• Disciplinary Group Banned

    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-)


  • @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-)

    Is this an act or are you really that immature and stupid in real life? To me, it appears you are nothing but your own hero in your own head… Your statements are annoying on their best day… that very statement you wrote above should probably be simply deleted.


  • Amen brother……while I do enjoy reading most of the posts on this board…this particular item is really “stinky”.  There has got to be an “Anti-Vann” formula, anti-dote, or gun out there somewhere!!!


  • @Loose:

    Amen brother……while I do enjoy reading most of the posts on this board…this particular item is really “stinky”.   There has got to be an “Anti-Vann” formula, anti-dote, or gun out there somewhere!!!

    Well, let’s face it, the “Vann Formulas” is pretty easy to understand…here it is:  “How to make an ass of yourself to an entire community in less then 20 posts - 100% success rate every time”


  • Is this somekind of A&A pyramid scheme?  😄


  • I bet Vann is secretly Larry Harris in disguise, simply trolling us lol

  • '16 '15 '14 Customizer

    Since we’re not worthy of the secret Vann formulas I’ll post this one for us:

    https://food-hacks.wonderhowto.com/how-to/colonel-sanders-kfc-recipe-revealed-0118355/

  • '17 '16

    It seems the Vann formula either ruins the game or allows to abuse it and becomes grand masters.
    Neither seems fair play, hence the secrecy…
    😐

    Now I will try KFC recipe and spices on real chicken.  😄

    http://www.snopes.com/horrors/food/friedrat.asp

  • '18 '17 '16

    You guys have got it all wrong.

    What Vann is trying to tell us is that each nation would be advised to purchase nothing but infantry because all of the other units are obsolete. It will take 4 or 5 rounds to kill off all of the other units on the board from the opening setup and be left with nothing but infantry, which as any Grandmaster will tell you is the only A&A unit that isn’t obsolete. Once this happens then the real game can begin.

    What he doesn’t want to share with you is that you can do all of this for a fraction of the cost of buying Europe 40 and Pacific 40. Here is the ultimate recipe;
    https://www.youtube.com/watch?v=yDaHAFm_Kus

    If you can’t afford to purchase this revolutionary game with zero obsolete units you can settle for this little gem;
    https://www.youtube.com/watch?v=m0drB0cx8pQ


  • @GeneralHandGrenade:

    What he doesn’t want to share with you is that you can do all of this for a fraction of the cost of buying Europe 40 and Pacific 40. Here is the ultimate recipe;
    https://www.youtube.com/watch?v=yDaHAFm_Kus

    Good idea, I do have this one also in my playroom.
    But without the deep knowledge of the VANN FORMULA, we can not be sure if a cavalry unit is really worth 5 infantrie or if it is a obsolete unit!  😮


  • Hello everyone,

    I have derived the VANN FORMULAS (or perhaps one of them) based on the unit strengths that VANN presented in a post on another thread.

    Here are his figures:

    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
    INF/ART          2.72/2.72
    MECH/ART       2.08/2.08
    MECH/TANK     1.33/1.67

    Here is how he got them: (DRUMROLL…)

    (power / 3*cost^2)*50

    For example, infantry:

    Attack:  (1 / 3*3^2)*50 = (1/27)50 = 1.852
    Defense: (2 / 3
    3^2)*50 = (2/27)*50 = 3.704

    Because this VANN FORMULA uses a square in the denominator, the implication is that a quadrupling in strength is required to justify a doubling in cost. One example of this would be sub defense (1 for 6) vs. bomber attack (4 for 12). Each of these unit configurations results in a strength of 0.463 according to this VANN FORMULA. Accordingly, VANN would likely only consider buying tanks with 3/3 attack/defense if they cost 5 IPC’s because this would give them a strength of 2, which is comparable to an artillery’s strength.

    He would likely argue that cruisers should cost 10 as well, as this would give them a “strength” of .551, which is comparable to a destroyer at .521.

    He probably didn’t have a battle calculator when he came up with all of this. It is evident that efficient attacks require a mix of cheaper and more powerful units. For example, VANN asserted previously that 100 infantry are better than 50 tanks for attacking 50 infantry. This may be true, But a mix of 50 infantry and 25 tanks is better than either of those.

    So who should use the VANN FORMULAS?

