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> Hit and Glitch Probabilities
Wizard
post Jan 3 2006, 12:55 PM
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The dice mechanic in the Fourth Edition intrigues me. It's simple in use but it's hard to determine probabilities when rolling multiple dice against various thresholds. I had a couple of spare hours so I thought I would write a simple program to calculate the various probabilities of getting hits and glitches. Here are the results:

CODE

                   -------------------- Dice Pool ----------------------
Threshold          1     2     3     4     5     6     7     8     9
    1              33.3% 55.6% 70.4% 80.2% 86.8% 91.2% 94.1% 96.1% 97.4%
    2              0.0%  11.1% 25.9% 40.7% 53.9% 64.9% 73.7% 80.5% 85.7%
    3              0.0%  0.0%  3.7%  11.1% 21.0% 32.0% 42.9% 53.2% 62.3%
    4              0.0%  0.0%  0.0%  1.2%  4.5%  10.0% 17.3% 25.9% 35.0%
                 
Glitches           0.0%  11.1% 2.8%  8.0%  2.2%  4.7%  1.4%  2.6%  0.8%
Critical Glitches  16.7% 19.4% 4.6%  5.2%  1.4%  1.5%  0.4%  0.4%  0.1%
Total Glitches     16.7% 30.6% 7.4%  13.2% 3.5%  6.2%  1.8%  3.1%  0.9%


Graphing these results produces nice curves that progress smoothly. It shows the non-linear aspect of the mechanic and is what I was hoping to see, damn good!

The glitches are another story. As discussed in another thread the problem lies in the fact that it is better to have an odd number of dice in the dice pool than an even number. It's not a big issue, especially once the dice pool has 5 or more dice, but it does bug me.

After a fair bit of trial and error the following modified glitch rule seems to resolve the issue.

If more than half of the dice pool rolled come up as 1s, then a glitch results. Also if exactly half of the dice pool rolled come up as 1s and the other half do not come up as 3s, 4s, 5s or 6s, then a glitch results.

The results from this modified glitch rule are:
CODE


                   -------------------- Dice Pool ----------------------
                   1     2     3     4     5     6     7     8     9
Glitches           0.0%  0.0%  2.8%  2.5%  2.2%  2.3%  1.4%  1.6%  0.8%
Critical Glitches  16.7% 8.3%  4.6%  3.3%  1.4%  1.1%  0.4%  0.4%  0.1%
Total Glitches     16.7% 8.3%  7.4%  5.8%  3.6%  3.5%  1.8%  2.0%  0.9%


The results are not perfectly smooth but I think it's good enough and it does resolve the issue of odd and even dice pools.

Here are a few examples:

1,3 = no hits, no glitch
1,2 = no hits, critical glitch
1,5 = 1 hit, no glitch
1,1,2 = no hits, critical glitch
1,1,3 = no hits, critical glitch
1,1,5 = 1 hit, glitch
1,1,2,3 = no hits, no glitch
1,1,1,5 = 1 hit, glitch
1,1,2,2 = no hits, critical glitch
1,1,1,2,2,3 = no hits, no glitch
1,1,1,1,2,5 = 1 hit, glitch


On a final note for those interested I am quite happy to send the program and source I wrote, it was written in C# so you will need to install the .NET Framework 2.0 to run it.

This post has been edited by Wizard: Jan 4 2006, 03:04 AM
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Darkness
post Jan 3 2006, 02:02 PM
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QUOTE (Wizard)
CODE

                   -------------------- Dice Pool ----------------------
                   1     2     3     4     5     6     7     8     9
1 Hit              33.3% 55.6% 70.4% 80.2% 86.8% 91.2% 94.1% 96.1% 97.4%
2 Hits             0.0%  11.1% 25.9% 40.7% 53.9% 64.9% 73.7% 80.5% 85.7%
3 Hits             0.0%  0.0%  3.7%  11.1% 21.0% 32.0% 42.9% 53.2% 62.3%
4 Hits             0.0%  0.0%  0.0%  1.2%  4.5%  10.0% 17.3% 25.9% 35.0%


For clarification:
These are the probabilites for at least the number of Hits on the left.
And yes, they describe the probabilities of success for a success-test against a given Threshold (which is the "Hits" on the left side).

Thats a difference to the probabilites of exactly the number of hits on the left, which are:
CODE

               ----------------------------Dice Pool--------------------------------
               1       2       3       4       5       6       7       8       9
Hits   0       66,7%   44,4%   29,6%   19,8%   13,2%   8,8%    5,9%    3,9%    2,6%
       1       33,3%   44,4%   44,4%   39,5%   32,9%   26,3%   20,5%   15,6%   11,7%
       2               11,1%   22,2%   29,6%   32,9%   32,9%   30,7%   27,3%   23,4%
       3                       3,7%    9,9%    16,5%   21,9%   25,6%   27,3%   27,3%
       4                               1,2%    4,1%    8,2%    12,8%   17,1%   20,5%
       5                                       0,41%   1,65%   3,84%   6,83%   10,24%
       6                                               0,14%   0,64%   1,71%   3,41%
       7                                                       0,05%   0,24%   0,73%
       8                                                               0,02%   0,09%
       9                                                                       0,01%


