GURPS Combat Choices: Introduction

Over at Gaming Ballistic, +Douglas Cole has been ruminating about GURPS combat, and what options become available to you as you increase in skill (see here, here, and here). His posts do a good job of helping the GURPS combatant deal with the vast array of choices available on each turn.

And they make me want to run some numerical comparisons. If you've got a choice between a Rapid Strike and a Dual-Weapon Attack, which is better? Is it worth it to try for the brain? When does Deceptive Attack improve your chances of landing a blow?

There are literally millions[1] of ways to structure an attack. In forthcoming posts, I hope to use some calculations to help clarify when one option is better than another. For the time being, this post is here to goad me into following up on the idea, and as justification to write this ridiculously long footnote.

[1] Yes, really, millions. In fairly common melee combat situations, it's easy to get that high.

Let's suppose you're squared off against another fighter at a range of one  yard, both of you equipped with thrusting broadswords, both of you standing, neither of you equipped with any armor. Only Basic Set rules apply, but none of the rules marked as optional. You have Broadsword-14 and Karate-14, and you are not incurring any other penalties for such things and darkness or bad footing. You want to make a striking attack on your opponent this turn.

Let's consider armed attacks first. To make an attack, you must decide to Thrust or to Swing, and you must pick a target. The legitimate targets depend on your Thrust/Swing choice, so let's take a look at this handy table.

Target	Thrust	Swing
Torso	yes	yes
Vitals	yes	no
Skull	yes	yes
Eye	yes	no
Face	yes	yes
Neck	no benefit	yes
Groin	yes	yes
Weapon Arm	yes	yes
Other Arm	yes	yes
Leg	yes	yes
Weapon Hand	yes	yes
Other Hand	yes	yes
Foot	yes	yes
Weapon to Disarm	yes	yes
Weapon to Break	yes	yes
Whatever target presents itself	yes	yes

A thrusting attack to the neck grants no benefit compared to the much easier thrust to the torso, so I do not count it as a real choice (keeping in mind for later that there may be other situations in which a thrust to the neck makes sense). Attacking the weapon hand or arm has different results compared to attacking the other hand or arm, so I consider these different targets. Contrariwise, an attack on one leg or foot or the other has the same consequences, and I don't consider those as separate targets. So that makes 15 targets for a thrust attack and 14 targets for a swing attack.

Any attack includes the option of Deceptive Attack (B370), and because a Deceptive Attack is limited to an adjusted skill of at least 10, there are three options: no DA, DA at -2, and DA at -4.

Multiplying these three options by the above number of targets gives us 3 * 15 = 45 ways to make a Thrust, and 3 * 14 = 42 ways to make a Swing. Putting these together, there are 45 + 42 = 87 ways to make a basic armed attack. I will use the letter A (for "armed") to stand for this number in counting the number of ways to use this in a maneuver.

So next you must chose a maneuver. Let's start with the Attack maneuver. You can make this a simple attack, or opt for a Rapid Strike. If you choose a simple attack, there are A different ways to do that, or if you choose a Rapid Strike, you get A choices and then A choices again.  To put it into a formula:

Options for armed Attack manuever = A + A*A

  = 87 + 7569

  = 7656.

This scenario stipulates that you are attacking this turn, and you are only one yard from your opponent, so Do Nothing, Move, Change Posture, Aim, Evaluate, Feint, Move and Attack, All-Out Defense, Concentrate, Ready, and Wait do not enter into the picture. That leaves All-Out Attack in its various forms.

For three forms of All-Out Attack, the arithmetic is the same as Attack:

Options for armed All-Out Attack (Deternined) = A + A*A = 7656.

Options for armed All-Out Attack (Strong) = A + A*A = 7656.

Options for armed All-Out Attack (Feint) = A + A*A = 7656.

For All-Out Attack (Double), either of the attacks can be at any target, and either attack (but not both) can be replaced by a Rapid Strike. That means you get either two or three picks from A attacks.

Options for armed All-Out Attack (Double) = A*A + A*A*A

  = 7569 + 658,503

  = 666,072.

Adding these all together comes to a splendidly pallindromic 696,696 possibilities for making an armed attack this turn. But what about unarmed attacks?

Sure, you're holding a sword, but it's a free action to drop it (B364), or you can hold onto it and attack with your off hand. You can then take a step into close combat and attack with fists, or stay where you are and attack with kicks, or both.