    Most likely, players who lack creativity and/or get confused when they try and figure out how to divide their IPC’s between different units.

  • '17 '16

    Wow, you are good at reverse engineering  (maths equations).

    How do you find it? With derivation? Equations with unknowns?
    If it is too complex  but have time, you can send me a PM.

    (power / 3*cost^2)*50
    Do you see any reason to multiply by 50?

    100 would have been better to work with less under 1 unit factor.

    Do you see any reason for 3*?
    Does a 2*cost^2, change something overall, for each relative number?

    Based on AACalc, to be 50%-50%
    an A2 D2 M2 unit should cost 4.5 IPCs
    and A3 D3 M2 Tank should cost 5.5 IPCs

    According to Vann formula :
    2/ (3*4.5^2)50 = 1.646
    3/ (3
    5.5^2)*50 = 1.653

    Also, 10 A1D1 C7 vs 7 A2D2 C10 gives 50%-50% odds of survival.

    So, if Artillery A2 D2 M1 is C4 then A1 D1 should cost 40% of 7 IPCs = 2.8 IPCs to get same combat factor.

    According  to Vann formula :
    Artillery: 2/ (3*4^2)50 = 2.083
    1/ (3
    2.8^2)*50 = 2.126 (not too far…)

    If Inf A1 Cost 3, it is 3/7 of reference unit.
    So A2 unit to be same strength of A1 need to cost 10*3/7 = 4.286 IPCs

    And Inf D2 cost 3 IPCs, so a D3 unit should cost 11/9 of 3 IPCs: 3.667 IPCs
    3/(3*3.667^2)*50= 3.718

    According to Vann formula, Inf on defence worth  3.7.

    So that works for me to confirme Vann unit value structure and formula.

    I still thinks the real thing is only:  power/cost^2.

    It can be the core formula to add the 2 hits factor, which I believe is forgotten because BB is weaker than Cruiser.


  • First I searched for patterns in the numbers. The first things I noticed were:

    1. That the sub defense and bomber attack were the same value. This clued me in to the principle that quadrupling the power resulted in a doubling of the cost. This sort of thing happens with area equations so I knew there was something with squares or square roots going on.
    2. Units with a cost of 10 resulted in numbers easily expressed as fractions. This showed me that the equation had to be a fraction of some kind with whole numbers in the numerator and denominator.
    3. the carrier had an attack of 0. This told me that the power had to be in the numerator.

    After making these observations, I determined that a cost of 10 resulted in a denominator of 6 as a baseline to go back and forth from. Fighter defense is 4/6 = .667; fighter attack is 3/6 = .5. Higher costs should have higher denominators and lower costs should have lower denominators. I figured out what the denominators had to be for each cost value to get the strength figures indicated. I then asked myself the question, how are we getting from the various costs to the denominators? With this I came up with my own equation that used a square and a variable to convert costs to denominators and fine tuned the variable (it turned out to be 4.08248). Next I applied this variable to all A&A powers and costs and verified that it resulted in the same strengths that VANN listed. Finally I used Excel to convert the resulting decimals into fractions and made observations about the numerators and denominators. It turned out that the numerators were always factors of 50, so I deduced that the strength was being multiplied by 50 and I changed all the fractions so that their numerators were multiples of 50. Then I looked at the pattern in the denominators, sorted largest to smallest, then I thought to divide them all by three and I got the familiar square pattern of 1,4,9,16 etc…

    Turns out that the decimal I came up with to get all the denominators is the square root of 50/3. This means you can divide any unit cost by this figure (roughly 4.08248) and then take the square to get a number to use in the denominator to come up with the VANN FORMULA strength, where the numerator is the unit’s power.

    As for why VANN decided to use 50 and 3, the best I could come up with is that the attack value of a tank in the original A&A game (power 3, cost 5) is 2 as a result, and this was probably used as some kind of benchmark.

  • '17 '16

    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 36
    4 / (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=

  • 2020 '19 '18 '17 '16 '15 '14 Customizer '13

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

    Mods remove this thread please.

  • '17 '16

    @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 36
    4 / (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.


  • 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.

  • '18 '17 '16

    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? :?

  • '17 '16

    @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.

  • '17 '16

    @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.


  • 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)

  • '17 '16

    @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


  • 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.

  • '17 '16

    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.

  • '17 '16

    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.

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