Analyzing Warlords II Battles



Written by Bob Heeter, with contributions from Glen Barnett and others.

Last Revised June 28, 1998

While the Military Advisor is useful, sometimes he just doesn't give you enough information (especially if you want to know the odds that your *enemy* will win if he/she attacks *you*!). And for cheat-free play-by-email games, it's important to keep your opponents honest and not let them win battles against incredible odds by simply reverting a gazillion times. With this in mind, we have analyzed the Warlords combat system, and learned how to analyze battles. A number of resources for doing this are listed below. WarBOT in particular is absolutely essential to the Warlords II World Tournament, and the Battle Bonuses documentation for it is very helpful for understanding how the bonuses work in any army set. An upcoming version of WarBOT should support arbitrary army sets, and then it will be useful for all Warlords games.

WarBOT, the ultimate Warlords Battle Odds Tool:

  1. If you email warlords@pixgen.com and put one of the following commands in the Subject: line, WarBOT will be emailed to you as (large!) attached file:
  2. If large email attachments are a problem for you, get WarBOT from the Web via http://www.pixgen.com/elam/warlords/
  3. If you have downloading problems, email Elam Birnbaum, elam@madness.net
  4. Alternate Download Site

  • Mathematica Source Code for Battle Calculations (old)

  • Complete documentation on Battle Bonuses.

    Each of these allows you to calculate the odds of victory for any set of attacker and defender strengths. (WarBOT will also figure out all the bonuses of all the units, and you just need to know which units are in the battle, what the terrain is, and whether units are blessed, carrying items, or otherwise enhanced.

    Additional Information below is useful for gaining intuition about how the battle odds will work out in a given situation.

    The Odds of Victory: A Table for One-on-One Combat

    Table shows percent chance that 1 attacker kills 1 defender

    (Note - this is normal combat - odds for Intense Combat are different.)

    ------------------------------------------------------------------------
    Def. | Attacker Strengths -->
    Str. |  1    2    3    4    5    6    7    8    9   10   11  12  13  14 
    -----|------------------------------------------------------------------
     1   | 50.  76.  87.  92.  95.  97.  98.  98.  99.  99. 100 100 100 100  
     2   | 24.  50.  67.  77.  84.  89.  92.  94.  96.  97.  98  99  99  99
     3   | 13.  33.  50.  63.  72.  79.  85.  89.  92.  94.  96  97  98  99
     4   | 8.0  23.  37.  50.  61.  69.  76.  82.  86.  90.  92  94  96  97
     5   | 5.1  16.  28.  39.  50.  59.  67.  74.  80.  84.  88  91  94  96
     6   | 3.3  11.  21.  31.  41.  50.  58.  66.  73.  78.  83  87  91  94
     7   | 2.2  7.7  15.  24.  33.  42.  50.  58.  65.  72.  78  83  87  91
     8   | 1.5  5.5  11.  18.  26.  34.  42.  50.  58.  65.  71  77  83  87
     9   | 1.1  3.9  8.3  14.  20.  27.  35.  42.  50.  57.  65  71  78  83
    10   | 0.7  2.8  6.1  10.  16.  22.  28.  35.  43.  50.  57  65  72  78
    11   | 0.5  2.0  4.4  7.7  12.  17.  22.  29.  35.  43.  50  58  65  73
    12   | 0.3  1.4  3.1  5.5  8.7  13.  17.  23.  29.  35.  42  50  58  66
    13   | 0.2  0.9  2.1  3.9  6.2  9.2  13.  17.  22.  28.  35  42  50  58
    14   | 0.1  0.6  1.4  2.6  4.3  6.5  9.2  13.  17.  22.  27  34  42  50
    15   | 0.1  0.4  0.9  1.7  2.8  4.3  6.2  8.7  12.  16.  20  26  33  41
    ------------------------------------------------------------------------
    (Note - all values were rounded off to 2 digits. 100% is really >99.5%)
    

    Rules of Thumb

    From the table above, one can observe a few things. Define A = strength of attacker, D = strength of defender.

    More Rules of Thumb

    (The following information was contributed by Glen Barnett. If anyone has an idea for a better way to format the table, let me know.)

    Table of relative stack values

    In the list below, a single value, such as 3, represents a single army. A value like 1^3 means a stack with 3 units of strength 1.

    On this list, stronger units are toward the bottom, weaker units near the top.

    Stacks represented on each line are of roughly equal "strength", with adjacent units within 2 percent of a 50/50 chance, and the slightly stronger units to the right. Units on the same line, but not immediately adjacent may be as much as 5% off a 50/50 chance. Units on separate lines are typically further apart in relative strength, though they could be as close as a 53/47 split. For example, the line "1^4 2^2 4" should be read as: "Two 2's is close in strength to four 1's or a single 4, but is slightly stronger than the four 1's and slightly weaker than the single 4."

    From this, a good guess at the relative strength of other stacks can be made - for example, a stack with three 3's and four 4's will lie between seven 3's and seven 4's, and so probably between a single 12 and 13, possibly around the strength of six 4's. In fact it lies somewhere between six 4's and a 13.

    The single unit strengths are all three lines apart, but the gaps are not "equivalent".

                Single
                unit
                  1
    
    
                  2 1^2
    
    
                  3 1^3
    
    
         1^4 2^2  4
    
         1^5
                  5
         1^6 2^3    3^2
    
         1^7      6
    
         1^8 2^4
                  7 4^2
                    3^3
    
                  8     2^5
                            5^2
                        2^6
             3^4  9 4^3
                        2^7
         6^2
                 10 3^5 2^8
    
             5^3    4^4
         7^2     11 3^6
    
                    3^7
     4^5 6^3 8^2 12         5^4
                    3^8
                    4^6
     9^2 7^3     13         5^5
         6^4        4^7
    
     8^3 5^6 4^8 14
         7^4 6^5
                    9^3
             6^6        8^4 7^5
                    9^4     7^6
                        8^5
                            7^7
                        8^6
                    9^5
                            7^8
                        8^7
                    9^6
                        8^8
                    9^7