Feint as a combat option

This subject came up in a thread on the GURPS forums: if a Feint can take the place of an attack in either part of an All-Out Attack (Double) or any part of a Rapid Strike, why not treat it as a combat option rather than a maneuver?

Here's the rules as they stand now. GURPS Martial Arts, p. 97, says

The GM should be generous about substituting feints for attacks, too. An All-Out Attack (Feint) is just an All-Out Attack (Double) that trades the first attack for a feint, so there's no reason why a fighter couldn't reverse the order: attack first and then feint to benefit a later attack. Other alternatives include using All-Out Attack (Determined) to feint at +4 and All-Out Attack (Long) to feint a distant foe.

And on Martial Arts, p. 127, discussing multiple attacks:

A fighter can trade melee attacks for feints (see Feint, p. B365) on a one-for one basis. Modifiers for maneuvers and attack options do affect skill for this purpose; e.g., a feint during a Rapid Strike is at -6. A warrior can use Move and Attack to "Move and Feint," but at -4 and with a skill limit of 9, it's self-defeating.

So we're most of the way there already. What remains is to go through the maneuvers and attack options to see what's compatible with the Feint attack option, and to figure out how opting for a Beat or a Ruse would make things any different.

Already, by RAW, these maneuvers are compatible with Feint:

Attack
All-Out Attack (Double)
All-Out Attack (Determined)
All-Out Attack (Long)
Move and Attack -- this is "self-defeating" with a skill cap of 9, but see Heroic Charge, below

And Rapid Strike is already compatible by RAW.

Here are my proposals for handling the rest:

Maneuvers

All-Out Attack (Strong): by RAW, an ordinary AOA (Strong) maneuver gets you +2 to damage, or +1 per die if that is better. This is approximately equivalent to +2 to Strength. I don't how increasing the power of a Feint would help to fool your opponent, so I say this one applies only to a Beat (MA p. 100).

Committed Attack (Determined): +2 to your Feint roll. You are penalized on Active Defenses as usual. This may not be your best option if you are a single-weapon fighter and you rely on your Parry for defense, but it could be effective for a two-weapon or unarmed fighter.

Committed Attack (Strong): Only available with a Beat. You get +1 to your roll.

Defensive Attack: you take -2 to your Quick Contest roll, and gain all the benefits of Defensive Attack as usual.

Wait: a Feint is not compatible with a Stop Hit (MA p. 108).

Combat Options

Deceptive Attack: For every -2 penalty on the Quick Contest roll you take, your opponent loses an additional -1 to defenses on your following attack. If you do not win the Quick Contest, your Deceptive Attack gains you nothing. You can also use Deceptive Attack on a Defensive Feint to impose a penalty to your opponent's next attack roll, but this will seldom be worthwhile.

Hit Locations: you gain nothing by targeting a hit location with a Feint, so this option is not so much incompatible as useless.

Dual-Weapon Attack: You may apply the Feint option to either half of a Dual-Weapon Attack. If the first attack is a Feint, only the remaining attacks in this round benefit from it.

Telegraphic Attack: Not compatible with Feint.

Slam and Shove: Not compatible with Feint.

Defensive Grip, Reversed Grip, Tip Slash: Compatible with Feint.

Extra Effort: Flurry of Blows, Giant Step, Great Lunge, and Heroic Charge are all compatible with Feint. In fact, Heroic Charge is about the only way to make a Feint work with a Move and Attack maneuver. Since a Feint does not make a weapon unready, Rapid Recovery is irrelevant.

Beats and Ruses: Except as noted above, Beats and Ruses are handled just like Feints.

I don't think there are any other problem combat options. Please let me know if you think I've missed anything.

GURPS Combat Choices: Deceptive Attack and Telegraphic Attack

Update: Martin Leuschen pointed out an error in the table, since fixed. My thanks to Martin for keeping my honest.

Patric Halter over at Renovating the Temple beat me to it with this post, but here is my take on Deceptive Attack and Telegraphic Attack.

In GURPS combat, Deceptive Attack is a combat option that lets you penalize your opponent's defense by -1 for every -2 you take to your attack roll. The only limits are your GM's indulgence, and a minimum final skill level of 10.

Telegraphic Attack, on the other hand, is a combat option that goes in the other direction: you can add +4 to your attack skill, but your opponent's defense increases by 2. Unlike DA, you don't get to pick how much Telegraphic Attack you want to use: it's +4/+2 or nothing. Also, TA doesn't affect your chances of scoring a critical hit. To determine if you got a critical, you use the skill you had before adding the TA bonus.

So, when do you want to use Telegraphic Attack? When do you want to use Deceptive Attack, and how much? Here's a handy table I made.

