• 2007 AAR League

    I’m not sure if I ever mentioned this before, so I apologize if I did.

    The formula comes from my experience playing the old version, where I used buy almost entirely infantry (and no tanks).  I ran several simulations and came up with this formula.  Frankly, it’s really amazing that it works and that I just figured it out inductively.

    My sister actually proved this formula - but I don’t recall the proof.

    The Formula
    Power= (number of units)* (number of units)* (number you need to hit)

    IF attacker power = defender power THEN you have a 50% chance of winning. 
    This only works if you are using units of the same level of strength (both attacker and defender - eg the defender can use a mixture of artillery and infantry as they both defend on ‘2’).

    So this formula is useful for calculating your odds of winning.

    For instance
    A:  3 inf  - power = 331 = 9
    D: 2inf  - power= 222 =8
    So the attacker has an advantage.

    Frood Says
    A. survives: 50.7%  D. survives: 45.5%  No one survives: 3.7%

    A: 40 inf - power = 1600 (40401)
    D: 20 fig - power = 1600 (20204)
    A. survives: 48.2%  D. survives: 51.4%  No one survives: 0.4%

    Now using larger numbers helps:
    A: 80 inf
    D: 40 fig
    A. survives: 49.3%  D. survives: 50.5%  No one survives: 0.1%

    As you move to infinity units, it approaches 50% to 50%.  There is some kind of limit/calculus going on.  It seems to be approaching 50% from below (for the attacker, eg the attacker odds start at 48% and increase to 50% as the number of units increases) which is weird.  If I didn’t get timeouts on Frood when using 10,000 simulations, and if it allowed me to use more than 100 units, then I might have better luck proving whether the approach is random (and purely due to standard deviation) or from below.

    I think it’d be possible to create a formula for calculating odds in general, but I’m not a complete math genius.


  • So.

    About your sister . . .

    Is she hawt?

    Lemme look at that formula a bit.

    (edit) It sounds familiar somehow.  I think I did something similar.  (/edit)


  • @akreider2:

    The formula comes from my experience playing the old version, where I used buy almost entirely infantry (and no tanks).  I ran several simulations and came up with this formula.  Frankly, it’s really amazing that it works and that I just figured it out inductively.

    My sister actually proved this formula - but I don’t recall the proof.

    Actually, what you are talking about was proved YEARS ago by a certain Don Rae, who posted his strategic essays and even had his on bulletin board that was quite the scene until he flamed out over some poliitcal activism thing.  But I digress – Don coined the term “Infantry Push Mechanic” for the mathematically provable FACT that, with correct purchases, mostly involving infantry and transports, the Allies should win, every time.  It is because they, collectively, have economies large enough to simply overwhelm the purchasing power of the Axis.  Small 1-2 infantry differences in purchases in any one turn become magnified over 10-15 turns to the point where you literally roll right over the Axis fronts (usually Germany first).

    Here, don’t take my word for it – read for yourself:

    http://donsessays.freeservers.com/

    (These were posted circa 1999, BTW)

    The more interesting question, IMO, is how the IPM applies in Revised.  I think it’s still applicable, but tanks are definitely more valuable in Revised than in Classic.


  • Say you have two infantry attacking a fighter.

    “Power= (number of units)* (number of units)* (number you need to hit)”

    So you have 2 * 2 * 1 for the infantry, and 1 * 1 * 4 for the fighter.

    Actually, if you carry the battle out, first round result is:

    25/36 infantry miss, 1/3 fighter misses.
    25/36 infantry miss, 2/3 fighter hits.
    11/36 infantry hit, 1/3 fighter misses.
    11/36 infantry hit, 2/3 fighter hits.

    Since the first of those four leads to repetition, you have 50, 11, and 22 for the other respective possibilities, for a total of 83.  The 50, 11, and 22 are taken as the eventual outcomes, hence:

    50/83 1 infantry, 1 fighter
    11/83 2 infantry, 0 fighter
    22/83 1 infantry, 0 fighter

    The 1 infantry 1 fighter result is broken down into

    5/6 infantry misses, 1/3 fighter misses
    5/6 infantry misses, 2/3 fighter hits
    1/6 infantry hits, 1/3 fighter misses
    1/6 infantry hits, 2/3 fighter hits

    of which the first result is ignored for

    10/13 0 infantry, 1 fighter, multiply by 50/83 to get 500/8313 for this result
    1/13 1 infantry, 0 fighter, multiply by 50/83 to get 50/83
    13 for this result
    2/13 0 infantry, 0 fighter, multiply by 50/83 to get 100/83*13 for this result

    Along with the earlier

    11/83 2 infantry, 0 fighter
    22/83 1 infantry, 0 fighter

    there is a

    11/83 of 2 infantry, 0 fighter, or 143/8313
    22/83 + 50/83
    13 for 1 infantry, 0 fighter, or 206/8313
    500/83
    13 for 0 infantry, 1 fighter
    100/83*13 for 0 infantry, 0 fighter.

