VANN FORMULAS TESTING

[Genghis Khan]

Yes I agree there are many factors that calculators do not help us with like the ability to move an extra space with a tank or combined arms or what the defender chooses to remove as casualties in some cases, there are many more examples of this. However it can help us predict the outcome of a battle and how many units we are left with if we decided to do a big stack battle. How many units we have left is important to determine if we retreat before the end of the battle or if we take the territory (based on potential of counter attack)

[baron Münchhausen]

@Genghis:

Yes I agree there are many factors that calculators do not help us with like the ability to move an extra space with a tank or combined arms or what the defender chooses to remove as casualties in some cases, there are many more examples of this. However it can help us predict the outcome of a battle and how many units we are left with if we decided to do a big stack battle. How many units we have left is important to determine if we retreat before the end of the battle or if we take the territory (based on potential of counter attack)

I agree with you. This intuitive thinking process during Combat Move and Combat resolution might get helped.
However, at the present stage, there is no guarantee that a Baron-Larrymarx formula:
36 Power/(cost^2) {1+[(nb hit -1)/11.618034] }= offense or defense factor* and table, even combined with Kreuzfeld formula:
(nb hit points in stack^2) * (avg strength of stack) will be efficient. It might work but can still be too hard for mind calculation, hence useless for F-2-F game.

In fact, such Vann or Baron-Larrymarx table and formula is just a way to tell the strength of the scale use due to a different combat value, and hit per IPCs. Almost each unit has a specific offense and defense factor which could have been used to scale up or down the combat value points per cost.

Infantry has its own, MI and Art then Tank,
2 hits Carrier by itself is on the same scale as the Cruiser, 2 hits BB is a bit above, Destroyer is in another scale.
Subs probably too.

Maybe the way to make something useful for the explicit purpose you just suggest is probably a kind of break even table based upon a few separate combat units, for instance:
11 Artillery (or AD2) are even to 9 Tanks (AD3), 5.5 (AD2) vs 4.5 (AD3)
or 10 Infantry (A1) are even against 7 Artillery (AD2), 5 (A1) vs 3.5 (AD2)
or 9 Infantry (A1) are even against 5 Tanks (AD3). 4.5 (A1) vs 2.5 (AD3)

or 10 Infantry (A1) 30 IPCs are even in offence as 4 Tanks (A3) and 2 Infs (A1) 30 IPCs, 5 (A1) = 2 (A3) + 1 (A1).

So, knowing you are just below or far below this break even point might help decide for retreat, or not.

As always, the issue is that usually there is a mix of units, but once fodder are out, it can be easier to evaluate on a glimpse.
IDK

[larrymarx]

My opinion is that if we are to assign numeric values representing the worth of units, we should do so with some awareness of what is happening on the board. As I said in my original post, it is evident that a mix of units is what is needed for a good strategy.

I mentioned that infantry and armor do better together than either alone. Carriers also do better in groups with destroyers to protect them. Mech infantry provide a good followup to a wave of artillery. Bombers and subs also have good synergy. Any combination of units, however, can only be evaluated in the context of the board on which it is placed. I would propose devising a set of common strategic situations and then identifying an optimal mix of units to buy in these situations.

Most players have an intuitive understanding of this concept, and they don’t need a calculator for it. This is GeneralHandGrenade’s point. He values the power of human analysis over numbers and formulas in this game. He is certainly correct - and I would argue that numbers and formulas are indispensable tools for us to use as part of that analysis. They cannot be the basis of a strategy, but they can enhance and sharpen any strategy.

Baron, I like the idea of the break even tables as opposed to trying to assign definite values to individual units. However, I think that the tables should be constructed with common mixes of units in mind, not just single unit types.

[baron Münchhausen]

Here is the table based on Baron-Larrymarx formula completed on effective cost vs combat points ratio:
For all 1 hit units, you use : 36 Power/(cost^2) = offense or defense factor* based on cost
For 2 hits and 3 hits unit : 36 Power/(cost^2) {1+[(nb hit -1)/11.618034] }= offense or defense factor* based on cost

To get the cost of a 1 hit unit for a given factor of reference: √(36*Power of unit / Offence or defence Factor)= Cost.
For a 2 hits unit for a given factor of reference:
√(36*Power of unit {1+[(nb hit -1)/11.618034] } / Offence or defence Factor)= Cost.

