compilation of house rules

[Durgil]

here is a table at TN 7  Dice on the left
formula for success is  =1-(((TN-1)/10)^#DICE)
TN-1 is the number of failures per die  / 10  gives % to fail on each die ^ by the number of dice is the probablity of failing on EVERY die

The formula you are using is just part of what you need.  You might want to take a look at this discusion Math Help.  What you actually need to use is a binomial distribution (look up BINOMDIST in Excel).

[Mike Holmes]

In all systems presented high TN makes fumbles more likely. Nobody argues against that. In fact one could argue that the effect you cite should be even more pronounced than it is.

What we argue against is that small aberation at TN 10 that you note. That in that odd case, if I give you more dice to indicate say some advantage that you have, it actually increases your chances of fumbling. I'm not sure why you're having trouble understanding this. It seems intuitive that if you have more dice that it should make fumbling less likely. But in some circumstances that's not true. That's the "problem".

Another sort of perceptual problem is that the ratio failures to fumbles always increases with more dice. Lets look at it using the d10 example.

Code Select Expand

D10 Failure Fumble Ratio
1   90.00%   0.00%   0.00%
2   81.00%   1.00%   1.23%
3   72.90%   2.70%   3.70%
4   65.61%   4.49%   6.84%
5   59.05%   6.19%  10.47%
6   53.14%   7.68%  14.45%
7   47.83%   8.92%  18.65%
8   43.05%   9.89%  22.97%
9   38.74%  10.59%  27.33%
10  34.87%  11.04%  31.67%
11  31.38%  11.28%  35.95%
12  28.24%  11.33%  40.12%
13  25.42%  11.22%  44.16%
14  22.88%  10.99%  48.03%
15  20.59%  10.65%  51.74%

Note that the same effect exists no matter what TN you look at.

In other words, the more dice I use the more likely that any failure that does occur is a fumble. Again, one would think that any advantage that one had would make the proportion of failures that were fumbles less.

This latter argument is more susceptible to the "effort" argument, but again that seems pretty specious to me in general.

As you note (and I've noted over and over), the first effect is such a small blip in such a small spot that nobody really cares. And the latter effect is also not particularly glaring in play, so again nobody cares. Nor should they be very concerned. The game plays fine as is.

Still, I don't see why it's a bad idea to see if a solution to the "problem" can be found. As a form of entertainment, rather than as a criticism of the system.

Mike

[Thirsty Viking]

here is a table at TN 7  Dice on the left
formula for success is  =1-(((TN-1)/10)^#DICE)
TN-1 is the number of failures per die  / 10  gives % to fail on each die ^ by the number of dice is the probablity of failing on EVERY die

The formula you are using is just part of what you need.  You might want to take a look at this discusion Math Help.  What you actually need to use is a binomial distribution (look up BINOMDIST in Excel).

I have Microsoft WORKS, not microsoft EXCEL unfortunately.  If you think my formula is missing something for accurate prediction of the chance os 1+ success I'd love to hear it....   but I believe it accurately represents the chance of having at least one success.  The Fumble perdictions were more involved,  employing 4 cells and brute force modeling the  combinations of Failures with 0 1 and 2+ ones as well as 10^dice for total number of combinations.  

0 one failure combinations  = total combinations that are failures - combinations with 1 one and - combinations with 2 ones .... this is how i originally did this: it is accurate, but easier method is (TN-2)^#d yielding identical results... A formula I should have thought of logically I discovered through observation when I got the other cells correct.

1 one failure combinations = TN-2 for one die , For all higher die values they equal ((TN-2) * the number of 1 one failure combinations when 1 less die is rolled ) + the number of 0 one failures when one less die is rolled  

2 one failures is the same concept. but since we don't need to track the number of failures with more than 3 dice and we want the total failures with 2 or more ones we tweak the formula .... (the number of failures with 2 ones for one less die)*(TN-1) + (the number of 1 die failures on 1 less die)    Obviously you have 0 two die failures when you roll 1 die.