	Defense
Attack	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
3	TA	TA	TA	TA	TA	TA	TA	TA	TA	TA	Flee	Flee	Flee	Flee	Flee	Flee	Flee	Flee
4	TA	TA	TA	TA	TA	TA	TA	TA	TA	TA	TA	Flee	Flee	Flee	Flee	Flee	Flee	Flee
5	TA	TA	TA	TA	TA	TA	TA	TA	TA	TA	TA	Flee	Flee	Flee	Flee	Flee	Flee	Flee
6	TA	TA	TA	TA	TA	TA	TA	TA	TA	TA	TA	Flee	Flee	Flee	Flee	Flee	Flee	Flee
7	TA	TA	TA	TA	TA	TA	TA	TA	TA	TA	Hold	Hold	Flee	Flee	Flee	Flee	Flee	Flee
8	TA	TA	TA	TA	TA	TA	TA	TA	TA	TA	Hold	Hold	Hold	Flee	Flee	Flee	Flee	Flee
9	TA	TA	TA	TA	TA	TA	TA	TA	Hold	Hold	Hold	Hold	Hold	Flee	Flee	Flee	Flee	Flee
10	TA	TA	TA	TA	TA	TA	TA	Hold	Hold	Hold	Hold	Hold	Hold	Flee	Flee	Flee	Flee	Flee
11	TA	TA	TA	TA	TA	TA	Hold	Hold	Hold	Hold	Hold	Hold	Hold	Flee	Flee	Flee	Flee	Flee
12	TA	TA	TA	TA	Hold	Hold	Hold	Hold	Hold	Hold	DA 1	DA 1	DA 1	DA 1	Flee	Flee	Flee	Flee
13	TA	TA	Hold	Hold	Hold	Hold	Hold	Hold	Hold	DA 1	DA 1	DA 1	DA 1	DA 1	Flee	Flee	Flee	Flee
14	Hold	Hold	Hold	Hold	Hold	Hold	Hold	DA 1	DA 1	DA 1	DA 1	DA 2	DA 2	DA 2	DA 2	Flee	Flee	Flee
15	Hold	Hold	Hold	Hold	Hold	Hold	Hold	DA 1	DA 1	DA 1	DA 2	DA 2	DA 2	TA	TA	TA	Hold	Hold
16	Hold	Hold	Hold	Hold	Hold	Hold	Hold	Hold	DA 2	DA 2	DA 2	DA 2	Hold	Hold	Hold	Hold	Hold	Hold
17	Hold	Hold	Hold	Hold	Hold	DA 1	DA 1	DA 1	DA 2	DA 2	DA 3	DA 3	Hold	Hold	Hold	Hold	Hold	Hold
18	Hold	Hold	DA 1	DA 1	DA 1	DA 1	DA 1	DA 1	DA 1	DA 3	DA 3	DA 3	DA 3	DA 1	DA 1	Hold	Hold	Hold
19	Hold	Hold	DA 1	DA 1	DA 1	DA 1	DA 2	DA 2	DA 2	DA 3	DA 3	DA 3	DA 4	DA 1	DA 1	Hold	Hold	Hold
20	Hold	Hold	DA 1	DA 2	DA 2	DA 2	DA 2	DA 2	DA 2	DA 2	DA 4	DA 4	DA 4	DA 4	DA 2	DA 2	Hold	Hold
21	Hold	Hold	DA 1	DA 2	DA 2	DA 2	DA 2	DA 3	DA 3	DA 3	DA 4	DA 4	DA 4	DA 5	DA 2	DA 2	Hold	Hold
22	Hold	Hold	DA 1	DA 2	DA 3	DA 3	DA 3	DA 3	DA 3	DA 3	DA 3	DA 5	DA 5	DA 5	DA 5	DA 3	DA 3	Hold
23	Hold	Hold	DA 1	DA 2	DA 3	DA 3	DA 3	DA 3	DA 4	DA 4	DA 4	DA 5	DA 5	DA 5	DA 6	DA 3	DA 3	Hold
24	Hold	Hold	DA 1	DA 2	DA 3	DA 4	DA 4	DA 4	DA 4	DA 4	DA 4	DA 4	DA 6	DA 6	DA 6	DA 6	DA 4	DA 4
25	Hold	Hold	DA 1	DA 2	DA 3	DA 4	DA 4	DA 4	DA 4	DA 5	DA 5	DA 5	DA 6	DA 6	DA 6	DA 7	DA 4	DA 4
26	Hold	Hold	DA 1	DA 2	DA 3	DA 4	DA 5	DA 5	DA 5	DA 5	DA 5	DA 5	DA 5	DA 7	DA 7	DA 7	DA 7	DA 5
27	Hold	Hold	DA 1	DA 2	DA 3	DA 4	DA 5	DA 5	DA 5	DA 5	DA 6	DA 6	DA 6	DA 7	DA 7	DA 7	DA 8	DA 5
28	Hold	Hold	DA 1	DA 2	DA 3	DA 4	DA 5	DA 6	DA 6	DA 6	DA 6	DA 6	DA 6	DA 6	DA 8	DA 8	DA 8	DA 8
29	Hold	Hold	DA 1	DA 2	DA 3	DA 4	DA 5	DA 6	DA 6	DA 6	DA 6	DA 7	DA 7	DA 7	DA 8	DA 8	DA 8	DA 9
30	Hold	Hold	DA 1	DA 2	DA 3	DA 4	DA 5	DA 6	DA 7	DA 7	DA 7	DA 7	DA 7	DA 7	DA 7	DA 9	DA 9	DA 9

Caveat: this table only considers Deceptive Attack and Telegraphic Attack. If you also considered Rapid Strike, Dual Weapon Attack, hit locations, or other combat options, things would change a lot. But that will have to wait for later.

The attacker's skill runs along the side, and the defense runs across the top. The entry for a given skill and defense shows your best choice. "Hold" means that you can't improve your chances with either a Deceptive Attack or a Telegraphic Attack; you're already at the best level. "Flee" means that no matter what you do, your attack is going to be worth less than zero. Yes, I mean that on your own turn, you are more likely to get hurt than to hurt your opponent. Might as well run away.