For combined arms and multiple units you have to average both combat points per unit and cost per unit.
Then you can add it into the formula.

Tank is the basic reference and gives also 3.00 offense and defense factor based on cost (same as attack or defense points).

Tank A3 D3 M2 C6
offense & defense factor: 36*3/(6^2)= 3.00

Mech Infantry A1 D2 M2 C4 would get
Offense factor:
36*(1/4^2) = 2.25
Defense factor:
36*(2/4^2)= 4.50

Artillery A2 D2 M1 C4
Offense & Defense factor:
36*(2/4^2)= 4.50

Infantry A1 D2 M1 C3
Offense:
36*(1/3^2) = 4.00
Defense:
36*(2/3^2) = 8.00

AIRCRAFTS:
Fighter A3 D4 C10, 1 hit
Offense factor:
36*(3/10^2) = 1.08
Defense factor:
36*(4/10^2) = 1.44

Tactical Bomber A3 D3 C11, 1 hit
Offense & Defense factor:
36*(3/11^2) = 0.89

Strategic Bomber A4 D1 C12, 1 hit
Offense factor:
36*(4/12^2) = 1.00
Defense factor:
36*(1/12^2) = 0.25

Combined ARMS:
Infantry & Artillery A4 D4 M1 C7, 2 hits
Offense factor:
36*(2/3.5^2) = 5.88
Defense factor:
36*(2/3.5^2)= 5.88

Mech Infantry & Artillery A4 D4 C8, 2 hits
Offense factor:
36*(2/4^2) = 4.50
Defense factor:
36*(2/4^2)= 4.50

Tactical Bomber & Tank A7 D6 C17, 2 hits
Offense factor:
36*(3.5/8.5^2) = 1.74
Defense factor:
36*(3/8.5^2)= 1.50

Tactical Bomber & Fighter A7 D7 C21, 2 hits
Offense factor:
36*(3.5/10.5^2) = 1.14
Defense factor:
36*(3.5/10.5^2)= 1.14

WARSHIPS:
Submarine A2 D1 C6
Offense:
36*(2/6^2) = 2
36*(3/6^2) = surprise strike 3.00
Defense:
36*(1/6^2) = 1
36*(1.33/6^2) = surprise strike 1.33

Destroyer A2 D2 C8, 1 hit
Offense & Defense factor:
36*(2/8^2) = 1.125

Cruiser A3 D3 C12, 1 hit
Offense & Defense factor:
36*(3/12^2) = 0.75

1942.2 Carrier A1 D2 C14, 1 hit
Offense factor:
36*(1/14^2) = 0.18
Defense factor:
36*(2/14^2) = 0.37

1942.2 Carrier Full Fighters A7 D10 C34, 3 hits
Offense factor:
36*(1/14^2) = 0.18
36*(3/10^2) = 1.08
36*(3/10^2) = 1.08
2.344/3= 0.78 to be revised, need to be below 0.74 but just above 0.72
36* (7/3)/(34/3)^2 = 0.65 Avg (0.78+0.65)/2= 0.72

Defense factor:
36*(4/10^2) = 1.44
36*(4/10^2) = 1.44
36*(2/14^2) = 0.367
3.247/3= 1.082 to be revised need to be below 1.00 but above 0.94
36* (10/3)/(34/3)^2 = 0.93

G40 Carrier A0 D2 C16, 2 hits
Offense factor:
36*[0/ (16^2)] * 2.618034 = 0
Defense factor:
36*[2/ (16^2)] * 2.618034 = 0.736

G40 Carrier A0 D2 C16, 2 hits with 2 Fgs A6 D8 C20, 2 hits
Offense factor:
   6/2  C36/2   2 additionnals hit/2
36*[3/ (18^2)] * 2.618034 = 0.873

Defense factor:
   10/2  C36/2  2 additionnals hit/2
36*[5/ (18^2)] * 2.618034 = 1.454 have to be below 1.44 but above 1.125 and just below 1.33

10/4  C36/4  1 additionnal hit considered as whole unit
36*[2.5/ (9^2)]  = 1.111
Until further investigation, I believe this average is better: (1.454+1.111)/2= 1.28
Or avg Defence would give (0.736+1.44+1.44) = 1.21

