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

[Sigma]

Huh. I had been pricing the wands as

d20 = full price
d12 = 3/4 price
d10 = 1/2price
d8 = 1/4 price

I guess it should be

d20 = full price
d12 = .6 price
d10 = .36 price
d8 = .16 price

I never considered that I was overcharging for the lower dice wands. Then again, I don't necessarily mind that because my players tend to try to do cheesy things like buy a wand of clw w/only ten charges because it is cheaper than ten scrolls or ten potions of clw.

 

[Coredump]

Be wary of 'averages' here.

Lets make a deal. Everyday you give me a dollar, and I will roll a D(million) die. On any roll except a 1, I keep the dollar. On a roll of a 1, I will give you 1,000,000 dollars.
On average, we will both break even.

Who wants to take me up on this?
---------------------
Or the flip side....

I will give you $1000, and you roll a D10. On any roll besides a 1, you keep the money. On a 1, you give me $10,000. On average, we will both break even.

Who wants to play?
--------------------


It is true, on average, it will take 20 rolls to roll a 20. But that is because you get a lot of the time it only takes 12 or 13 times, but it will rarely take 35 times.

So, if you have 3-4 wands, chances are you will *not* get 50 charges on any of them. If you go through 30-40 wands, chances are you will get over 50 on some of them. But may still average at less than 50 charges.

Still a fun mechanic....

"do ya feel lucky punk...?"

 

[Primitive Screwhead]

Agreed you have to watch the averages.. but out of those hundreds of wands run through upthread... one had 136 charges! Talk about a bargain!

 

[Denaes]

I think part of the point of averages is that "on average" you'll get X results. It's not more or less likely to go over. You're just as likely going to roll 5 numbers above 10 in a row as 5 numbers below 10 in a row.

It's only when you get into multiple dice, like 2d10 that the results are weighted in a bell curve closer to 9-11.

So whatever results you think are more likely towards a lower number on single die rolls are purely imagined. It's an even spread throughout the die.

Chances are that after 20 times on a d20 you'll roll a 1, but it could happen sooner or later. Could be on the first roll or on the 50th roll. Yes, chances are against both results, ie - they're not average results.

Thats all gambling is, is betting money that you'll beat the odds. Sometimes skill is involved like cards - while in craps the only skill you have is betting management on the odds.

I think this is a great idea. I can totally see Charcters (not the players) getting totally pissed off at buying a "fully charged wand" and only getting 10 charges on it. They'd go and find the seller and try to get a partial refund. The players will know better, but their characters wouldn't.

On the other hand, the players may have a run of luck with a particular seller and might consider him their "lucky merchant".

 

[Borlon]

Using my variant, a wizard could make a brand-new wand, and with the very first use he could roll a (1,0), which means it is now empty. The player would understandably be peeved.

Sigma's rule wouldn't allow that to happen. Sure a player could, on subsequent uses, roll a 20, a 12, a 10 and an 8, and thus only get 4 charges out of the brand-new wand, but this is much more improbable than rolling a (1,0) or a (0,1). About 1 chance in 20,000 to get only 4 charges, compared to about a 1 in 12 chance of getting 4 charges or less with my variant.

 

[Denaes]

Using my variant, a wizard could make a brand-new wand, and with the very first use he could roll a (1,0), which means it is now empty. The player would understandably be peeved.

Sigma's rule wouldn't allow that to happen. Sure a player could, on subsequent uses, roll a 20, a 12, a 10 and an 8, and thus only get 4 charges out of the brand-new wand, but this is much more improbable than rolling a (1,0) or a (0,1). About 1 chance in 20,000 to get only 4 charges, compared to about a 1 in 12 chance of getting 4 charges or less with my variant.

Yeah, I think that's part of the appeal of the Sigma's method. There is a more difined downward spiral... you know it's lessening in power - and because of these steps it's fairly easy to steadily decline.

True it's not as abrupt. with your method it could be working fine for a year then go dead from out of the blue... or go dead on the first try.

It depends on what you're going for as a GM. I'm partal the the downward spiral. It's mechanics prevent too long of a run and help prevent a really premature end. It's what I'm looking for personally. Now if my GM agrees with me...

