VANN FORMULAS TESTING

Does anyone know any A&A-like games that are free and require no download?

@TheGheko91 Are you wanting to make it harder to beat the AI when playing solo?
If so you can use the unit edit.Make the nation you are playing weaker by removing some starting units and/or add a few staring units to your AI controlled opposition.I find the AI will never capture 2 enemy capitals,so set it for economic victory,which you can adjust the numbers when setting up your game.

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

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-)

OMG GUYZ

I’ve BEEN REVIEWING THE VANN FORMULA AND HAVE DISCOVERED A FATAL FLAW

LOOK AT THE RESULTS OF THE VANN FORMULA BELOW.

Attack/defense=A/D
INFANTRY        1.85/3.7
MECH              1.04/2.08
ARTILLERY      2.08/2.08
TANK              1.39/1.39
FIGHTER          .5/.667
TECHBOMB      (.413/.551)/.413
BOMBER          .463/.116
SUB                1.39/.463
DESTROYER      .521/.521
CRUISER          .347/347
CARRIER          0/.139
BATTLESHIP    .267/.267

THE GOAL OF THE VANN FORMULA AS STATED BY VANN ON MULTIPLE OCCASSIONS IS TO DETECT OBSOLETE AND USELESS AXIS AND ALLIES UNITS.

YOU WILL NOTE BY COMPARISON THAT THE VANN VALUE FOR TRANSPORTS MUST BE 0.

MEANING IT’S THE MOST USELESS AND OBSOLETE UNIT IN THE GAME, THAT SERVES NO PURPOSE, AND CLEARLY ANYONE WHO WOULD EVER BUY ONE WOULD CLEARLY BE A FOOL.

THIS IS A FATAL FLAW!  AS THE ALLIES and/OR JAPAN WOULD CERTAINLY LOSE IF THEY NEVER BOUGHT TRANSPORTS.

I DEMAND A FULL RESPONSE FROM VANN  HIS NEW GAME ALLIES AND AXIS IS DOOMED TO FAIL UNLESS HE UNDERSTANDS THIS CRITICAL FLAW!

And we haven’t even talked about Complexes and Air/Naval BASES yet.
OMG WHAT IS VANN GOING TO DO GUYZ?

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