GURPS (3rd Ed) Combat Notes

The following are some archived posts on combat in Third Edition GURPS.


Statistics on a Knight vs Knight Battle

From: Ian Harding (paperweightpress@argonet.co.uk)
Subject: Statistics on knights v knights 
Newsgroups: rec.games.frp.gurps
Date: 2002-09-01 19:15:52 PST 

Following on from the thread "GURPS Sucks!" I've done some statistical analysis of knight v knight combat. This is a long post but I think the results are worth it. They may surprise some people.

All the calculations are done using the basic combat rules but with stunning, shock, knockdown and picks getting stuck ignored. I think that's how the average newbie GM would run his first fight. Replacing defence rolls with quick contests of skill is in advanced combat so I've ignored that option. The calculations have been done using a BASIC program which takes the details of two characters, including their weapons and strategies, and simulates 100 000 combats. The ratio of wins and the average duration of the combat are then calculated. Characters with identical basic speeds take the first strike in 50 000 combats each. I'm reasonably happy that the program works correctly but if you think any of the results are wrong please play out the combat a few times (the more the better) and see if your results contradict the program's.

Here's a 100pt knight -

 ST 14             45pts
 DX 15             60pts
 IQ  8            -15pts
 HT 10              0pts

Advantages
 Very wealthy      30pts (starting wealth $20,000)

Disadvantages
 Chivalric code
  of honour       -15pts
 Honesty          -10pts
 Truthfulness     - 5pts
 Overconfidence   -10pts

Quirks
 5 quirks         - 5pts

Skills
 Broadsword-17            -1 due to helm, -2 due to large shield
  P/A DX+2          8pts   = Broadsword-14
 Shield-17                -1 due to helm = Shield-16
  P/E DX+2          4pts
 Riding (horse)-16
  P/A DX+1          4pts
 Lance-17                 -1 due to helm, -2 due to large shield = Lance-14
  P/A DX+2          8pts
 Savoir-Faire-8
  M/E IQ            1pt

Total             100pts

Equipment
 Heavy plate     $6000  110 lbs
 Chainmail        $550   45 lbs
 Large shield      $90   25 lbs
 Broadsword       $500    3 lbs
 Heavy warhorse  $5000
 Lance             $60   (6 lbs, only when mounted)
 Barding             ?    ?

 Total          $12200  183 lbs

Calculated stats
 Basic speed = (DX+HT)/4 = (15+10)/4 = 6.25
 Encumberance: ST*12 < 183lbs < ST*20 so encumberance=4
 Move=2
 Thrust damage = 1d
 Swing damage = 2d

Passive defenses
 Heavy plate = 4
 Large shield = 4

 Total PD=8

Active defenses
 Parry (broadsword) = 14/2 = 7
 Dodge = 2
 Block = 16/2 = 8

DR
 Heavy plate = 7
 Chain mail under plate = +2

 Total DR=9

Weapons
 Broadsword cr  thr+1 1d+1
            cut sw+1  2d+1

The penalty for all the armour this knight carries is that if a fight lasts more than ten rounds he will lose five fatigue points after the fight. His effective strength is then 9 and since 183lbs > (20*9)lbs he can't move more than a few feet without having to stop for a rest. He will need to regain at least one point of fatigue before he can move normally. If another foe appeared before he had rested he would be in serious trouble. (As an aside, would you let him regain fatigue whilst riding at a walk or only from complete rest? Riding at a walk is not particularly strenuous so would regaining one fatigue point every fifteen or twenty minutes be reasonable?)

Suppose this knight fights his twin brother. The obvious choice, as pointed out in the thread, would be to joust. A lance does 5d+5 impaling damage when the mount is at full speed which will cleave through DR9 easily. Minimum damage done by a hit is 2*(10-9)=2 and average damage is 2*(22.5-9)=27. An average hit will leave the recipient needing to make two HT rolls to stay alive.

However, if the knights meet on foot they will have to thrash it out with swords. If both knights choose 'Attack' every round the fight will last on average 155 rounds.

Summarised results of the simulation:

Wins by A/Wins by B = 1.00154306 

Percentage of bouts lasting
   1 to  10 rounds =  0.322%
  11 to  20 rounds =  1.211% : Costs five fatigue points
  21 to  30 rounds =  1.996%
  31 to  45 rounds =  4.385%
  46 to  60 rounds =  5.594%
  61 to 120 rounds = 28.290%
 121 to 180 rounds = 25.113% : Costs extra fatigue points at GM's discretion
 181 to 240 rounds = 16.163%
 241 to 300 rounds =  9.131%
 301 to 360 rounds =  4.467%
 361 to 420 rounds =  1.970%
 421 to 480 rounds =  0.835%
 481 to 540 rounds =  0.330%
 541 to 600 rounds =  0.133%
 601 to 660 rounds =  0.041%
 661 to 720 rounds =  0.011%
 721 to 780 rounds =  0.006%
 781 to 840 rounds =  0.001%
 841 to 900 rounds =  0.001%

What effect does strategy have? I have run the simulation with six different strategies.