And by the way these are the Probabilites for an "Attacker" to win (<- has at least one success more) against a "Defender". It also results in some nice graphs:
CODE
               -----------------------------Attacker----------------------------                                                              
Defender          1       2       3       4       5       6       7       8       9
       1       22,22%  40,74%  55,56%  67,08%  75,86%  82,44%  87,32%  90,90%  93,50%
       2       14,81%  29,63%  43,21%  55,01%  64,88%  72,93%  79,35%  84,39%  88,29%
       3       9,88%   21,40%  33,20%  44,40%  54,52%  63,34%  70,82%  77,02%  82,08%
       4       6,58%   15,36%  25,24%  35,36%  45,12%  54,13%  62,19%  69,20%  75,18%
       5       4,39%   10,97%  19,02%  27,84%  36,85%  45,62%  53,83%  61,29%  67,91%
       6       2,93%   7,80%   14,23%  21,70%  29,76%  37,97%  45,99%  53,58%  60,56%
       7       1,95%   5,53%   10,57%  16,77%  23,79%  31,25%  38,84%  46,28%  53,37%
       8       1,30%   3,90%   7,80%   12,86%  18,84%  25,46%  32,45%  39,54%  46,51%
       9       0,87%   2,75%   5,73%   9,79%   14,80%  20,56%  26,86%  33,45%  40,13%

I used Excel by the way.

On the topic of Glitches:
I had similar but slightly different results than you. And i will check the probabilites for your proposal as well, as soon as i find the time.
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Inigo Carmine
post Jan 3 2006, 06:15 PM
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Removed because I can't seem to get my statistics right.
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Wizard
post Jan 4 2006, 03:07 AM
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QUOTE (Darkness)
For clarification:
These are the probabilites for at least the number of Hits on the left.
And yes, they describe the probabilities of success for a success-test against a given Threshold (which is the "Hits" on the left side).

Thanks for the clarification. I have adjusted the wording in my initial post, hopefully it makes more sense now.
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Hasaku
post Jan 4 2006, 03:47 AM
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QUOTE (Darkness)
I used Excel by the way.

Could I get a copy of the spreadsheet? I've been trying to do a little statistics and graphing work in Excel, but I know next to bloody nothing about the program. I'd really like to see some sort of example.

PM me for my email if that's cool.
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Feshy
post Jan 4 2006, 04:24 AM
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QUOTE (Hasaku)
QUOTE (Darkness @ Jan 3 2006, 07:02 AM)
I used Excel by the way.

Could I get a copy of the spreadsheet? I've been trying to do a little statistics and graphing work in Excel, but I know next to bloody nothing about the program. I'd really like to see some sort of example.

PM me for my email if that's cool.

I'd like a copy too. TNX.
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Wizard
post Jan 4 2006, 05:16 AM
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Just thinking about it, maybe the rule would be clearer if it was phrased like this:

If more than half of the dice pool rolled come up as 1s, then a glitch results. Also if exactly half of the dice pool rolled come up as 1s and all the other dice come up as 2s, then a glitch results.

Note that you cannot roll exactly half the dice as 1s for a odd dice pool, since half of say 3 is 1.5. Thus the second part of the rule only effects even dice pools.
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Darkness
post Jan 4 2006, 12:55 PM
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Mmmh. The sheet is in german, so i will whip up a quick translation and put it on my webspace for easy downloading. (as well as adding some comments for clarification). I used them for myself, so I know what they do ^^.

And i'm far from being a professional myself ^^.
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Darkness
post Jan 4 2006, 02:07 PM
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*ping*
Done!
Well here it is anyways.
Shadowrun 4 Probablilities Excel Sheet(s)
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Skippy
post Jan 4 2006, 03:29 PM
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Thanks, Wizard! This Illustrates the points about glitches that I've been trying to make to my gaming group. Namely, that glitches need some work. And now you've done that work before i even had a chance to!

The only other thing I've been considering is removing the '-1die from a dice pool for defaulting' rule.

I got to thinking about ordinary people in the Shadowrun world. People with average ability scores of 3 and 0 ranks in skills (Which is, of course, the common knowledge level). That means that for EVERY action out there that needs a test, the ordinary person is going to be rolling 2 dice (3 ability -1 for defaulting). And of course, as written, that gives people an incredibly high glitch or critical glitch rate. The chances of glitches drops dramatically as soon as the 3rd die gets added to the pool, and I think that probably reflects a more normal world where people aren't setting themselves on fire in droves when cooking, crashing their cars every third time they take a steep turn or slashing their throats while shaving. A world like that would quickly fall to ruin. Just because it's the 6th world, doesn't mean it has to be a world of Inspector Clouseaus.

Heh. I know that since we aren't playing ordinary people, we suffer from things like this less often, but I think a game mechanic should at least try to simulate reality on SOME level. Of course, if I convince them to use your modified glitch rule, we might not need to adjust this anyways.

Anyways, enough of that. Great work!

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Wizard
post Jan 4 2006, 03:44 PM
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I have created a PDF that explains things and shows the graphs. It can be downloaded from here.

This post has been edited by Wizard: Jan 6 2006, 11:37 AM
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