G40 Carrier A0 D2 C16, 2 hits with 1 Fg & 1 TcB A7 D7 C21, 2 hits
Offense factor :
    7/2  C37/2   2 additionnals hit/2
36*[3.5/ (18.5^2)] * 2.618034 = 0.964

Defense factor:
    9/2  C37/2  2 additionnals hit/2
36*[4.5/ (18.5^2)] * 2.618034 = 1.239

9/4  C37/4  1 additionnal hit considered as whole unit
36*[2.25/ (9.25^2)]  = 0.947
Until further investigation, I believe this average is better: (1.239+0.947)/2= 1.093
Or avg Defence would give (0.736+1.44+0.89) = 1.02

G40 Carrier A0 D2 C16, 2 hits with 2 TcBs A6 D6 C22, 2 hits
Offense factor :
    6/2  C38/2   2 additionnals hit/2
36*[3/ (19^2)] * 2.618034 = 0.783

Defense factor:
    8/2  C38/2  2 additionnals hit/2
36*[4/ (19^2)] * 2.618034 = 1.044

8/4  C38/4  1 additionnal hit considered as whole unit
36*[2/ (9.5^2)]  = 0.798
Until further investigation, I believe this average is better: (1.044+0.798)/2= 0.921
Or avg Defence would give (0.736+0.89+0.89) = 0.84

Battleship A4 D4 C20, 2 hits
Offense & Defense factor:
36* 4 / (20^2) * 2.618034 = 0.94

Battleship flag ship A4 D4 C24, 3 hits
Offense & Defense factor:
36* 4 / (24^2)* (1+21.618034) = 1.06
Real factor according to AACalc simulation: Fg A3 36(3/10^2) = 1.08

Sound very good…

This last example confirmed that the formula is right on!!!  :mrgreen: :mrgreen: :mrgreen:

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HR unit examples:

Mech Artillery A2 D2 M2 C5 gives +1A to Inf or MI
Offense & Defense factor:
36*(2/5^2) = 2.88

Mech Infantry & Mechanized Artillery A4 D4 M2 C9, 2 hits
Offense factor:
36*(2/4.5^2) = 3.56
Defense factor:
36*(2/4.5^2)= 3.56

Now, is it the end of Tank purchase? Not if you restrict Blitz to Tank only.
Or, add a combined arms with Tank and Mech Artillery.
That way,  Tank will remain interesting.

Here is what it can be:
Tank giving +1D to same Mechanized Artillery above A5 D6 M2 C11, 2 hits
Offense factor:
36*(2.5/5.5^2) = 2.98
Defense factor:
36*(3/5.5^2)= 3.57

This means that you get a similar attack factor because it cost 1 less IPC than 2 Tank.
And an higher defense factor per cost than Tank but similar to MI+MechArt.
Meaning that these 2 units defending @2 for 9 IPCs has same power per cost than 2 units defending @3 for 11 IPCs.

---

Another example for Naval, a 2 hits Cruiser at 14 or 15 or 16 IPCs to replace OOB Cruiser?

Cruiser A3 D3 C???, 2 hits
Offense & Defense factor:
36* 3 / (14^2) * 2.618034 = 1.44

36* 3 / (15^2) * 2.618034 = 1.26

36* 3 / (16^2) * 2.618034 = 1.10

Do you want it better than a Battleship A4 D4 C20, 2 hits at 0.94?
Weaker than a Destroyer? A2 D2 C8 at 1.13

If you want this progression SS>DD>CA>BB, then you go for 16 IPCs.

Now rise the question of an OOB obsolete BB…

But, you can change for a 3 hits BBs… of very similar strength to Cruiser, but 3 hits give more latitude for strafing enemy’s fleet:
Strong Battleship A4 D4 C24, 3 hits
Offense & Defense factor:
36* 4 / (24^2)* (1+2*1.618034) = 1.06

Or maybe at 22 IPCs?
36* 4 / (22^2)* (1+2*1.618034) = 1.26

And you get a similar factor with 15 IPCs 2 hits Cruiser.
36* 3 / (15^2) * 2.618034 = 1.26

It remains up to the designer to choose among these possibilities.