You probably don't want to waste time looking things up on this table all the time, so let me try to reduce this information to a few rules of thumb.

1. Don't use Deceptive Attack if your opponent's defense is already at 3 or 4. 
2. Don't use Deceptive Attack unless you can get your opponent's defense below 13.
3. If the sum of your skill and your opponent's defense is above 24, try to bring it down to the range of 22 to 24. Each level of DA will reduce the sum by 3.
4. If the sum of your skill and your opponent's defense is 19 or below, use Telegraphic Attack.
5. But don't use Telegraphic Attack if your skill is above 13.
6. If your opponent's defense beats your skill by 8 or more, don't even try making an attack this turn. 

These rules don't get you optimal results in all cases, but they cover most of the chart pretty well.

For those of you interested in all the math behind the scenes, for now I'll just say that in this table, I considered the value of a normal hit to be 1, and discounted it by the probability that it gets past the defense. Then I valued a critical hit on the attack at 1.3, a critical failure on attack at -1.5, and a critical failure on defense as worth an extra 0.1. A critical success on defense imposes a critical failure on the attacker, and so is also worth -1.5.

These numbers are somewhat arbitrary, and anyone could reasonably question them, but after fiddling around with various values, I find that they don't alter the results very much.

A more detailed explanation of the number-crunching behind the chart will have to wait for another day.

GURPS Combat Choices: Thrust or Swing?

When a GURPS combatant is deciding what to do in an attack, one of the most basic decisions is whether to Thrust or Swing. In some cases, this is a straightforward decision, either because the weapon's listing doesn't give you any options (brass knuckles, for instance), or because Thrust and Swing attacks do the same kind of damage, but Swings do more (a club, for instance).

But for many weapons, you face a choice between a Thrust for Impaling damage and a Swing for Cutting damage. The Thrust does less damage, but Impaling gets a x2 wounding modifier, versus a x1.5 modifier for Cutting. When does the greater damage for a Swing outweigh the smaller wounding modifier?

A few days ago, I posted a table showing the thrust and swing damage from all weapons with swing-cutting damage and thrust-impaling damage. Grouped according to their damage characteristics, these weapons fall into 23 classes (which number I attribute the the Illuminati at work). In the table below, I've listed each weapon class, with entries for each level of Strength from 5 to 20. The entries show the expected benefit in injury from making a thrusting attack versus a swinging attack. Negative numbers, with a blue background, mean that you are better off thrusting than swinging. Positive numbers, with a yellow background, mean that it's a better bet to swing. Remember, this is injury, not damage. The numbers in the chart reflect what you get after applying the wounding modifier.

	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Katar	-2	-2	-3	-3	-4.01	-3.51	-4.33	-3.33	-4.39	-3.11	-3.72	-2.25	-3.47	-2	-2	-2
Pata	-3.51	-3.51	-4.33	-4.33	-5.33	-4	-4.5	-3	-4.25	-2.75	-3.25	-1.75	-3	-1.5	-1	0.5
Large Katar-LT	-2.67	-2.67	-3.51	-3.51	-4.33	-3.33	-4	-2.5	-3.72	-2.25	-2.75	-1.25	-2.5	-1	-0.5	1
Main Gauche	-1.34	-1.34	-2	-2	-2.67	-2.17	-2.67	-1.67	-2.39	-1.11	-1.72	-0.25	-1.47	0	0	0
Longsword 2	-2.67	-2.67	-3.33	-3.33	-4	-2.5	-3	-1.5	-2.75	-1.25	-1.75	-0.25	-1.5	0	0.5	2
Saber	-1.67	-1.67	-2.17	-2.17	-2.67	-1.67	-2	-0.5	-1.72	-0.25	-0.75	0.75	-0.5	1	1.5	3
Large Knife	-1.34	-1.34	-1.67	-1.67	-2.17	-1.33	-1.67	-0.34	-1.11	0.28	-0.25	1.25	0	1.5	1.5	1.5
Bastard 2	-1.67	-1.67	-2	-2	-2.5	-1	-1.5	0	-1.25	0.25	-0.25	1.25	0	1.5	2	3.5
Small Knife	-1	-1	-1.34	-1.34	-1.67	-1.17	-1.33	-0.33	-0.73	0.55	0.28	0.28	0.28	0.28	0.28	0.28
Broadsword	-1.33	-1.33	-1.67	-1.67	-2	-0.5	-1	0.5	-0.75	0.75	0.25	1.75	0.5	2	2.5	4
Jian	-1.17	-1.17	-1.33	-1.33	-1.67	-0.34	-0.5	1	-0.25	1.25	0.75	2.25	1	2.5	3	4.5
Long Knife	-1.01	-1.01	-1.17	-1.17	-1.33	-0.33	-0.34	1.16	0.28	1.75	1.25	2.75	1.5	3	3.5	5
Glaive	-0.34	-0.34	-0.5	-0.5	-1	0.5	0	1.5	0.25	1.75	1.25	2.75	1.5	3	3.5	5
Katana 1	-0.33	-0.33	-0.33	-0.33	-0.34	1.16	1	2.5	1.25	2.75	2.25	3.75	2.5	4	4.5	6
Kukri	-0.67	-0.67	-0.51	-0.51	-0.33	0.67	1	2.5	1.94	3.41	3.25	4.75	3.5	5	5.44	6.94
Shortsword	-0.51	-0.51	-0.33	-0.33	-0.33	1	1.16	2.66	1.75	3.25	2.75	4.25	3	4.5	5	6.5
Small Falchion	-0.17	-0.17	0.67	0.67	1.34	2.67	3.5	5	4.75	6.25	6.42	7.92	7	8.5	8.78	10.28
Duelling Halberd	1.16	1.16	1	1	0.5	2	1.5	3	1.75	3.25	2.75	4.25	3	4.5	5	6.5
Katana 2	0.67	0.67	1	1	1.16	2.66	2.5	4	2.75	4.25	3.75	5.25	4	5.5	6	7.5
Halberd	2.66	2.66	2.5	2.5	2	3.5	3	4.5	3.25	4.75	4.25	5.75	4.5	6	6.5	8
Dao	1.33	1.33	2	2	2.5	4	4.16	5.66	4.75	6.25	5.75	7.25	6	7.5	8	9.5
Falchion	0.67	0.67	1.67	1.67	2.67	4.17	5	6.5	6.25	7.75	7.92	9.42	8.5	10	10.28	11.78
Large Falchion	1.67	1.67	2.66	2.66	3.5	5	5.5	7	6.41	7.91	7.75	9.25	8	9.5	9.94	11.44

