The Stainless Steel Rat
Mar 27 2006, 03:36 PM
So here's a pet project I've been working on lately for my group, and thought I would offer it up to Dumpshock.
The basic SR mechanic is one of my favorites, but there are some issues that I have always felt needed addressing and I think I have solved 2 of them.
 Piles & Piles of D6s : We all know how many dice can be allocated to a single test, and double that for opposed tests. Spending the time to count out the dice, then roll them (rerolling 6's, rererolling 12's etc.), then count and compare successes can really slow things down. You may not think this is a problem, but I think it's clunky.
 6=7: In fact, 7 doesn't really exist, and since the majority of rolls in the games I play tend to have target numbers of 48 this problem is the elephant in the corner, silently mocking us as we try to ignore it.
Here's how I solved problem #1:
I calculated the odds of rolling any given number of successes against any given target number with any given number of D6's and organized these odds as percentages on a series of charts. Each target number will have it's own chart with the number of D6's across the top, and number of successes down the side. Roll 2 D10's for percentage, and find the number of successes that roll correlates to.
Example:
CODE 
TGT#4 Base Value = 50 % chance of a hit per die  # hits  1D6  2D6  3D6  4D6  5D6  6D6   1  50.0%  75.0%  87.5%  93.8%  96.9%  98.4%  2  25.0%  50.0%  68.8%  81.3%  89.1%  3  12.5%  31.3%  50.0%  65.6%  4  6.3%  18.8%  34.4%  5 Roll under the # Listed  3.1%  10.9%  6  1.6%   
So, I have 5 dice for the test, TGT #4: I roll 2 D10 and get a 36. The lowest number I have rolled under is 50, so I achieved 3 successes. If I happen to roll exactly on one of the limits, say 18, I would roll again to see which side of the .8 I fall on. Yeah, it takes some time to find the right chart, then reference it for the % roll, but I don't think it will take any longer than counting a die pool, rolling & rerolling, then counting  and it could be quite a bit faster once the players get used to it.
Here's how I solved problem #2:
Now that we are rolling percentages, changing the probability of rolling any given number is child's play. I can simply declare that 6 =\= 7 and recalculate the odds. What I chose to do was plot the probabilities, then normalize them into a smooth curve. Compare the odds below:
CODE 
# Actual Odds Modified Odds 2 83.33% 83.00% 3 66.67% 63.00% 4 50.00% 46.00% 5 33.33% 34.00% 6 16.67% 25.00% 7 16.67% 18.00% 8 13.89% 14.00% 9 11.11% 10.00% 10 8.33% 7.00% 11 5.56% 5.00% 12 2.78% 4.00% 13 2.78% 3.00% 14 2.31% 2.00% 15 1.85% 1.50% 16 1.39% 1.00% 17 0.93% 0.80% 18 0.46% 0.70% 19 0.46% 0.50% 20 0.39% 0.40% 21 0.31% 0.30% 22 0.23% 0.21% 23 0.15% 0.15% 24 0.08% 0.11% 25 0.077% 0.08% 26 0.064% 0.065% 27 0.051% 0.047% 28 0.039% 0.034% 29 0.026% 0.025% 30 0.013% 0.017% 31 0.013% 0.013% 32 0.011% 0.011% 33 0.009% 0.009% 34 0.006% 0.006% 35 0.004% 0.004% 36 0.002% 0.002% 
Using these smoother probabilities, I recalculated the odds:
Example
CODE 
TGT#4 Base Value = 46 % chance of a hit per die  # hits  1D6  2D6  3D6  4D6  5D6  6D6   1  46.0%  70.8%  84.3%  91.5%  95.4%  97.5%  2  21.2%  44.0%  62.5%  75.9%  84.8%  3  9.7%  25.5%  42.5%  57.9%  4  4.5%  14.1%  27.2%  5 Roll under the # Listed  2.1%  7.6%  6  0.9%   
I made a similar table for Open Ended tests (what are the odds of rolling the highest number X with Y number of D6's  using the modified odds) and another for rolling initiative, where you add the total of all dice rolled.
So there you have it: Shadowrun 3 converted to D10 without actually changing the whole system. Attributes, Skills, Target Numbers, Modifiers  these all stay exactly the same. (Although an enterprising GM could choose to apply percentage modifiers instead of (or in addition to) the standard target number modifiers.
I also included another category across the top, which represents the chance of rolling all ones for the Rule of One. This is generally 0.1% or less, so any roll of 99.9 results in catastrophic failure. Conversely, a roll of all zeros results in the maximum number of successes.
At the very least I have compiled a list of all roll percentages so power gamers can use them to metagame every test.
If anyone is interested in getting these charts (or the Excel tool I made to create them) send me a pm and I'll get it to you. If I get enough requests I'll post the thing somewhere.
Rat out.
ShadowDragon8685
Mar 27 2006, 04:04 PM
Alternatively, some of us are fine with 6=7, and we play with computerized random dice rollers that automatically explode dice for us and count our hits against any given TN.
The Stainless Steel Rat
Mar 27 2006, 04:14 PM
QUOTE (ShadowDragon8685) 
Alternatively, some of us are fine with 6=7