HTH

P.S. To get the cost for a given factor of reference:
√(36*Power/Strength of offence or defence Factor)= Cost.

[baron Münchhausen]

I agree, this kind of formula might help HR designer or, at best, and I’m doubtful, help deal with some tactical decisions in F-2-F combat if a player can easily remember some essential datas.
For now, I’m far from being convinced it might work.

At least, in this table numbers are easier to grasp for ground combat compared to Vann table.

IDK if I can somehow combined Kreuzfeld formula into Baron-Larrymarx formula.

[GeneralHandGrenade]

@larrymarx:

Most players have an intuitive understanding of this concept, and they don’t need a calculator for it. This is GeneralHandGrenade’s point. He values the power of human analysis over numbers and formulas in this game. He is certainly correct - and I would argue that numbers and formulas are indispensable tools for us to use as part of that analysis. They cannot be the basis of a strategy, but they can enhance and sharpen any strategy.

It’s not that I don’t run the numbers myself, it’s just that I do it in my head and not on a machine. My brain takes everything into account though, just like it would for anyone who is willing to put their calculators away and teach themselves to play the game like a human being. You know, like a board game was meant to be played.

I will never play A&A against a person with a calculator in their hands. If the player doesn’t have the guts to play the game without a crutch, then they should go back to playing Risk or Checkers.

[baron Münchhausen]

So, are you just crunching attack and defense points or do you have a better way to mentally calculate the impact of hit and fodder in a small stack?

Sometimes, on smaller board you wonder if 1 plane is going to help 1 battle or another, or add this plane on 1 side but move 1 infantry in the other. You don’t want to overkill somewhere and get a pyrrhic victory on the other because 1 fodder was missing.

It is much harder playing daredevil with tactical retreat and counter in Russia than simply retreating and exchanging 1 TT while stacking Moscow.

[General 6 Stars]

This thread is still here !!!

[Genghis Khan]

@GeneralHandGrenade:

@larrymarx:

I will never play A&A against a person with a calculator in their hands. If the player doesn’t have the guts to play the game without a crutch, then they should go back to playing Risk or Checkers.

That’s a very silly proposition to be honest. You’re willing to add up the numbers in your head but refuse to pull out a calculator for large battles? Why? You have a tool, so use it. It’s like saying I cheated on my differential equations homework because I used a calculator. It’s a tool that helps you but you still need to use your brainpower and judgement/experience to make decisions in the game. The calculator is not a magic wand that will win the game for you.

[GeneralHandGrenade]

This isn’t homework. It is a board game where you are competing against other people. There is no formula required. All you need to bring to the table is what you were born with.

We might as well walk away from this ridiculous thread, SS. As long as there are players who feel they need to cheat to be competitive, they will continue to do so. Have fun staring at your calculators while the honest players are playing the best board game in the world.  :roll:

[General 6 Stars]

@GeneralHandGrenade:

This isn’t homework. It is a board game where you are competing against other people. There is no formula required. All you need to bring to the table is what you were born with.

We might as well walk away from this ridiculous thread, SS. As long as there are players who feel they need to cheat to be competitive, they will continue to do so. Have fun staring at your calculators while the honest players are playing the best board game in the world.  :roll:

My Last quote in this thread.

I don’t use or allow any gadget calculators in any of my games Period.  :-D

[baron Münchhausen]

@Genghis:

@GeneralHandGrenade:

@larrymarx:

I will never play A&A against a person with a calculator in their hands. If the player doesn’t have the guts to play the game without a crutch, then they should go back to playing Risk or Checkers.

That’s a very silly proposition to be honest. You’re willing to add up the numbers in your head but refuse to pull out a calculator for large battles? Why? You have a tool, so use it. It’s like saying I cheated on my differential equations homework because I used a calculator. It’s a tool that helps you but you still need to use your brainpower and judgement/experience to make decisions in the game. The calculator is not a magic wand that will win the game for you.

@GeneralHandGrenade:

This isn’t homework. It is a board game where you are competing against other people. There is no formula required. All you need to bring to the table is what you were born with.

We might as well walk away from this ridiculous thread, SS. As long as there are players who feel they need to cheat to be competitive, they will continue to do so. Have fun staring at your calculators while the honest players are playing the best board game in the world.  :roll:

There is always the luck factor, time and boozes too. All this affect the focus you put on a game at a given moment.