Table 1: Advantage of average swing/cutting attack over thrust/impaling attack in points of injury

Let me just say right now that I'm posting this analysis as I do it. I don't know yet whether this is going to lead to something that will be useful at the table while actually gaming. I made these charts to see what general trends, if any, pop out, and also just for the hell of it. Will it ever pay off, or am I just noodling around? Stay tuned.

Here are the 23 weapon classes. Because GURPS Low-Tech changed the stats for some weapons, the large katar, shortsword, and cutlass appear twice, and are noted with (LT) in the list below. Some weapons can be wielded one-handed or two-handed, so these also appear twice. Note also that the naginata could be used one-handed with Broadsword skill in Basic Set, but Low-Tech removed that.

Eleven weapons are in classes by themselves:

• Katar
• Pata
• Large Katar (LT)
• Main Gauche
• Longsword 2
• Long Knife
• Kukri
• Small Falchion
• Dao
• Falchion
• Large Falchion

I named the other twelve classes after the weapon in the class I thought was most prominent.

• Saber -- saber, light edged rapier, large katar, shotel
• Large Knife -- large knife, bladed hand
• Small Knife -- small knife, bladed hand
• Bastard 2 -- bastard sword 2-handed, naginata 1-handed, dueling bill, dueling glaive
• Broadsword -- broadsword, bastard sword 1-handed, longsword 1-handed
• Jian - jian, edged rapier, shortsword (LT), cutlass (LT)
• Glaive -- naginata 2-handed, greatsword, bill
• Katana 1 -- katana 1-handed, late katana 1-handed, cavalry saber, backsword, qian ku ri yue dao
• Shortsword -- shortsword, cutlass
• Dueling Halberd -- dueling halberd, light horsecutter
• Katana 2 -- katana 2-handed, late katana 2-handed
• Halberd -- halberd, heavy horsecutter

I should point out the rule on maximum effective ST (B270). Your maximum effective ST with a weapon is three times its ST rating. If your ST is higher than that, then you do damage as if your ST were at the lower figure. So given that small knives have an ST rating of 5, if your ST is higher than 15, you do damage as if your ST were 15. This affects the small knife, large knife, katar, and main-gauche classes.

So, what does this chart tell us? Some obvious points are confirmed. If you have a falchion, a weapon designed for swinging, then you should swing it. Conversely, patas are made for thrusting.

Also obvious: swing damage climbs faster with ST than thrust damage does, so stronger characters are better off swinging with weapons where weaker ones are better off thrusting. So even though patas are made for thrusting, when you have enough ST, swinging a pata makes sense.

There are also some non-obvious things that turn up. There is a middle range of weapons that are built to be versatile, and it's good to know how you can best gain the advantage of your Strength with them. At ST 13, there are several weapons you're better thrusting with, where the same weapons in the hands of a ST 14 character would be more useful at a swing.

The real oddity here is that some weapons go back and forth between swing-is-better and thrust-is-better as you go up in ST. That's an artifact of the way the Basic Damage table is structured, with swing damage going up every step, but thrust damage going up only every other step. This is especially noticeable with the Bastard 2 class. I imagine a master-at-arms teaching students to use a bastard sword two-handed: "Alright, I've lined you up from weakest to strongest. You lot, up to here, you're better off making thrusting attacks. Now, you fellows, from here to here, are better off swinging. But from here to here -- you'd better go back to thrusting. Now, from here on, again, swinging is better. Oh, except for you and you -- it doesn't matter which way you go."

It's silly, and more than a little unrealistic, but does it really matter? Here's Table 2, which shows expected swing/cutting injury as a percentage of expected thrust-impaling injury. As before, a blue background, where numbers are less than 100%, means you're better off thrusting, and a yellow background, where numbers are above 100%, means you're better off swinging.