  1. 'Attack'
  2. 'Feint' and 'Attack' in alternate rounds
  3. 'All out attack: damage+2'
  4. 'All out attack: two attacks'
  5. 'All out attack: skill+4'
  6. 'All out attack: feint then attack'

The results are:

    Average number of rounds

                   Knight B
       1     2     3     4     5     6

  1 155.1 180.3  22.6  22.9  22.8  23.1

K 2 180.3 221.0  39.0  38.5  39.4  40.8
n
i 3  22.6  39.0   7.5   8.3   9.3   9.4
g
h 4  22.9  38.5   8.3   9.6  11.5  11.6
t
  5  22.8  39.4   9.3  11.5  15.6  16.0
A  
  6  23.1  40.8   9.4  11.6  16.0  16.3
   Ratio of (wins A)/(wins B)

e.g. for Knight A using 1 and Knight B using 2 the result is
Wins by A = 63983 wins by B = 35935 draws = 80 (draw if both 
passed out/died in the last round of combat)
  ratio=63983/35935=1.78

                   Knight B
      1     2     3     4     5     6

  1  1.00  1.78 17.75 14.67 22.93 45.87

K 2  0.56  1.00  5.57  4.72  6.11 12.40
n
i 3  0.06  0.18  0.99  1.91  6.02  7.04
g                1.01
h 4  0.07  0.21  0.52  1.00  3.26  3.80
t
  5  0.04  0.16  0.17  0.31  0.99  1.08
A                            1.01
  6  0.02  0.08  0.14  0.26  0.92  1.01
                                   0.99

(When both knights are using the same strategy the number of wins by A should equal the number of wins by B over an infinite number of bouts. However in a limited number of bouts (even as many as 100 000) the number of wins may not be equal, just as if you tossed a coin ten times you would necessarily get five heads and five tails. When the ratios were not equal to 1 to two significant figures I have given the ratios A/B and B/A. So for A using 3 v B using 3 the ratio (wins A)/(wins B)=0.99 to 2s.f.)

Consider the results. If you want a quick combat the obvious answer is for both combatants to choose 'All out attack: damage+2'. However, look at the win ratios. All the win ratios above the diagonal are greater than one. This means that a knight using strategy 1 will probably beat a knight using any other strategy. A knight using strategy 2 will probably beat one using any of 3,4,5 or 6 and so on. Therefore the best choice of strategy is 1 - 'Attack'. Looking at the average times, expect to take 155 rounds or more to resolve the combat. This is probably quite realistic. Knights used their shields in battle and it might take an average of two and half minutes for one to bash the other into unconsiousness (though I suspect the winner will be exhausted even if he hasn't been hit very much).

Note that feinting is absolutely pointless against someone doing all-out attacks yet a knight alternating between feints and ordinary attacks is still the favourite against any all-out attack. Even though he is effectively wasting every second turn the action of blocking instead of relying on PD is enough to tip the scales in his favour. Berserkers beware!

A further analyis considers the effects of picks and warhammers. Five different weapon/strategy combinations were considered for the knight above: 1) Broadsword and shield - 'All-out attack: two attacks' if the opponent's weapon is unready otherwise 'Attack' 2) Broadsword and shield - 'All-out attack: damage+2' if the opponent's weapon is unready otherwise 'Attack' 3) Pick and shield - 'Attack' if pick is ready otherwise 'Ready' 4) Pick and shield - 'All-out attack: damage+2' if pick is ready otherwise 'Ready' 5) Warhammer - 'All-out attack: damage+2' if warhammer is ready otherwise 'Ready' Results:

Average number of rounds

                   Knight B
       1     2     3     4     5

K 1 155.2 155.0  52.7  20.9  11.4
n
i 2 155.0 155.1 135.7  16.2   9.5
g                
h 3  52.7 135.7 222.7  83.8  18.2
t
  4  20.9  16.2  83.8  12.3   7.1
A 
  5  11.4   9.5  18.2   7.1   3.5

Ratio of (wins A)/(wins B)

                   Knight B
      1     2     3     4     5

K 1  0.99  0.99 23.28 12.43  4.12
n    1.01  
i 2  1.01  1.00  3.44 16.78  5.37
g                
h 3  0.04  0.29  0.99  1.33  1.73
t                1.01
  4  0.08  0.06  0.75  1.00  1.46
A 
  5  0.24  0.19  0.58  0.68  1.00

As you can see the lower attack rate of picks and warhammers negates their damage advantage. Using a warhammer particularly disadvantages the user because he no longer has a shield. All he has is PD4 and dodge 2 - a total defence of 6! The final conclusion: combination 1 (Broadsword and shield - 'All-out attack: two attacks' if the opponent's weapon is unready otherwise 'Attack') is the best bet.

I suspect that most people would not have come to this conclusion without doing the maths. Hence this post.

I think that the original point of the "GURPS Sucks!" thread is quite valid. Using the basic combat rules from Basic the optimal strategy for this knight (who could reasonably be created by a newbie) produces a very tedious combat. An alert GM, seeing that defense rolls were the problem, might force all the combatants to use all-out attacks to resolve the situation more quickly but he might not. Bearing in mind that Basic warns about the lethality of combat (which in many cases it is) one would not expect a fight to last 155 rounds on a first reading. Extending Basic with notes, both for the GM and the player, on combat describing pitfalls, like berserk being suicidal and heavy armour slowing down more than just the characters, would be a really good idea.

Since it would be a bad idea to change Basic too much because of the page references from other sourcebooks and since adding extra pages would push the price up I wonder if adding a CD-ROM to the hypothetical fourth edition would work. All the rules would be in a book as before because you don't want to have to lug a computer to every game session but all sorts of goodies could be put on the CD-ROM. Things I can think of are:

(I've posted this paragraph in a separate thread "Suggestion for Basic 4th edition (from GURPS Sucks!)")


John H. Kim <jhkim-at-darkshire-dot-net>
Last modified: Thu Jan 25 09:30:28 2007