As per norm, this will be in GURPS terms, since that's where the zombies are!
Why don't you want to use a shotgun? The answer is the ammo is heavy and bulky. The bulky part doesn't really come up in game.
On the surface a 12ga pump seems ideal.
00 Buck does a mere 1d+1 pi, but you get nine per shot and you can take two shots per round. That makes the RoF an effective 18 and you get a +4 to hit with a Rcl of just 1!
The downside to buck is your range is kinda pathetic. 1/2 damage range is 40 yards and max is 800.
Birdshot seems a great deal, you get 2x203 for a rate of fire. +9 to hit! Range is 20/300. Damage is woefully pathetic, 1d-5(0.5) pi-. What that means is any armor encountered is doubled and any damage that penetrates the armor is halved, with 0 DR counted as 1. So the average 0 points rolled (min 1) becomes 0 pentrated and that becomes 0 actually done.
Shotguns have a lot of special rules. Inside 10% of the 1/2d range the RoF changes from 2x9 to just 2. You get to multiply the basic damage by 4 though. The enemy gets to, likewise, multiply their DR by 4. Against unarmored zombies, DR isn't really a problem.
Slugs are pretty devastating. They get that x4 damage at all ranges and no increase to the target's DR. They also increase the 1/2d range 2.5x and max 1.5x (100/1,200). So instead of nine 1d+1 pi per shot they do a single 5d pi++ per shot (shotguns are large bore!). Of course Rcl is now FIVE!!
Averaged... A 00 Buck pellet should do 4 points each and a skill 14 character at 20 yards will land three of them on a person. At 4 yards you may as well just take one shot because on average you just get the one, but it will do 16 points. Slugs at 20 yards do 34 points on average but the average to hit roll is a miss (best do some aiming!).
#4 Bird will land 8 pellets (out of 406!) at 20 yards with that average roll and then will do no damage.
Hey, the rules even reinforce the "you don't need to aim" myth. Except what we real world shooters think of as aiming, GURPS considers pointing. The aim maneuver is a bit more involved.
Next a tactical pump shotgun holds 7+1 rounds. A hunting gun, 4+1. Seven rounds weighs 0.9 lb. Reloads take two seconds per shot. Four rounds of shooting, sixteen rounds of loading.
It's not a lack of puissance that makes a shotgun a poor zombie apocalypse gun.
By comparison. Your bog-standard 16" AR-15 carbine...
Damage is 4d+2 pi (average 16), RoF is 3 and ranges are 750/2,900. A magazine holds 30 rounds and takes 3 seconds to replace. Ten rounds of shooting, three rounds of loading. An AR gets 60 shots in the time it takes a shotty to get reloaded from 8! It has the same aiming issue as slugs, but you can take shots farther out. Oh, those 30 rounds only weigh a pound.
Even more fun if your scenario allows you to grab a military or police gun (or if you're "good with tools") the RoF for an AR is around 15! That's a +3 to hit and makes two hits at 20 yards!
But those are averages. What about best cases?
Our skill of 14 at 20 yards is a mere 8 (-6 for range). The best we can roll is a 3.
12ga 00 Buck. +4 for RoF, so a 3 makes it by 9 so 10 of 18 pellets hit! If there's no DR on that target that's 20-70 points of damage.
12ga slug. No bonus to hit, so a 3 makes it by 5, so both rounds hit. 20-120 points of damage.
12ga #4. +9 for RoF so a 3 makes it by 14 so 15 pellets hit. Those do 15 raw damage, -15 for the DR of an unarmored target for 0 penetrating and then 0 actual damage done once the pi- adjustment is made.
5.56x45mm semi-auto. No bonus to hit, so a 3 makes it by 5, so all three rounds hit! 18-78 points.
5.56x45mm full-auto. +3 to hit, so a 3 makes it by 8. Five rounds hit. 30-130 points of damage.
As you can see, the damage is very similar, but the reloads and weight are the clincher.
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