep inside Eurasia are too strong and too mobile.  Axis can use its positional advantage to exploit the excessive strength of mechanized infantry by conquering Eurasia.

A selected post (more to read in this Revised thread) about the change from Tank A3 D2 C5 to A3 D3 C5 and how it changes the Infantry Push Mechanic:
IPM Dead in AaA:Revised?
@Magister:

[DarthMaximus said]
I think IPM is still valid.
Simply put if you are buying 10 inf (30 ipc) per turn it is going to take your opponent at least 40 ipc to defeat you.

Right, it’s mostly about how Defender’s advantage changed from Classic to Revised. The addition of arty decreased it.
I define here Defender’s advantage as the ratio of IPC costs for attacker to be ‘equivalent’ to defender (both grind to zero with average luck). Any better for one side gets a cascading victory.

Pure infantry is still the best at pure defender.
Inf vs inf: the advantage is ~1.41 (SQRT 2) from Lanchester’s theory. Would need slightly more than 14 inf to defeat 10 inf. And this is mutual - if the other side wants to attack the 14 inf, they would need 20 inf. A mutual advantage of 2 x.

A simple mix to defeat pure inf would be Inf+Arty in equal proportions.
5 inf+5 arty (35 IPC) are exactly equal to 10 inf defending (30 IPC). Each unit hits at 2.
The defender’s advantage would be 35/30 = 1.166 x.

Actually, the optimal mix for large attacking forces would be in the proportion of 60% inf, 30% arty, 10% tanks (calculated with a detailed, mathematically quite ugly model). 6+3+1 would cost the same 35IPC.
I’ve tested on simulators, for large forces (30+15+5) this is very slightly better than 25 inf 25 arty. But 6 inf 3 arty 1 tnk is very slightly worse than 5inf 5 arty to attack 10 inf (or 5 inf 5 arty). In general, most optimization problems have a ‘flat optimum zone’ around which small variations in decision result in extremely small variations in value.

If opposed by a similar force, the 50-50-0 force would have no defender’s advantage. The two forces each would cost 35 IPC and fight the same. On defence, the 6+3+1 would be a bit superior due to the 3 firepower of tank. (Roughly like 0.5 inf more, but without its staying power).

They have the props on top. Its 1940. Still cost 3.

you are correct

our UI uses Swing,

and to be Android / iStuff compatible, someone would need to redo our UI in a different library that is specially made for those platforms.

our code is open source, anyone is welcome to do this
http://sourceforge.net/projects/triplea/develop