VANN FORMULAS TESTING

[baron Münchhausen]

Thanks for the answer, really genius.

Since 3 and 50 are purely arbitrary, I think this formula can be refined.
For now, I will verify another case:
Based on AACalc to be 50-50%, a A3D3 should cost 20 compared to a A4D4 cost 23.1
If we divide by 4, this means a A3D3C5 would be even with a C5.775 A4 D4 unit.

Or if we take Cruiser A3 D3 C12 as basis, it is 3/5 of 20.
A A4 D4 should cost 23.1*0.6= 13.86 almost 14.

Now we can compare with Vann formula:
4/(3*14^2)*50= 0.340

It is very near .347 of Cruiser.
So, this work but I only consider 1 hit value unit.

In Classic time, there was no 2 hits unit.

At first glance, do you think we can introduce this factor in the equation?

I’m also pretty sure that taking Tank A3 D3 C6 as reference, it is easy to modify the formula to get 3 instead of 2.
What do you think?

Here is a simplify first draft of what I would call Larrymarx formula, in your honor:
*Power/(cost^2)36

*Tank offense & defense factor: 3/(6^2)36= 3

So **Mech Infantry A1 D2 M2 C4 would get as offense factor:
(1/4^2)*36 = 2.25

Defense factor:
(2/4^2)36= 4.50*

So, a C6 Tank strength A/D value is 3/3 but MI is 2.25/4.5

That show how useful it is for defense compared to Tank.

When Tank was 5 IPCs, (3/5^2)*36= 4.32/4.32

Almost same than MI defense factor.
So C6 Tank is 69.4% of a C5 Tank, so 30.6% weaker.

To find the target number for 2 hits Battleships:
41 Cruiser A3 D3 M2, 1 hit vs 22 Battleship A4 D4, 2 hits are 50%-50%
So, a 11 IPCs Cruiser worth a 20.5 IPCs Battleship.

Such Cruiser would get as offense factor:
363 / (11^2) = 0.8926 or 108/121
BB 364 / (20.5^2) = 0.34265 or 144 / 420.25, if it was 1 hit unit.

.8926/0.34265 = 2.60 for 2 hits

Here is the complete Baron-Larrymarx formula:
36 Power/(cost^2) {1+[(nb hit -1)/11.618034] }= offense or defense factor*

36* 4 / (20.5^2) {1 + (2-1)/11.618034} = 0.8971

Now if I try for BB A4 D4 C20, 2 hits:
36* 4 / (20^2) * 2.618034 = 0.9425 offense and defense factor.

A Cruiser A3 D3 C12, 1 hit would get:
36*3 / (12^2) = 108/144 or 0.75 offense and defense factor.

A G40 Carrier A0 D2 C16, 2 hits factor:
36*2/ (16^2) * 2.618034 = 0.736 defense factor

Does it work?
It seems because AACalc put them nose to nose with a slight advantage for Cruiser:
http://calc.axisandallies.org/?mustland=0&abortratio=0&saveunits=0&strafeunits=0&aInf=&aArt=&aArm=&aFig=&aBom=&aTra=&aSub=&aDes=&aCru=8&aCar=&aBat=&adBat=&dInf=&dArt=&dArm=&dFig=&dBom=&dTra=6&dSub=&dDes=&dCru=&dCar=6&dBat=&ddBat=&ool_att=Bat-Inf-Art-AArt-Arm-Sub-SSub-Des-Fig-JFig-Cru-Bom-HBom-Car-dBat-Tra&ool_def=Tra-Bat-Inf-Art-AArt-Arm-Bom-HBom-Sub-SSub-Des-Car-Cru-Fig-JFig-dBat&battle=Run&rounds=&reps=10000&luck=pure&ruleset=AA1942&territory=&round=1&pbem=

[General 6 Stars]

:roll: :roll: :roll: :roll: Enough

Mods remove this thread please.

[baron Münchhausen]

@Baron:

Thanks for the answer, really genius.