You can also apply Jedi mind trick.

So why not use your mental calculator?
It is not cheating.

[Imperious Leader]

rename Vann anything to Larrymarx formula. This is perfect. If everyone did this the whole problem would go away. Im starting today forward with this idea.

[Genghis Khan]

I don’t understand why using a calculator is considered cheating. If I used an abacus would that be cheating? How about using dice to count up my attacking power? How are you going to justify preventing me from doing that? How about using my fingers to count…where do you draw the line?

[General 6 Stars]

@Genghis:

I don’t understand why using a calculator is considered cheating. If I used an abacus would that be cheating? How about using dice to count up my attacking power? How are you going to justify preventing me from doing that? How about using my fingers to count…where do you draw the line?

When you use a Electronic device or  beads slides.

Hip oh ray now I got to use my brain and fingers !!! Bingo there you go,  :-D

aaahhh back to the red wagon days and riding big wheels and playing army guys outside
and doing battles with out a  ???

@SS:

@GeneralHandGrenade:

This isn’t homework. It is a board game where you are competing against other people. There is no formula required. All you need to bring to the table is what you were born with.

We might as well walk away from this ridiculous thread, SS. As long as there are players who feel they need to cheat to be competitive, they will continue to do so. Have fun staring at your calculators while the honest players are playing the best board game in the world.  :roll:

My Last quote in this thread.

I don’t use or allow any gadget calculators in any of my games Period.  :-D

I tried. I failed.  :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry: :cry:

[Imperious Leader]

Kreuzfeld formula

is the new advanced calculating technique. vann whatever is the new dodo bird

[GiddyXray]

I don’t really understand why there is so much noise about the Vann formula!
I hate to play against people using battle calculators, because it takes fun out of the game and slows it down too! But If I would play against somebody using the Vann formula I will seriously have fun! By every turn going by, I would see the expression of unbelief growing on their faces while they are loosing while sticking correctly to their formula!

The thing with this formula is that it works perfect in a 2 dimensional world. And that is where it has its origins: A&A classic! It had so less territories that things like positioning were no issue. You stack a territory next to the enemy. If you are faster, then the enemy you win the game. Then all what matters is the cost/attack ratio! Buy as cost efficient as possible and you win. Mister Vann has missed the last 30 years of discussion about this topic. But is generally called the infantry push mechanism.

However the world has changed! And so did the A&A boards and rules. Mister Vann even admits that he doesn’t know the rules of the 1940 games, but his formula applies anyway! It says something about this person I guess!

So, what is wrong with the formula? It is missing essential input. Input that is not possible to put into a static number. And one of them is speed and distance! Welcome in the new world with more dimensions mister Vann! This is like the French sitting in their Marginot line laughing at the Germans because their tanks are obsolete! They are prepared for a 2 dimensional war, but had missed the developments of the last 2 decades! Of course you don’t use tanks for a dumb push against a fortified position! You go around it! That is possible in A&A 1940! since the board is so much bigger you need mobility and speed. If you have both, you have an advantage over a nation that is buying inf and need more time to bring them into the action! Plus A&A is an economic game. If you conquer territories faster than your opponent, your economy is growing, while that of your opponent is shrinking! That means he’ll buy less inf next time, while you buy more mechanized units! All this is not taken into consideration in the static 2 dimensional formula! If you could, what I doubt, then you really had gold, but now mister Vann is nothing more then a fraud. Claiming to be something he is not!

Therefor I would love to play against anybody using his formula! That would be one of the masters he is revering to. Because there is only one possible outcome! They loose every game against anybody knowing the game a little bit!

[Genghis Khan]

You misunderstand what the formula is used for. It’s not for comparing two units that have different movement values. You have to compare the ones that have the same role in the game. For example you can choose to use a destroyer or cruiser to defend your fleet. I we want to determine what the ACTUAL cost of a cruiser should be if we want it to be as effective as a destroyer, then we can use the Baron-larymarx formula to determine this. It’s actually 9.78 so a cruiser should really cost 10 IPCs.