	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Katar	33	33	25	25	25	34	38	52	51	65	66	80	73	85	85	85
Pata	34	34	38	38	41	56	59	73	67	79	78	88	82	91	94	103
Large Katar-LT	33	33	34	34	38	52	56	72	66	80	79	90	83	93	97	106
Main Gauche	43	43	33	33	33	46	50	69	66	84	81	97	87	100	100	100
Longsword 2	50	50	52	52	56	72	73	86	79	90	88	98	91	100	103	111
Saber	44	44	46	46	50	69	71	93	81	97	93	107	96	108	111	121
Large Knife	43	43	44	44	46	67	69	94	84	104	97	114	100	114	114	114
Bastard 2	69	69	71	71	72	89	86	100	90	102	98	108	100	109	111	119
Small Knife	50	50	43	43	44	61	67	92	86	110	104	104	104	104	104	104
Broadsword	67	67	69	69	71	93	89	106	93	107	102	113	103	113	116	125
Jian	61	61	67	67	69	94	93	114	97	114	107	120	108	119	121	132
Long Knife	57	57	61	61	67	92	94	122	104	125	114	131	114	127	129	142
Glaive	94	94	93	93	89	106	100	114	102	113	108	118	109	118	119	128
Katana 1	89	89	92	92	94	122	114	136	114	131	120	134	119	131	132	143
Kukri	67	67	78	78	89	122	125	163	136	164	146	168	139	156	154	169
Shortsword	78	78	89	89	92	125	122	150	125	146	131	147	127	141	142	154
Small Falchion	92	92	134	134	158	215	217	267	219	256	220	249	200	221	207	225
Duelling Halberd	122	122	114	114	106	122	114	127	113	125	118	128	118	126	128	136
Katana 2	122	122	125	125	122	150	136	157	131	147	134	148	131	142	143	154
Halberd	150	150	136	136	122	139	127	141	125	137	128	138	126	135	136	144
Dao	157	157	167	167	163	200	178	206	168	189	164	181	155	168	167	179
Falchion	134	134	184	184	215	279	267	317	256	294	249	277	221	243	225	243
Large Falchion	184	184	214	214	217	267	238	275	220	248	211	232	189	206	199	214

Table 2: Advantage of average swing/cutting attack over thrust/impaling attack in percent

In some cases, I would say it does matter. At the transition from blue to yellow, most values aren't that far from 100%, but a few are large enough to make me want to pay attention. The jian class, for instance, which includes the jian, the edged rapier, and Low-Tech versions of the shortsword and cutlass. At ST 12 and 14, you're taking a 14% discount if you're not swinging. There appears to be no simple way to describe the patterns here, so I guess you just have to know where your advantages are. That's not that bad a problem, since most characters don't change weapons very often, and change ST even less often.

Overall, I think the chart shows that GURPS does a pretty good job of delivering results. The see-sawing effect with with some of the weapons in the middle range looks weird, but it doesn't look broken. I can live with a 14% difference in the blue-yellow border area. For the other weapons, the takeaway lesson is that you should try to use them as they were designed to be used -- thrust with a knife, unless you're very strong. Swing with a polearm, if at all possible.

Now, what about the effect of hit location and Damage Resistance? DR comes off before the wounding modifier, the neck offers a x2 cutting modifier, and the vitals a x3 impaling modifier. I expect that will change things somewhat, but I'll have to take that up at another time.

For the rest of this post, I'm just going to describe how I arrived at the tables above, in case anyone wants to double-check my work. You can ignore everything below here if you're not into the heavy number-crunching.

After compiling the list of all the thrust-impaling/swing-cutting weapons, I found that their damage statistics ran from Thrust-2 to Thrust+3 and Swing-3 to Swing+5. I created tables listing the damage roll for each of these stats at ST levels from 5 to 20.

	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Thr-2	1d-6	1d-6	1d-5	1d-5	1d-4	1d-4	1d-3	1d-3	1d-2	1d-2	1d-1	1d-1	1d	1d	2d-3	2d-3
Thr-1	1d-5	1d-5	1d-4	1d-4	1d-3	1d-3	1d-2	1d-2	1d-1	1d-1	1d	1d	1d+1	1d+1	2d-2	2d-2
Thr	1d-4	1d-4	1d-3	1d-3	1d-2	1d-2	1d-1	1d-1	1d	1d	1d+1	1d+1	1d+2	1d+2	2d-1	2d-1
Thr+1	1d-3	1d-3	1d-2	1d-2	1d-1	1d-1	1d	1d	1d+1	1d+1	1d+2	1d+2	1d+3	1d+3	2d	2d
Thr+2	1d-2	1d-2	1d-1	1d-1	1d	1d	1d+1	1d+1	1d+2	1d+2	1d+3	1d+3	1d+4	1d+4	2d+1	2d+1
Thr+3	1d-1	1d-1	1d	1d	1d+1	1d+1	1d+2	1d+2	1d+3	1d+3	1d+4	1d+4	1d+5	1d+5	2d+2	2d+2