 

[Halcyon]

A series of die rolls is just a geometric distribution. In terms of rolling a 1 on a d20, the mean would be 20 rolls, but the variance is very large since all outcomes are equally likely on each trial. The probability of rolling a 1 on the 20th or earlier roll is roughly 64.2%. In other words, if you continuously rolled a d20 until you got a 1, noted how many rolls that took and repeated that process over and over, 64.2% of the time you would roll a 1 by the 20th roll. The table below shows the probablitilty of getting a 1 on the nth roll or less. The left column is the number of rolls and the right column is the cumulative probability. Another way of thinking of the results in this table is to take 1-a given probability, which equals the probability of it taking more than N rolls to get a 1. (E.g. 1-.642=.358, or a 35.8% chance it takes more than 20 rolls to roll a 1). Ive only included the first 50 n's for brevity , but it's easy to extrapolate beyond this (or to other dice (e.g. d12)).
1 0.05
2 0.0975
3 0.142625
4 0.18549375
5 0.226219063
6 0.264908109
7 0.301662704
8 0.336579569
9 0.36975059
10 0.401263061
11 0.431199908
12 0.459639912
13 0.486657917
14 0.512325021
15 0.53670877
16 0.559873331
17 0.581879665
18 0.602785682
19 0.622646397
20 0.641514078
21 0.659438374
22 0.676466455
23 0.692643132
24 0.708010976
25 0.722610427
26 0.736479906
27 0.74965591
28 0.762173115
29 0.774064459
30 0.785361236
31 0.796093174
32 0.806288516
33 0.81597409
34 0.825175385
35 0.833916616
36 0.842220785
37 0.850109746
38 0.857604259
39 0.864724046
40 0.871487843
41 0.877913451
42 0.884017779
43 0.88981689
44 0.895326045
45 0.900559743
46 0.905531756
47 0.910255168
48 0.91474241
49 0.919005289
50 0.923055025

 

[Denaes]

A series of die rolls is just a geometric distribution. In terms of rolling a 1 on a d20, the mean would be 20 rolls, but the variance is very large since all outcomes are equally likely on each trial. The probability of rolling a 1 on the 20th or earlier roll is roughly 64.2%. In other words, if you continuously rolled a d20 until you got a 1, noted how many rolls that took and repeated that process over and over, 64.2% of the time you would roll a 1 by the 20th roll. The table below shows the probablitilty of getting a 1 on the nth roll or less. The left column is the number of rolls and the right column is the cumulative probability. Another way of thinking of the results in this table is to take 1-a given probability, which equals the probability of it taking more than N rolls to get a 1. (E.g. 1-.642=.358, or a 35.8% chance it takes more than 20 rolls to roll a 1). Ive only included the first 50 n's for brevity , but it's easy to extrapolate beyond this (or to other dice (e.g. d12)).
1 0.05

Something isn't right here. Rolling a 1 on a 1 sided die (a ball?) should be 100%. Rolling a 1 on a 2 sided die should be 50%.

Did you include a 0 on the sides (so 1 is really 0 & 1) or round funnily?

 

[Patryn of Elvenshae]

Denaes:

The numbers on the chart are specific to a d20. The methodology can be extrapolated to cover all dice.

EDIT:

The chance to roll a 1 on any attempt is:

Attempt) Chance
1) Chance to roll a 1
2) (Chance you didn't roll a 1 on Attempt 1) * Chance to Roll a 1
3) (Chance you didn't roll a 1 on Attempts 1 or 2) * Chance to Roll a 1
...

Therefore, the chance that you've rolled a 1 on any attempt is:

Attempt) Chance
1) Chance to roll a 1
2) Sum of Chance to roll a 1 on Attempt 1 + Chance to roll a 1 on Attempt 2
3) Sum of Chance to roll a 1 on Attempt 1 + Chance to roll a 1 on Attempt 2 + Chance to roll a 1 on Attempt 3
...

Etc.

For your ball, you've got values of 100% after roll 1 and 0% for everything else.

 

[Denaes]

Denaes:

The numbers on the chart are specific to a d20. The methodology can be extrapolated to cover all dice.

I gotcha. I thought that was a chart for rolling a 1 on Nth sided die. It's the percentage of rolling a 1 on Nth roll.

My bad.

::hides in a ball of shame::