Quick Dice Probability Question

[Agback]

Instead of keeping track of each shot fired (yeah right!), but still wanting someone's power pack coming up empty now and then, I figured I would use critical fumbles. And by using different numbers for each different weapon's stats, I can accuratly simulate how many shots per power pack and the correct probability (per dice roll) where one could wind up empty.

I've come across this approach before, and I don't like it. A diligent charcter ought to be able to make sure that he does not run out of ammo: under this approach there is no way to do that. And any charcter ought to be able to slap in a fresh magazine to make sure that a single important shot will come off. You can't do that under this system either.

A sniper who spends ages sneaking into position, waits for a clear shot, aims carefully, and then snaps the trigger on an unloaded weapon looks like an idiot. You don't want that sort of thing happening in your game. Characters ought to be able to find out, and plan on the basis of, how many shots they have left in their weapons.

Regards,

 

[frisbeet]

frisbeet,

Possible solution for your 1d47 problem:

I can understand where you are coming from. However the solution is simple yet perfect.

To roll a 1d47, roll a perfect, non-bias 1d100. If it's between 1 and 47, that's your number, if not re-roll until you get a result. There is a perfectly distributed chance of getting any number between 1 and 47.
However, because you don't want to have to re-roll most of the time, take 1d60 (A 1d6 and a 1d10) and use the same method (assume that the 6 on the 1d6 is a 0).
A somewhat crass solution but one that is perfect. Is this what you were referring to as approximated? You obviously know your stuff when it comes to probability and I'm sure this idea is something that you've already thought of. If I'm barking up the wrong tree (you only want to roll once?), please tell me.

As for the 3 in 500, make it 6 in 1000 and roll 1d1000.

Just going across to your link now, it should be interesting.

Best Regards
Herremann the Wise

Yup, that is an Exact way of rolling odds of 1-in-prime number.

The approximation I was thinking of wouldn't involve rerolling. Instead play with dice probabilities such that their product = the probability of, say, 1 in 47, or 0.0213. One crazy fix would be:

roll d20, accept 1
then roll d6, accept 5 or less
then roll d20, accept 14 or less
then roll d20, accept 18 or less
then roll d20, accept 19 or less
then roll d20, accept 19 or less
then roll d20, accept 19 or less
then roll d20, accept 19 or less

Making all these rolls is an outcome which happens with a probability of 0.0214 (2.14%). This is quite close to 1/47. Good enough? Ought to be. But dang, what a pain. I pulled these dice out of the air and futzed with the acceptances to get the probability close. There almost certainly is a series forumla which could better guide dice/acceptance selection. But I'd rather skewer my eyeballs with toothpicks for a special garnish than bother to find, figure, or use such a thing.

The rerolling method is indeed much simpler, and exact.

gobbledeegook,

fris

 

[jonesy]

What are the odds of rolling a natural 1 (on a d20) and then following it up with a roll of 1-5?

I'd say the chances are pretty much 95% when it really matters.