Mostly it’s to determine the cost efficiency of units with similar roles. So comparing an infantry with a tank does not work. However you could compare the battleship with destroyer or cruiser with destroyer for example. In order to determine if you will win a stack battle, better to use AAcalc or punch formula, Vann or baron-larymarx will not help with this.

You’re dismissing the formulas without having read any of the logic behind the derivation of the formulas. If you even bothered to read the thread you would see that they make sense for their intended purpose.

[baron Münchhausen]

Hi TripleA XRay,
all that you said is true about the game and how Vann formula does not work in modern Second Edition compared to Classis Edition, when he first developed it and use it.
The pretenses of Vann about his formula and what can be done with it, are two different things.
I was mostly aware of all you said about G40 big map, even if I mainly played on 1942.2 or AA50.

However, I stick into this Vann table he provided because I wanted to know if the formula was something real or just pure crap day-dreaming.
I was waiting to someone cracking the code: Larrymarx get it right.
Then, I crunched numbers and AACalc to see if it was working. And it did.
During the meantime, Vann showed up again and revealed two formulas.

Now, he still want to be an active member on the forum, I cannot deny the basic accuracy of the formula.
I just adapted it to the second edition roster and included another part to take account of 2 hits units such BB and G40 Carriers. I cannot deny that he found really something back then in the '80.
So, out of respect for him (he discovered the core of it) and also for Larrymarx (he retro-engineered the formula based on Vann table), I would like to name this formula in a more general way.

What do you think people about the Enigma Formula of Axis and Allies?

Now, it has been revised we can talk about what this formula can do or not.

The second formula was first introduced in the thread quoted below. It was Kreuzfeld which bring it to my attention.

This one is much better to compare stack and their relative strength. For now, I named it Stack formula (until someone suggest something better) compared to the Punch Formula.

@Baron:

@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 see they also use this Metapower formula to get an optimized purchase.
And it is confirmed by AACalc.
If there is 24 IPCs to spend on Inf, Art, MI and Tank, it will be easier to decide since in case of combined arms, you can add it too.

8 Infs             A8 D16    8 hits     8^21= 64  /   8^22= 128   tot.: 192
6 Artillery       A12 D12   6 hits     6^22= 72  /   6^22= 72    tot.: 144
4 Tanks          A12 D12   4 hits     4^23= 48  /   4^23= 48     tot.: 96

1 Tk & 6 Infs   A9 D15    7 hits    7^21.29= 63.2 / 7^22.14= 104.9  tot.: 168.1
2 Tk & 4 Infs   A10 D14  6 hits    6^21.67= 60.1 / 6^22.33= 83.9    tot.: 144
3 Tk & 2 Infs   A11 D13  5 hits    5^22.2= 55 / 5^22.6= 65             tot.: 120
3 Art & 4 Infs   A14 D14  7 hits    7^22= 98 / 7^22= 98                 total: 196

1 Tk, 3 Art, 2 Infs            A13 D13 6 hits  6^22.17= 78.1 / 6^22.17= 78.1  tot.: 156.2
1 Tk, 2 Art, 1 MIs, 2 Infs  A12 D13 6 hits  6^22 = 72        / 6^22.17= 78.1  tot.: 150.1
1 Tk, 1 Art, 2 MIs, 2 Infs  A10 D13 6 hits  6^21.67= 60.1 / 6^22.17= 78.1  tot.: 138.2
1 Tk, 3 MIs, 2 Infs            A8 D13 6 hits  6^21.33 = 47.9 / 6^22.17= 78.1  tot.: 126

Even with such low 24 IPCs, it seems rather complex to sort out these numbers.
Unless having a few tables with various combinations, it only points out that it is cumbersome and also, Artillery with combined arms clearly gives better offensive.

It might help choose but the Punch formulas might be enough in this case.

Probably the things were different in Classic time with Tank A3 D2 C5.

So, this formula seems more useful when calculating odds between two stacks.

[Genghis Khan]

it’s normal that Infantry + Artillery seems optimal in the stack formula. it’s because the movement value isn’t taken into account. And tanks pay a premium for that extra point of movement and ability to blitz. Perhaps mech infantry and tanks is better if you want to put pressure on the enemy faster.

For comparing two stacks I will stick to the punch formula to determine number of hits and leftover units after the battle.