It's a Wand! It's a Crossbow Bolt! It's a Floor Wax!

[Sigma]

Before I begin, a quick explanation of a house rule. Rather than keep track of charges, we randomly determine whether a wand's charges have expired (using a "charge die"). A fully charged wand uses a d20, and on a roll of a 1, it degrades to a d12, a d10, and finally a d8. (As a side question, can anyone with any level of sophistication in math tell me how close I will get to 50 using this method).

In the ongoing quest to spice up the game, I was playing with the idea of a wand of magic missiles that is also a +1 ghost touch crossbow bolt. Here's the game design theory issue - how do I handle the survival of the the wand when you shoot it as a bolt.

Option 1: Use the regular ammunition rules. It breaks if it hits, there's a 50% chance of breaking if it misses.

Option 2: "Use" a charge. Roll the charge die as if you had used the wand to cast a spell. If you get a 1, you downgrade as explained above. The wand/bolt is not destroyed unless all charges are used up.

Option 3: Chance of breaking is equal to the chance of downgrading. Each time you use the wand, roll the charge die. On a 1, the wand/bolt breaks.

Now here's my question. How do you compare these options? Option 2 is clearly the most powerful, option 1 clearly the least powerful. But how much more powerful is option 2 than option 1? I like the flavor of 2 or 3, but worry that I am effectively giving out a +1 ghost touch crossbow with a small chance of breakage.

 

[IcyCool]

This looks more like a house rules question.

Otherwise you're going to get answers that pretty much look like #1.

You'll probably have better luck in House Rules. A Mod can move the thread for you, if you like.

 

[Corsair]

Well in regard to the die-rolling for wands...

between those four dice, you have a total of 50 sides. The only way you'll get 50 charges out of a want would be if you rolled every number on a die BEFORE you rolled a one. I don't know the math, but odds are you'll probably roll a 1 before you roll every other number 2-20.

Admittedly you could in theory get more than 50 shots, but I bet you'll average much lower, like in the high 30s.

 

[Borlon]

If the dice are fair, the average number of rolls before you get a 1 on an N-sided die is N. So the average lifespan of a wand with those ruls is 50 charges. While you are unlikely to roll all the numbers between 2-20 before you roll a 1, you will probably roll some other number two or three times.

To see this, imagine that you roll a 20 sided dice 2000 times. How many 1s do you expect? Around 100. 2000/200 is 20; the average wait between 1s is 20 rolls. How many 2s do you expect. Around 100; the average wait between 2s is 20 rolls. And so on for all the numbers. Sometimes the wait is more, sometimes less; you could roll three 1s in a roll, for example. But the average wait between repeats of a particular number on an N-sided die is N rolls.

 

[Nim]

Interesting. I thought you were wrong, Borlon, but looking at it more closely, I figured out why it looked wrong to me even though you were logically correct.

If the game is 'roll this d20 until you roll a 1, and count the number of times you roll', then your mean result WILL be 20.

The mode (most commonly occuring single result) is 1.

The median (the point at which half of the results are lower and half of the results are higher) is between 13 and 14 - a fractional result wouldn't make sense, since you can't make a fractional roll

So, if you do this 10000 times and average the results, you'll come up with something near 20. But half (51.23%) of your results will be 14 or less.

Very long stretches without a 1 (say, 100 rolls or more) are very unlikely, but they're possible...and because the numbers involved are big, that moves the mean pretty far from the median.

 

[Borlon]

Maybe some kind soul who knows how to simulate this on a computer (I think excel can be persuaded to do it) might simulate rolling a d20 a few thousand times, and let us know what the mean and median really is.

 

[Primitive Screwhead]

I am not that hot on means and medians.. averages are easy

Running an average across sets of 100 wands..

? Procedure Wand_Die
Wand number 100, Average charges = 31.65 , best charge = 82
Wand number 100, Average charges = 20.74 , best charge = 82
Wand number 100, Average charges = 20.12 , best charge = 97
Wand number 100, Average charges = 21.31 , best charge = 78
Wand number 100, Average charges = 12.97 , best charge = 64
Wand number 100, Average charges = 19.88 , best charge = 68
Wand number 100, Average charges = 20.49 , best charge = 116
Wand number 100, Average charges = 15.54 , best charge = 65
Wand number 100, Average charges = 17.84 , best charge = 67
Wand number 100, Average charges = 24.18 , best charge = 47
Wand number 100, Average charges = 19.62 , best charge = 59
Wand number 100, Average charges = 18.67 , best charge = 91
Wand number 100, Average charges = 16.68 , best charge = 51
Wand number 100, Average charges = 16.52 , best charge = 89
Wand number 100, Average charges = 24.12 , best charge = 77
Wand number 100, Average charges = 17.03 , best charge = 55
Wand number 100, Average charges = 23.12 , best charge = 104
Wand number 100, Average charges = 20.06 , best charge = 66
Wand number 100, Average charges = 20.88 , best charge = 59
Wand number 100, Average charges = 22.73 , best charge = 136

Meaning Nim's estimate is pretty good, and this variant looks like it may make it into my game

 

[Borlon]

Note that the average of those averages is 20.2075; pretty close to the 20 I said it would be.

Dunno what the median number of charges would be, though.

 

[Nim]

Note that the average of those averages is 20.2075; pretty close to the 20 I said it would be.

Dunno what the median number of charges would be, though.

Yeah, I think he meant your estimate, not mine

 

[SidusLupus]

I really like this idea.

Did you also apply it to staves?