    The result is 349 for infantry surviving, 500 for fighter surviving, and 100 for mutual destruction.

    The formula I remembered was from a cost effectiveness formula that I wrote for a different game.  Basically, it’s like - since an infantry costs 3 IPC and a tank costs 5 IPC, when you have a number of infantry attacking a number of tanks (for example), your expected attack cost efficiency is 55attack value of infantry (the first 5 because you can get FIVE infantry for the cost of three tanks, and the second 5 because each time you destroy a tank, that’s a tank worth FIVE IPCs),  etc. etc. etc.


  • @Weekend:

    Actually, what you are talking about was proved YEARS ago

    Where are the formulas?

    I remember reading Don’s stuff too.

    I do not remember formulas.


  • Hey guys.

    For this type of calculation, you’re better off with “count equivalents”.

    Policy Paper #05 at the Caspian Sub:

    Count Equivalents (Combination Technique #1)
    Ok, so basic punch, count, and skew can tell you who generally has an edge.  What if the methods give different results, such as the offense having greater punch but the defense having a greater count?  This is where the tactics get tricky and we’ll have to cover most of the techniques in the Advanced Tactics paper.  However, there is one simple tool you can use without doing lots of math.  It is called the Count Equivalent (CE).

    The Count Equivalent is the equalizing ratio for one offensive attack value vs one defensive value.  More simply, it’s the ratio at which the sides kill each other at the same rate.  That means that if the dice treat each side equally, the battle would result in a mutual kill.  More in paper…

    http://games.groups.yahoo.com/group/Caspian_Sub/files/1PolicyPapers/

  • Moderator

    Just use a LowLuck type system.  It is easier and is close enough to provide an accurate baseline for attacks.

    Edit:  CrazyStraw snuck in a post with a C-Sub link.

    @Weekend:

    @akreider2:

    The formula comes from my experience playing the old version, where I used buy almost entirely infantry (and no tanks).  I ran several simulations and came up with this formula.  Frankly, it’s really amazing that it works and that I just figured it out inductively.

    My sister actually proved this formula - but I don’t recall the proof.

    Actually, what you are talking about was proved YEARS ago by a certain Don Rae, who posted his strategic essays and even had his on bulletin board that was quite the scene until he flamed out over some poliitcal activism thing. But I digress – Don coined the term “Infantry Push Mechanic” for the mathematically provable FACT that, with correct purchases, mostly involving infantry and transports, the Allies should win, every time. It is because they, collectively, have economies large enough to simply overwhelm the purchasing power of the Axis. Small 1-2 infantry differences in purchases in any one turn become magnified over 10-15 turns to the point where you literally roll right over the Axis fronts (usually Germany first).

    Here, don’t take my word for it – read for yourself:

    http://donsessays.freeservers.com/

    (These were posted circa 1999, BTW)

    The more interesting question, IMO, is how the IPM applies in Revised. I think it’s still applicable, but tanks are definitely more valuable in Revised than in Classic.

    Yeah, the tanks defend at 3 helps, but inf are still better.
    The game still revolves around the Axis as the aggressor.  If both sides never attack eventually the Allies would win, they have the greater economy.
    In order to counteract that, the Axis must either 1)  gain the economic adv or 2) gain a positional advantage.  Both would be great!   :-)

    But neither can be accomplished without attacking.  Once stacks start reaching 10+ units you reach a point where the aggressor must out spend the defender 4:3 in order to kill the stack.  Meaning if the Allies are just dumping Inf on the board the Axis need a pretty big econmoic adv to be able to kill the moster Allied stacks.
    This is where position and supply lines can come into play.  Good thing for the Axis is the Allies must spend a few turns on Navy and a few more to get troops into the appropriate theatre.

    In Classic, I used to play by the general guidleline (as the Axis) that I needed the IPC lead by the end of rd 3 (70+).

    In Revised, you’re right it is a bit different and I haven’t played enough games yet to get a real feel for generic targets for the Axis IPC’s.  But I think having the combined Axis IPC total ~80+ by the end of rd 3 and 4 is pretty darn good.
    However, I think the positional adv in Revised is far superior to that in Classic, so you don’t quite need the economic lead as the Axis, but it certainly helps.
    I say this b/c in revised you have Wrus and Kaz, both boarder Cauc and Mos (in Classic Japan could not boarder Kar without going through Mos) and that forces the Allies into a some very tough decisions on what to defend.