Table 3: Damage rolls for thrusting attacks by ST

	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Sw-3	1d-6	1d-6	1d-5	1d-5	1d-4	1d-3	1d-2	1d-1	2d-4	2d-3	2d-2	2d-1	3d-4	3d-3	3d-2	3d-1
Sw-2	1d-5	1d-5	1d-4	1d-4	1d-3	1d-2	1d-1	1d	2d-3	2d-2	2d-1	2d	3d-3	3d-2	3d-1	3d
Sw-1	1d-4	1d-4	1d-3	1d-3	1d-2	1d-1	1d	1d+1	2d-2	2d-1	2d	2d+1	3d-2	3d-1	3d	3d+1
Sw	1d-3	1d-3	1d-2	1d-2	1d-1	1d	1d+1	1d+2	2d-1	2d	2d+1	2d+2	3d-1	3d	3d+1	3d+2
Sw+1	1d-2	1d-2	1d-1	1d-1	1d	1d+1	1d+2	1d+3	2d	2d+1	2d+2	2d+3	3d	3d+1	3d+2	3d+3
Sw+2	1d-1	1d-1	1d	1d	1d+1	1d+2	1d+3	1d+4	2d+1	2d+2	2d+3	2d+4	3d+1	3d+2	3d+3	3d+4
Sw+3	1d	1d	1d+1	1d+1	1d+2	1d+3	1d+4	1d+5	2d+2	2d+3	2d+4	2d+5	3d+2	3d+3	3d+4	3d+5
Sw+4	1d+1	1d+1	1d+2	1d+2	1d+3	1d+4	1d+5	1d+6	2d+3	2d+4	2d+5	2d+6	3d+3	3d+4	3d+5	3d+6
Sw+5	1d+2	1d+2	1d+3	1d+3	1d+4	1d+5	1d+6	1d+7	2d+4	2d+5	2d+6	2d+7	3d+4	3d+5	3d+6	3d+7

Table 4: Damage rolls for swinging attacks by ST

The next step was to calculate expected injury for each of these damage rolls. It was not possible to take the average of 1d, 2d, or 3d and apply simple arithmetic because of two complications. First, the minimum damage for cutting and impaling attacks is 1. That means it's not possible to say that the average of 1d is 3.5, so the average of 1d-2 is 1.5. In fact, the average of 1d-2 with a minimum of 1 is the average of (1, 1, 1, 2, 3, 4), which is 2. Roughly a third of the damage rolls had to be treated this way.

Second, for a x2 injury modifier, you can simply multiply the average damage roll by 2, but because of rounding, you can't treat cutting damage the same. Injury is rounded down, which means that the possible damage results from 1d, which are (1, 2, 3, 4, 5, 6) with an average of 3.5, become (1, 3, 4, 6, 7, 9) with the cutting injury modifier of 1.5. This gives an average of 5, rather than an average of 3.5 * 1.5 = 5.25.

The upshot of all this calculating is shown in table 5, which gives the average of the damage, cutting injury, and impaling injury for all the die rolls I worked with.

	Die Roll	x1.5	x2
1d-6	1.00	1.00	2.00
1d-5	1.00	1.00	2.00
1d-4	1.17	1.33	2.33
1d-3	1.50	1.83	3.00
1d-2	2.00	2.67	4.00
1d-1	2.67	3.67	5.33
1d	3.50	5.00	7.00
1d+1	4.50	6.50	9.00
1d+2	5.50	8.00	11.00
1d+3	6.50	9.50	13.00
1d+4	7.50	11.00	15.00
1d+5	8.50	12.50	17.00
1d+6	9.50	14.00	19.00
1d+7	10.50	15.50	21.00
2d-4	3.28	4.61	6.56
2d-3	4.11	5.89	8.22
2d-2	5.03	7.28	10.06
2d-1	6.00	8.75	12.00
2d	7.00	10.25	14.00
2d+1	8.00	11.75	16.00
2d+2	9.00	13.25	18.00
2d+3	10.00	14.75	20.00
2d+4	11.00	16.25	22.00
2d+5	12.00	17.75	24.00
2d+6	13.00	19.25	26.00
2d+7	14.00	20.75	28.00
3d-4	6.52	9.53	13.04
3d-3	7.50	11.00	15.00
3d-2	8.50	12.50	17.00
3d-1	9.50	14.00	19.00
3d	10.50	15.50	21.00
3d+1	11.50	17.00	23.00
3d+2	12.50	18.50	25.00
3d+3	13.50	20.00	27.00
3d+4	14.50	21.50	29.00
3d+5	15.50	23.00	31.00
3d+6	16.50	24.50	33.00
3d+7	17.50	26.00	35.00

Table 5: Expected die rolls and injury for cutting and impaling attacks

Equipped with these results, I converted tables 3 and 4, showing damage rolls, to tables 6 and 7, showing expected injury for thrust and swing attacks.

	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Thr-2	2	2	2	2	2.33	2.33	3	3	4	4	5.33	5.33	7	7	8.22	8.22
Thr-1	2	2	2.34	2.34	3	3	4	4	5.34	5.34	7	7	9	9	10.06	10.06
Thr	2.34	2.34	3	3	4	4	5.34	5.34	7	7	9	9	11	11	12	12
Thr+1	3	3	4	4	5.34	5.34	7	7	9	9	11	11	13	13	14	14
Thr+2	4	4	5.34	5.34	7	7	9	9	11	11	13	13	15	15	16	16
Thr+3	5.34	5.34	7	7	9	9	11	11	13	13	15	15	17	17	18	18