Since 3 and 50 are purely arbitrary, I think this formula can be refined.
For now, I will verify another case:
Based on AACalc to be 50-50%, a A3D3 should cost 20 compared to a A4D4 cost 23.1
If we divide by 4, this means a A3D3C5 would be even with a C5.775 A4 D4 unit.

Or if we take Cruiser A3 D3 C12 as basis, it is 3/5 of 20.
A A4 D4 should cost 23.1*0.6= 13.86 almost 14.

Now we can compare with Vann formula:
4/(3*14^2)*50= 0.340

It is very near .347 of Cruiser.
So, this work but I only consider 1 hit value unit.

In Classic time, there was no 2 hits unit.

At first glance, do you think we can introduce this factor in the equation?

I’m also pretty sure that taking Tank A3 D3 C6 as reference, it is easy to modify the formula to get 3 instead of 2.
What do you think?

Here is a simplify first draft of what I would call Larrymarx formula, in your honor:
*Power/(cost^2)36

*Tank offense & defense factor: 3/(6^2)36= 3

So **Mech Infantry A1 D2 M2 C4 would get as offense factor:
(1/4^2)*36 = 2.25

Defense factor:
(2/4^2)36= 4.50*

So, a C6 Tank strength A/D value is 3/3 but MI is 2.25/4.5

That show how useful it is for defense compared to Tank.

When Tank was 5 IPCs, (3/5^2)*36= 4.32/4.32

Almost same than MI defense factor.
So C6 Tank is 69.4% of a C5 Tank, so 30.6% weaker.

To find the target number for 2 hits Battleships:
41 Cruiser A3 D3 M2, 1 hit vs 22 Battleship A4 D4, 2 hits are 50%-50%
So, a 11 IPCs Cruiser worth a 20.5 IPCs Battleship.

Such Cruiser would get as offense factor:
363 / (11^2) = 0.8926 or 108/121
BB 364 / (20.5^2) = 0.34265 or 144 / 420.25, if it was 1 hit unit.

.8926/0.34265 = 2.60 for 2 hits

Here is the complete Baron-Larrymarx formula:
36 Power/(cost^2) {1+[(nb hit -1)/11.618034] }= offense or defense factor*

36* 4 / (20.5^2) {1 + (2-1)/11.618034} = 0.8971

Now if I try for BB A4 D4 C20, 2 hits:
36* 4 / (20^2) * 2.618034 = 0.9425 offense and defense factor.

A Cruiser A3 D3 C12, 1 hit would get:
36*3 / (12^2) = 108/144 or 0.75 offense and defense factor.

A G40 Carrier A0 D2 C16, 2 hits factor:
36*2/ (16^2) * 2.618034 = 0.736 defense factor

Does it work?
It seems because AACalc put them nose to nose with a slight advantage for Cruiser:
http://calc.axisandallies.org/?mustland=0&abortratio=0&saveunits=0&strafeunits=0&aInf=&aArt=&aArm=&aFig=&aBom=&aTra=&aSub=&aDes=&aCru=8&aCar=&aBat=&adBat=&dInf=&dArt=&dArm=&dFig=&dBom=&dTra=6&dSub=&dDes=&dCru=&dCar=6&dBat=&ddBat=&ool_att=Bat-Inf-Art-AArt-Arm-Sub-SSub-Des-Fig-JFig-Cru-Bom-HBom-Car-dBat-Tra&ool_def=Tra-Bat-Inf-Art-AArt-Arm-Bom-HBom-Sub-SSub-Des-Car-Cru-Fig-JFig-dBat&battle=Run&rounds=&reps=10000&luck=pure&ruleset=AA1942&territory=&round=1&pbem=

@SS:

:roll: :roll: :roll: :roll: Enough

Mods remove this thread please.

No wait SS, there is maybe a real breakthrough here.

A player have only limited IPCs, he may count this factor to optimized his purchase either for offense or defense or both.

With basic Tank taken at 3/3, easy to remember.

