Idea for ammo depletion

[Huw]

I'd like everyone's opinion of this idea for tracking ammo/charges.

Ammo starts "full" - i.e., a quiver full of arrows. Everytime an arrow is fired, roll 2d6. If a double 1 is rolled, then the level drops to "low". At low ammo, everytime an arrow is fired, roll 1d6. If a 1 is rolled, you run out.

Similar thing with wands, staffs, maybe even potions. Different dice can be used - d4 for throwing knives, d8 for charges in a wand. The system is partly inspired by the Doom boardgame.

 

[hong]

Hm.

Average #shots to get snakeyes = 36
Average #shots to get 1 = 6
---------
Average #shots before running out = 36x6 = 216

That's a big quiver....

 

[Nifft]

Average #shots to get snakeyes = 36
Average #shots to get 1 = 6
---------
Average #shots before running out = 36x6 = 216

Err... that's the chance of running out in two shots. (216:1)

Since it's possible to never run out, there's no such thing as "average # of shots", but you could have the number of shots by which you expect 50% (or more) of archers will have run out.

By shot 24, we have a 50.86% chance of NOT being "low". By shot 25, that's fallen to 49.45% -- pretty good for a (presumed) 30 shot quiver.

Once you're low, the probability of depletion is worse, of course. At three shots, you have a 57.87% chance of still having arrows, while at four shots you have only a 48.22% chance of not being empty.

Cheers, -- N

 

[hong]

Err... that's the chance of running out in two shots. (216:1)

Since it's possible to never run out, there's no such thing as "average # of shots", but you could have the number of shots by which you expect 50% (or more) of archers will have run out.

By shot 24, we have a 50.86% chance of NOT being "low". By shot 25, that's fallen to 49.45% -- pretty good for a (presumed) 30 shot quiver.

Once you're low, the probability of depletion is worse, of course. At three shots, you have a 57.87% chance of still having arrows, while at four shots you have only a 48.22% chance of not being empty.

Cheers, -- N

Bwuh?

http://en.wikipedia.org/wiki/Geometric_distribution

 

[Nyeshet]

Average #shots before running out = 36x6 = 216

That's a big quiver....

I'm more impressed by the wands, actually. I can just see a certain rogue I know really liking this idea . . . .

 

[Pbartender]

Hm.

Average #shots to get snakeyes = 36
Average #shots to get 1 = 6
---------
Average #shots before running out = 36x6 = 216

That's a big quiver....

The trouble with that math, Hong, is that the second probability doesn't kick in until the first is satisfied.

So, until you go to low, you have a 1/36 chance of going low, and 0 chance of going empty.

Once you go low, you've 0 chance of going low (you're already there), and a 1/6 chance of going empty.

So, typically, by those odds, you'll fire about 36 shots before going low, and once you're there, you'll likely fire another 6 or so shots before going empty. Odds are, you'll shoot between 30 and 50 arrows, before you run out.

It'd be easy enough to make a simple program to test it out...

 

[hong]

Oops, you're right. Should be 36 + 6, not 36 x 6.

 

[Pbartender]

Oops, you're right. Should be 36 + 6, not 36 x 6.

Right.

 

[Celebrim]

So, you want to add two throws of the dice to every missile attack resolution?

This will reduce the time spent on book keeping?

 

[Huw]

BTW, I've done the maths for several different dice. 2d6 gives you a 50% chance of getting at least 24 arrows before running low. You then have 50% chance of getting at least another 4 shots.