Yeah, base 5 + 1 reduces successes by half, and base 6 + 1 has no effect whatsoever. It's totally cool.
QUOTE (ShadowDragon8685) 
we play with computerized random dice rollers 
They have those!?! I did all this with an abacus and a slide rule...
nezumi
Mar 27 2006, 10:10 PM
You could get rid of the 6=7 problem whilst having the least impact on the probability charts by simply using d7s instead of d6s. I'd like a game based entirely around dice of prime numbers.
ChuckRozool
Mar 28 2006, 12:55 AM
QUOTE (nezumi @ Mar 27 2006, 05:10 PM) 
You could get rid of the 6=7 problem whilst having the least impact on the probability charts by simply using d7s instead of d6s. I'd like a game based entirely around dice of prime numbers. 
John Campbell
Mar 28 2006, 01:32 AM
I'm not convinced that using a lookup table to simulate the probability curve of a bunch of d6es using d10s saves any useful amount of effort over, y'know, just rolling an actual bunch of d6es.
Edward
Mar 28 2006, 03:25 AM
The fast solution to the 67 problem is to rewrite the rule of 6 as follows. “When you role a 6 reroll that dice and add 5” this dose make high difficulty tasks even harder but some people where complaining about that anyway.
Edward
eidolon
Mar 28 2006, 04:32 AM
Not caring is faster.
nezumi
Mar 28 2006, 02:44 PM
QUOTE (ChuckRozool) 
QUOTE (nezumi @ Mar 27 2006, 05:10 PM)  You could get rid of the 6=7 problem whilst having the least impact on the probability charts by simply using d7s instead of d6s. I'd like a game based entirely around dice of prime numbers. 

Something tells me those dice aren't exactly 'fair'. Two sides are far bigger than the other five, so if it lands on the big 6 or 7 it's highly unlikely to roll over, whereas 15 it's quite possible that it'll actually stop on another number.
That said, pretty neat.
ChuckRozool
Mar 28 2006, 03:47 PM
QUOTE (nezumi) 
Something tells me those dice aren't exactly 'fair'. Two sides are far bigger than the other five, so if it lands on the big 6 or 7 it's highly unlikely to roll over, whereas 15 it's quite possible that it'll actually stop on another number.
That said, pretty neat. 
Well according to the site I found they had this to say...
QUOTE 
This is a true 7sided dice that has been tested over 10,000 times for randomness. The numbers one through 5 are along the edges of the die... 
nezumi
Mar 29 2006, 06:12 PM
It's been tested 10,000 times for randomness... And what were the results? ;P
I don't have the URL, so I really have no idea what the rest of that quote says, or if there's any reason why it makes me feel more confident about using said dice in my Shadowrun dPrime games.
Ankle Biter
Mar 29 2006, 09:14 PM
But my gm solved 6 =! 7 ages ago.. if the TN is seven, half the number of sevens you roll count as successes, and count all other results normally.
He also rounded up for us and down for the baddies to give us a little free edge.
Ankle Biter
Mar 29 2006, 09:18 PM
QUOTE (ChuckRozool) 
QUOTE (nezumi @ Mar 27 2006, 05:10 PM)  You could get rid of the 6=7 problem whilst having the least impact on the probability charts by simply using d7s instead of d6s. I'd like a game based entirely around dice of prime numbers. 

Fine, now I want a D(Pi), a D(infinity), and a D(i).
You are not going to convince me that them dice are fair.
ChuckRozool
Mar 30 2006, 03:50 PM
They also have three and five sided die...
http://www.gamestation.net/departments.asp?dept=1009and binary dice
nezumi
Mar 30 2006, 04:37 PM
5 sided don't look especially fair either. I guess they're only marketing to fringe, crazy gamers with no understanding of probability?
Platinum
Mar 30 2006, 04:44 PM
I just took a d10 or d6 and divided the number by 2. I am crazy like that I guess.
John Campbell
Mar 30 2006, 07:17 PM
The d5 description says, "this 5sided wonder has been precisioncrafted, handnumbered, and tested over 10,000 rolls for randomness, with NO side coming up more than 20% of the time". Since there are only five sides, the only way for those rolls to add up to 100% with no side being more than 20% of the results is if no side is less than 20% of the results, either. In other words, if they rolled it 10,000 times, every result came up EXACTLY 2,000 times. Zero margin of error. That's ridiculously improbable to the point that it says less about the fairness of their dice than about the fakeness of their assurances.
ChuckRozool
Mar 30 2006, 11:59 PM
I just find it funny that this went from a thread about a house rules to fix the target number 7, to a discussion of prime number dice...
That's forums for you, i guess
peace, i'm out
ShadowDragon8685
Mar 31 2006, 05:19 AM
QUOTE (John Campbell) 
The d5 description says, "this 5sided wonder has been precisioncrafted, handnumbered, and tested over 10,000 rolls for randomness, with NO side coming up more than 20% of the time". Since there are only five sides, the only way for those rolls to add up to 100% with no side being more than 20% of the results is if no side is less than 20% of the results, either. In other words, if they rolled it 10,000 times, every result came up EXACTLY 2,000 times. Zero margin of error. That's ridiculously improbable to the point that it says less about the fairness of their dice than about the fakeness of their assurances. 
I'm pretty sure there's some rounding involved there, JC.
nezumi
Mar 31 2006, 02:38 PM
QUOTE (John Campbell) 
The d5 description says, "this 5sided wonder has been precisioncrafted, handnumbered, and tested over 10,000 rolls for randomness, with NO side coming up more than 20% of the time". Since there are only five sides, the only way for those rolls to add up to 100% with no side being more than 20% of the results is if no side is less than 20% of the results, either. In other words, if they rolled it 10,000 times, every result came up EXACTLY 2,000 times. Zero margin of error. That's ridiculously improbable to the point that it says less about the fairness of their dice than about the fakeness of their assurances. 
That, or it simply didn't fall on ANY side for some significant percentage of the time.
I notice they didn't specify how they tested it. Maybe they threw it on a pillow and simply counted all the 'no side clearly up' as a successful test with no numeric result? As I said though, I can't imagine how that geometric figure is possibly fair.
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