For example,  you may invest 24 IPCs.
Unit  Cost Offense / Defense factors
MI 4$ 2.25 / 4.5
Tk 6$ 3 / 3

4 Tanks give you 12 / 12 while
6 MIs 13.5 / 27

2Tk+3MI 6 / 6 + 6.75/13.5 = 12.75 /  19.5

If you count combat points:
4  Tk is A12 D12 4 hits,
6 MI is A6 D12 6 hits,
2Tk+3MI A9 D12 5 hits

In all 3 cases, you get same def points but the formula show you that 6 MIs are twice stronger in defense than 4 Tanks.

Even more, a mix of 2 Tks and 3 MIs is not better for offense than 6 MIs, this is counter intuitive if you compare attack points: A6 6 hits vs A9 5 hits.

AACalc gives in fact 50%-50% if you compare these 2 attacks, so you go all the way with 6 MIs: same attack double defense.

http://calc.axisandallies.org/?mustland=0&abortratio=0&saveunits=0&strafeunits=0&aInf=6&aArt=&aArm=&aFig=&aBom=&aTra=&aSub=&aDes=&aCru=&aCar=&aBat=&adBat=&dInf=&dArt=&dArm=2&dFig=&dBom=3&dTra=&dSub=&dDes=&dCru=&dCar=&dBat=&ddBat=&ool_att=Bat-Inf-Art-AArt-Arm-Sub-SSub-Des-Fig-JFig-Cru-Bom-HBom-Car-dBat-Tra&ool_def=Bat-Inf-Art-AArt-Arm-Bom-HBom-Sub-SSub-Des-Car-Cru-Fig-JFig-dBat-Tra&battle=Run&rounds=&reps=10000&luck=pure&ruleset=AA1942&territory=&round=1&pbem=

The formula say that 6 MIs are slightly stronger on Attack but it is a good approximation nonetheless.

[Genghis Khan]

what? no way 6 MI is better than 4T on offense…I don’t need AAcalc to know that. Look: 6MI have 6 combat punch but 4T have 4x3=12 combat punch.

[GeneralHandGrenade]

Honestly, I wish you would just come to the realization that you are on the wrong track.

1. Mechs don’t blitz unless you have a tank.
2. You need 6 transports at a cost of 42 IPC to move 6 Mechs across water.
3. You need 4 transports at a cost of 28 IPC to move 4 tanks across water.
4. This is only the beginning of what your calculator doesn’t know jack sh*t about.

Your calculators don’t factor in the all of the information that you need to win a game. You need intuition. You need to be creative. You need to understand much, much more than your precious numbers which tell you how well you MIGHT do when you attack the adjacent territory with no other units on the board anywhere in reach of you when you get there. What will you need those units to do next turn? How about the turn after that? What are your opponents tendencies? Are they aggressive? Do they retreat easily? What are the chances that they will be more inclined to spend their income to attack 6 transports but not 4 of them? Will you need an extra Destroyer and maybe an extra Submarine to protect those extra 2 transports that are a juicier target than 4 transports because of your opponents tendencies and their current level of income considering all of the other needs that they have?

These questions and a thousand others can’t be answered by a calculator. There is no substitute for learning how to play the game like a human being, using all of your senses that can’t be quantified. The human brain is infinitely more sophisticated than the most powerful computer in the world. At work my main function is to correct the errors that the high tech computers make. The only reason that I’m needed to do that is because of what I’m trying to tell you here…that you are smarter than your stupid calculator.

And have I mentioned that the game is a lot of fun to play too? :?

[baron Münchhausen]

@Genghis:

what? no way 6 MI is better than 4T on offense…I don’t need AAcalc to know that. Look: 6MI have 6 combat punch but 4T have 4x3=12 combat punch.

I was waiting for this comment because it seems improbable to me too.
I checked on AACalc, 4 Tk are better than 6 MIs.
I checked if my calculations were wrong. It is not the case.
So, I cannot use Vann formula or a variant as it is actually to predict the relative strength of unit in place of AACalc. (It needs to add something from Kreutzfell formula to work. See G40 Vann formula’s thread.)