Punching is a thrust attack only and does Crushing damage. The eyes and vitals aren't legitimate hit locations for these punches, so we are left with 14 choices for hit location. As with armed attacks, you have the three options of no Deceptive Attack, DA at -2, or DA at -4. Multiplying those two together gives 3 * 14 = 42 ways to deliver a punch, which I will represent with the letter P.

With kicks, things are slightly different. Kicks are made at -2, and Deceptive Attack limits your adjusted skill to 10 or better, so you can't do a Deceptive Attack at -4, and your two choices are no DA or DA at -2. Multiplying that by the 14 legitimate targets gives 2 * 14 = 28 ways to deliver a kick, which I will represent with the letter K.

In cases where you can either punch or kick, you have to total of P + K = 42 + 28 = 70 ways to make an unarmed attack, which I will represent with the letter U. (I will need to introduce cases where you can kick but not punch later.)

The accouting here looks much the same as the accounting for an armed attack. An Attack maneuver can be either a simple attack with U choices, or a Rapid Strike with U times U choices.

Options for unarmed Attack Maneuver = U + U*U

  = 70 + 4900

  = 4970.

The arithmetic is just the same for three forms of All-Out Attack:

Options for unarmed All-Out Attack (Deternined) = U + U*U = 4970.

Options for unarmed All-Out Attack (Strong) = U + U*U = 4970.

Options for unarmed All-Out Attack (Feint) = U + U*U = 4970.

All-Out Attack (Double) is, again, where the big numbers come in.

Options for unarmed All-Out Attack (Double) = U*U + U*U*U

= 4900 + 343,000

= 347,900.

So the total number of ways to make unarmed attacks is 367,780.

We're not done yet, though. What about mixing armed and unarmed attacks in the same maneuver? For maneuvers other than All-Out Attack (Double), this is only possible with a Rapid Strike. Furthermore, the order matters. The scenario has you starting 1 yard away from your opponent. If you step into close combat to deliver a punch, you cannot then attack with your sword for a second attack. You can, however, kick at range 1 and then make an armed attack. So your options for an Attack maneuver featuring a Rapid Strike with both armed and unarmed strikes are Armed followed by Unarmed or Kick followed by Armed.

Options for mixed armed/unarmed Attack maneuver = A*U + K*A

  = 87 * 70 + 28 * 87

  = 6090 + 2436

  = 8526.

The first three All-Out Attack options are again the same.

Options for mixed armed/unarmed All-Out Attack (Deternined) = A*U + K*A = 8526.

Options for mixed armed/unarmed All-Out Attack (Strong) = A*U + K*A = 8526.

Options for mixed armed/unarmed All-Out Attack (Feint) = A*U + K*A = 8526.

An All-Out Attack (Double) without a Rapid Strike is also the same.

Options for mixed armed/unarmed All-Out Attack (Double), no Rapid Strike = A*U + K*A = 8526.

But for an All-Out Attack (Double) with a Rapid Strike, things get yet more complicated. With three strikes, which may be either armed or unarmed, there are eight possibilities:

Armed/Armed/Armed,
Armed/Armed/Unarmed,
Armed/Unarmed/Armed,
Armed/Unarmed/Unarmed,
Unarmed/Armed/Armed,
Unarmed/Armed/Unarmed,
Unarmed/Unarmed/Armed, and
Unarmed/Unarmed/Unarmed.

The first and last of these eight aren't mixed attacks, so they've already been accounted for in the purely armed or unarmed sections above. That leaves six possibilities. These are further constrained by the requirement that if an unarmed attack is followed by an armed attack, the unarmed attack has to be a kick.

So these are the rest of your choices.

Options for mixed armed/unarmed All-Out Attack (Double) with Rapid Strike
  = A*A*U + A*K*A + A*U*U + K*A*A + K*A*U + K*K*A
  = 529,830 + 211,932 + 426,300 + 211,932 + 170,520 + 68,208
  = 1,618,722.

Adding up all of these mixed armed/unarmed attacks gives us 1,661,352.

Adding that to the totals for purely armed and purely unarmed brings us to

696,696 + 367,780 + 1,661,352 = 2,725,828

total ways to make an attack.

Are we done now? Well, we could go on. I stipulated making striking attacks for this scenario, but of course you also have the option of grappling. Or you could bite instead of punching or kicking. You could also use the Pull your punches rule from B401, which would increase the number of possibilities quite a bit, depending on your Strength.

And then if you begin adding in optional rules such as Dual-Weapon Attack or Extra Effort in Combat, the possibilities increase again. And if you add in the options from GURPS Martial Arts...I think you get the idea. You've got millions of possibilities in even quite simple situation. Millions, at least.