Table 6: Average injury for thrust/impaling attacks by ST

	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Sw-3	1	1	1	1	1.33	1.83	2.67	3.67	4.61	5.89	7.28	8.75	9.53	11	12.5	14
Sw-2	1	1	1.33	1.33	1.83	2.67	3.67	5	5.89	7.28	8.75	10.25	11	12.5	14	15.5
Sw-1	1.33	1.33	1.83	1.83	2.67	3.67	5	6.5	7.28	8.75	10.25	11.75	12.5	14	15.5	17
Sw	1.83	1.83	2.67	2.67	3.67	5	6.5	8	8.75	10.25	11.75	13.25	14	15.5	17	18.5
Sw+1	2.67	2.67	3.67	3.67	5	6.5	8	9.5	10.25	11.75	13.25	14.75	15.5	17	18.5	20
Sw+2	3.67	3.67	5	5	6.5	8	9.5	11	11.75	13.25	14.75	16.25	17	18.5	20	21.5
Sw+3	5	5	6.5	6.5	8	9.5	11	12.5	13.25	14.75	16.25	17.75	18.5	20	21.5	23
Sw+4	6.5	6.5	8	8	9.5	11	12.5	14	14.75	16.25	17.75	19.25	20	21.5	23	24.5
Sw+5	8	8	9.5	9.5	11	12.5	14	15.5	16.25	17.75	19.25	20.75	21.5	23	24.5	26

Table 7: Aveage injury for swing/cutting attacks by ST

Next I listed the weapons and copied their expected damage for thrust and swing attacks from tables 6 and 7 to create tables 8 and 9. Note that maximum effective ST for the katar, main-gauche, and large knife classes is 18, and for the small knife class it is 15.

	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Katar	3	3	4	4	5.34	5.34	7	7	9	9	11	11	13	13	13	13
Pata	5.34	5.34	7	7	9	9	11	11	13	13	15	15	17	17	18	18
Large Katar-LT	4	4	5.34	5.34	7	7	9	9	11	11	13	13	15	15	16	16
Main Gauche	2.34	2.34	3	3	4	4	5.34	5.34	7	7	9	9	11	11	11	11
Longsword 2	5.34	5.34	7	7	9	9	11	11	13	13	15	15	17	17	18	18
Saber	3	3	4	4	5.34	5.34	7	7	9	9	11	11	13	13	14	14
Large Knife	2.34	2.34	3	3	4	4	5.34	5.34	7	7	9	9	11	11	11	11
Bastard 2	5.34	5.34	7	7	9	9	11	11	13	13	15	15	17	17	18	18
Small Knife	2	2	2.34	2.34	3	3	4	4	5.34	5.34	7	7	7	7	7	7
Broadsword	4	4	5.34	5.34	7	7	9	9	11	11	13	13	15	15	16	16
Jian	3	3	4	4	5.34	5.34	7	7	9	9	11	11	13	13	14	14
Long Knife	2.34	2.34	3	3	4	4	5.34	5.34	7	7	9	9	11	11	12	12
Glaive	5.34	5.34	7	7	9	9	11	11	13	13	15	15	17	17	18	18
Katana 1	3	3	4	4	5.34	5.34	7	7	9	9	11	11	13	13	14	14
Kukri	2	2	2.34	2.34	3	3	4	4	5.34	5.34	7	7	9	9	10.06	10.06
Shortsword	2.34	2.34	3	3	4	4	5.34	5.34	7	7	9	9	11	11	12	12
Small Falchion	2	2	2	2	2.33	2.33	3	3	4	4	5.33	5.33	7	7	8.22	8.22
Duelling Halberd	5.34	5.34	7	7	9	9	11	11	13	13	15	15	17	17	18	18
Katana 2	3	3	4	4	5.34	5.34	7	7	9	9	11	11	13	13	14	14
Halberd	5.34	5.34	7	7	9	9	11	11	13	13	15	15	17	17	18	18
Dao	2.34	2.34	3	3	4	4	5.34	5.34	7	7	9	9	11	11	12	12
Falchion	2	2	2	2	2.33	2.33	3	3	4	4	5.33	5.33	7	7	8.22	8.22
Large Falchion	2	2	2.34	2.34	3	3	4	4	5.34	5.34	7	7	9	9	10.06	10.06