    On the flip side, if the Allies can successfuly inf stack in Wrus you’re in some big trouble.  I think Wrus is the new Kar.


  • @newpaintbrush:

    @Weekend:

    Actually, what you are talking about was proved YEARS ago

    Where are the formulas?

    I remember reading Don’s stuff too.

    I do not remember formulas.

    Okay, newpaintbrush, I am no mathematician, so I don’t mean “proof” in the strict mathematical sense you math geeks mean.  That said, this is not a new idea.  I am not criticizing akreider2 or anything – good for him (and everyone else) for figuring it out.  I am just pointing out this is not a new discovery or anything.

    DarthMaximus – interesting comments.  I’ve only played a few games of Revised, but I agree that West Russia is possibly THE most critical territory in the European theater (aside from capitals, of course  :-D) and possibly on the entire map.  I would say the Caucuses is a close second, only because it probably gets taken much easier than West Russia because, once Russia is in serious trouble, the Caucuses must be abandoned if Moscow is to be held.  All in all, a MUCH better map with far more tactical possibilities than in Classic.  It definitely changes your strategies from Classic, especially for the Allies.


  • @akreider2:

    … It seems to be approaching 50% from below (for the attacker, eg the attacker odds start at 48% and increase to 50% as the number of units increases) which is weird.

    It’s not really that weird.  I do not know the exact mathematical expression for it, but as you increase the numbers of each unit the odds will approach 50%.  You will never get exactly there, but you get closer and closer with more units.  Each unit either hits or it misses (two outcomes - there’s your 50%), and the more units you add to each side allow for more combinations that allow the hits and misses to equalize.  The hit percentage for the different units and the ratio between Attackers and Defenders becomes marginalized as the units on each side scale up to infinity.  It happens in your example more noticeably since you chose a battle that was fairly even to start with.  Theoretically, this is true for every battle…however you have to use extremely large numbers to begin to see it.

  • 2007 AAR League

    @akreider2:

    … It seems to be approaching 50% from below (for the attacker, eg the attacker odds start at 48% and increase to 50% as the number of units increases) which is weird.

    It’s not really that weird.

    What’s weird is that it approaches 50% from below (why isn’t the approach randomly distributed? or from above?).

    General note - I’m not claiming to have invented the infantry push by any means.  I’m claiming that i figured out this silly formula which some of us math geeks like =)


  • dont worry they post in jest.

  • 2007 AAR League

    I read the Caspian Sub Paper.  Looks like the same formula!

    I’m guessing that one could develop a formula that would deal with mixed unit battles.  Though I’m not sure where you’d start.  Could involve summations or combinations (I don’t have too much experience with either).  That would be amazing!

  • 2007 AAR League

    It makes sense that unit count would be squared in Aaron’s formula, because the # of units you have helps in 2 ways - it increases both the damage you can deliver and the damage you can sustain.


  • Just in case you’re interested, a similar phenomenon has been observed in real-life military strategy.  It’s called the Lanchester Square Law.  Basically, the power of an army is proportional to the square of its size.  Check out http://tinyurl.com/37npjl
    Of course, it works in real life for different reasons than it works in Axis & Allies!


  • SO in following Lanchester Square Law if I had 12 INF and they had 5 INF, 2 ARM and 1 FTR I take 12X12 and thats my square (144) How do I figure they other sides? Do I throw them all into one pile then sq. them? Do I sq. them by unit them add them? I mess around with it. More to follow……

    -LT04


  • I’m not sure how to get it to work. Even if I did I think I’d stick with my formula:

    Attacker:

    Need 6 INF for 1 hit
    Need 3 ART for 1 hit
    Need 2 ARM for 1 hit
    AA GUN N/A
    Need 2 FTR for 1 hit
    Need 3 Bomber for 2 hits
    Need 3 Battleship for 2 hits
    Need 6 CV for 1 hit
    TRN N/A
    Need 3 SUB for 1 hit
    Need 2 DST for 1 hit

    I’m sure you all see how I came up with this (In case you didn’t INF = 1 in 6 chance of a hit so 6 INF are needed for 1 hit.) I know its not by any means 100% so I figure how many hits I should average then subtract how many units will be left then check the surrounding area (like Don recommends) for any dead zones then I choose to attack or not.

    I’m sure there are better ways this one doesn’t require to much thinking so I like it so I can focus on more important matters in the game.

    -LT04

  • '17 '16

    Bumped.
    Please, Wittmann or Panther, move this thread into Player help.
    Thanks.

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