However, it can provide a way to give balanced combat value compared to a given unit of reference. Which maybe useful for those who have many customs units in HRs.

Just an example, if I want to develop a costlier Panther Tank A4 or a Mech Art A2 D2 with same strength as Tank A3 D3 C6: off/def factor 3

**Basic formula: (Power/cost^2)*36 = off or def factor

Cost= sq roots (Power  /  (off or def factor /36)**
sq [4 / ( 3/ 36)] = sq rt 48 = 6.9628

This means a 7 IPCs Tank A4 D4 is same cost ratio than OOB Tk A3 D3 C6.

Sq rt [2 / 3/36)] = sq rt 24 = 4.899
This means a MechArt of same cost ratio than OOB Tk is A2 D2 M2 C5

Of course, this does not consider special combined arms bonus, like +1A to MI or Inf.
Or if it receive blitz capacity.
Since the chosen price is rounded up compare to formula, this means OOB Tank is a bit better.
So, there is room for combined arms. But for the essential, this means classic Tank A3 D2 have mostly same defense value than OOB 2nd ed Tank.

It is just two examples, that way HR unit creator don’t rely on multiple try on Calc to find the balanced cost in pure combat.

Of course, if you decide to create a A3 D3 unit based on Artillery strength (4.5 / 4.5 ) you get different results:

Cost= sq rt [3 / (4.5/36)] = sq rt 24 = 4.899, so this heavy Art A3 D3 M1 will be 5 IPCs too.

I’m not that good with equation, probably a simpler formula can be derived from the basic formula.

[baron Münchhausen]

@GeneralHandGrenade:

Honestly, I wish you would just come to the realization that you are on the wrong track.

1. Mechs don’t blitz unless you have a tank.
2. You need 6 transports at a cost of 42 IPC to move 6 Mechs across water.
3. You need 4 transports at a cost of 28 IPC to move 4 tanks across water.
4. This is only the beginning of what your calculator doesn’t know jack sh*t about.

Your calculators don’t factor in the all of the information that you need to win a game. You need intuition. You need to be creative. You need to understand much, much more than your precious numbers which tell you how well you MIGHT do when you attack the adjacent territory with no other units on the board anywhere in reach of you when you get there. What will you need those units to do next turn? How about the turn after that? What are your opponents tendencies? Are they aggressive? Do they retreat easily? What are the chances that they will be more inclined to spend their income to attack 6 transports but not 4 of them? Will you need an extra Destroyer and maybe an extra Submarine to protect those extra 2 transports that are a juicier target than 4 transports because of your opponents tendencies and their current level of income considering all of the other needs that they have?

These questions and a thousand others can’t be answered by a calculator. There is no substitute for learning how to play the game like a human being, using all of your senses that can’t be quantified. The human brain is infinitely more sophisticated than the most powerful computer in the world. At work my main function is to correct the errors that the high tech computers make. The only reason that I’m needed to do that is because of what I’m trying to tell you here…that you are smarter than your stupid calculator.

And have I mentioned that the game is a lot of fun to play too? :?

Interesting post GHG,
it probably explains why lower puncher ground units are more cost efficient than higher ones such as Tanks.
As someone showed, 1 Tank and 1 Inf get same punch 1 Inf+1 Art, but if second unit is a higher puncher, the first play much a fodder role.
Lower values needs more units (even with less IPCs overall) to compete with costlier and fewer higher puncher.

However, warships and planes does not have the same restrictions but you follow the same rule: lower puncher are more cost efficient (except for Cruiser, a broken case for desperate situation: 1 round build up before defending, only 1 unit to built, not much money, etc.).

My intent was to validate Vann formulas and find some applications.
Of course, even a working formula to optimize ground purchase for example, is limited in usefulness. And only if this does not require too many calcs, because using a cell phone as a calculator or going straight to AACalc is very similar, and putting digit in AACalc might be faster anyway.

[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:

---

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.