Table 8: Average thrust/impaling injury for various weapons by ST

	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Katar	1	1	1	1	1.33	1.83	2.67	3.67	4.61	5.89	7.28	8.75	9.53	11	11	11
Pata	1.83	1.83	2.67	2.67	3.67	5	6.5	8	8.75	10.25	11.75	13.25	14	15.5	17	18.5
Large Katar-LT	1.33	1.33	1.83	1.83	2.67	3.67	5	6.5	7.28	8.75	10.25	11.75	12.5	14	15.5	17
Main Gauche	1	1	1	1	1.33	1.83	2.67	3.67	4.61	5.89	7.28	8.75	9.53	11	11	11
Longsword 2	2.67	2.67	3.67	3.67	5	6.5	8	9.5	10.25	11.75	13.25	14.75	15.5	17	18.5	20
Saber	1.33	1.33	1.83	1.83	2.67	3.67	5	6.5	7.28	8.75	10.25	11.75	12.5	14	15.5	17
Large Knife	1	1	1.33	1.33	1.83	2.67	3.67	5	5.89	7.28	8.75	10.25	11	12.5	12.5	12.5
Bastard 2	3.67	3.67	5	5	6.5	8	9.5	11	11.75	13.25	14.75	16.25	17	18.5	20	21.5
Small Knife	1	1	1	1	1.33	1.83	2.67	3.67	4.61	5.89	7.28	7.28	7.28	7.28	7.28	7.28
Broadsword	2.67	2.67	3.67	3.67	5	6.5	8	9.5	10.25	11.75	13.25	14.75	15.5	17	18.5	20
Jian	1.83	1.83	2.67	2.67	3.67	5	6.5	8	8.75	10.25	11.75	13.25	14	15.5	17	18.5
Long Knife	1.33	1.33	1.83	1.83	2.67	3.67	5	6.5	7.28	8.75	10.25	11.75	12.5	14	15.5	17
Glaive	5	5	6.5	6.5	8	9.5	11	12.5	13.25	14.75	16.25	17.75	18.5	20	21.5	23
Katana 1	2.67	2.67	3.67	3.67	5	6.5	8	9.5	10.25	11.75	13.25	14.75	15.5	17	18.5	20
Kukri	1.33	1.33	1.83	1.83	2.67	3.67	5	6.5	7.28	8.75	10.25	11.75	12.5	14	15.5	17
Shortsword	1.83	1.83	2.67	2.67	3.67	5	6.5	8	8.75	10.25	11.75	13.25	14	15.5	17	18.5
Small Falchion	1.83	1.83	2.67	2.67	3.67	5	6.5	8	8.75	10.25	11.75	13.25	14	15.5	17	18.5
Duelling Halberd	6.5	6.5	8	8	9.5	11	12.5	14	14.75	16.25	17.75	19.25	20	21.5	23	24.5
Katana 2	3.67	3.67	5	5	6.5	8	9.5	11	11.75	13.25	14.75	16.25	17	18.5	20	21.5
Halberd	8	8	9.5	9.5	11	12.5	14	15.5	16.25	17.75	19.25	20.75	21.5	23	24.5	26
Dao	3.67	3.67	5	5	6.5	8	9.5	11	11.75	13.25	14.75	16.25	17	18.5	20	21.5
Falchion	2.67	2.67	3.67	3.67	5	6.5	8	9.5	10.25	11.75	13.25	14.75	15.5	17	18.5	20
Large Falchion	3.67	3.67	5	5	6.5	8	9.5	11	11.75	13.25	14.75	16.25	17	18.5	20	21.5

Table 9: Average swing/cutting injury for various weapons by ST

Finally, I used these two tables to compute tables 1 and 2, above.

GURPS Combat Choices: Cutting/Impaling Weapons Chart

Here's a table I've drawn up in preparation of analysis of some thrust/swing mechanics. It shows all the weapons from Basic Set, GURPS Martial Arts, and GURPS Low-Tech that have listings for both thrusting-impaling damage and swinging-cutting damage. It's mostly swords, plus some polearms and a couple of oddities.

	Thrust-2	Thrust-1	Thrust	Thrust+1	Thrust+2	Thrust+3
Swing-3		Small Knife, Balisong	Main-Gauche	Katar
Swing-2			Large Knife, Bladed Hand
Swing-1		Kukri	Long Knife	Saber, Light Edged Rapier, Large Katar, Shotel	Large Katar (LT)
Swing	Small Falchion		Shortsword, Cutlass	Jian, Edged Rapier, Shortsword (LT), Cutlass (LT)		Pata
Swing+1	Falchion			Katana 1-handed, Late Katana 1-handed, Cavalry Saber, Backsword, Qian Ku Ri Yue Dao	Broadsword, Longsword 1-handed, Bastard Sword 1-handed	Longsword 2-handed
Swing+2		Large Falchion	Dao	Katana 2-handed, Late Katana 2-handed		Naginata 1-handed, Bastard Sword 2-handed, Duelling Bill, Duelling Glaive
Swing+3						Glaive, Naginata 2-handed, Greatsword, Bill
Swing+4						Duelling Halberd, Light Horsecutter
Swing+5						Halberd, Heavy Horsecutter

Note that in Low-Tech, some weapon stats changed. Shortswords, cutlasses, and large katars were bumped up one level in thrusting damage, and one-handed use of the naginata was removed.

Two trends really stand out in this table. On a diagonal axis running from upper left to lower right, weapons go from small to large. Not surprisingly, bigger weapons do more damage.

On the other diagonal, from lower left to upper right, weapons go from more choppy to more stabby. (I hope I may be excused for lapsing into technical jargon there.) On one extreme, a falchion has barely any point to it at all, and is nearly an axe. On the other extreme, the katar and the pata are about as far as you can go toward specialization in stabbing while still retaining a cutting edge. I think these two diagonal axes are more important to understanding how the weapons got their stats than the stats themselves are, and if I knew how to do it, I'd rotate this table 45 degrees and make a diamond-shaped chart with size running top to bottom, and choppy vs. stabby running left-right. Sadly, my HTML skills are not up to that.

Another thing that this chart shows is the effect of enchantment and weapon quality. Add Puissance +1 to any weapon, or make it Fine quality, and you move one space diagonally down and to the right. So a Puissance +1 jian becomes, as far as damage is concerned, a broadsword. Very Fine or Puissance +2 moves you two spaces, so a Very Fine small knife hits like a saber -- but it's rather expensive and you still can't parry with it.

In my next post on this subject, I'll crunch a great big pile of numbers and see what I have to say about swinging versus thrusting damage for these weapons.

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.