Code Select Expand


EX TN7       Failed 0 ones      1 one failure                       2+ one failures
1d@tn7               5                      1                                  0
2d@TN7              25          (5 * 01) +  005 =  010                      1
3d@TN7             125          (5 * 10) +  025 =  075        (6 * 1) + 10 = 16
4d@TN7             625          (5*  75) +  125 =  500        (6*16) + 75 = 161


now you are welcome to take out your formula with execel,  I wish I had access to it...  It should verify the validity of the columns for 0 and 1 one failures....   the last column  i stopped striping out the fumbles with more than two dice..   they are still just a fumble...  though a sadistic Seneschal could magnify fumbles as # of 1's increase.
for the Probability for the above results devide the number by 10^#d  

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                            Failures with exact # of 1's
                0          1          2         3         4
TN&@4d          .0625    .0500       .0145    .0015     .0001      

the above chart combines the last three in it's formula because they weren't worth tracking individually.  
These should be the results From your binomial distribution for the probability of an exact number number of 1's rolled WITHOUT a success  If they don't match your results then talk to me and we will try to figure out where the flaw is between us....   but manually plotting the die rolls on paper convinces me i've gotten this right.  It's ugly, It's brute Force.  but I believe it works.

I spent too long developing this...  A because i haven't had math in many years,  and B because i don't have many advanced functions in WORKS.

[Durgil]

Okay MIke, I think the problem that we're having here, for the most, has to do with the way we are looking at the Math.  I agree with the odds for failing in your previous post.  The numbers you have for the chance to fumble are good until you get up to rolling 5 dice, then our numbers don't match.  Here's what I've got:

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# of Dice     Fumble
1              N/A
2              1.0%
3              2.7%
4              4.9%
5              7.3%
6              9.8%
7             12.4%
8             14.9%
9             17.2%
10            19.4%
11            21.3%
12            23.0%
13            24.5%
14            25.7%
15            26.7%
16            27.5%
17            28.0%
18            28.4%
19            28.5%
20            28.5%
That is only true though for rolling two 1s with that many dice.  To fumble, there has to be no successes with two 1s rolled.  That means that to find out the odds of fumbling, you have to multiply the odds of rolling two 1s with the odds of getting 0 successes.  This will give you the following odds of rolling a fumble:

Code Select Expand

# of Dice          Fumble
1               N/A
2               0.8%
3               2.0%
4               3.2%
5               4.3%
6               5.2%
7               5.9%
8               6.4%
9               6.7%
10              6.8%
11              6.7%
12              6.5%
13              6.2%
14              5.9%
15              5.5%
16              5.1%
17              4.7%
18              4.3%
19              3.9%
20              3.5%
The chance for rolling two 1s does go up with the number of dice that are rolled, but as the number of dice increases, the chance of not getting a single success or more goes down.  At first, this second factor does not change enough from one dice to two etc., but eventually the chance of getting 0 successes goes down enough to offset the increase chance of rolling two 1s with more dice and you see the overall chance of a fumble go down once you get past dice pools of 10 or more.

As for the Thirsty Viking, MS Works or Excel, I don't know the difference, but if you use the formula =BINOMDIST(# of Successes,# of Dice, % of Rolling a Success Per Dice,FALSE), you will get the odds of getting that many successes while rolling that many dice with that Target Number.  Just Like my post back on Math Help says, I've developed a couple of Excel Spreadsheets that have all of the work done for you, you just have to pick the Target Number, and it gives you the odds for all of this stuff.  All you need to tell me is where to send it to.

[Mike Holmes]

Binomdist does not work in Works nor do any of the statistical distribution formulae. Just not included. That said, the Binomdist function can be worked out "manually" so to speak. That is, I think that using the FACT function and the formula in the Math Help thread that Jeff came up with that you can do just fine.

I'm not arguing with anyone's math, it all looks correct to me.

What I'm referring to as a "problem" (note how I've taken to using quotes to try and emphasize how little of a problem this really is) is those few places where the combination of TNs and dice are such that adding dice the odds of fumbling go up. Looking at what you have there (I'm assuming that this is TN10) if I am a guy researching my ancestry in a disorganized library, and I have a pool of 4 dice, and I get 4 extra dice for my Drive: Find Roots, my odds of fumbling double. Yes, my odds of failing go down. But my odds of fumbling go up. In absolute terms.

Now you could explain this as effort or zeal or something in ths case, and it counds good. But why then doesn't this happen in other circumstances? It only happens in this limited set of circumstances. So it's an aberration of the system.

Now, it only happens on TN 10, and only for a limited part of the range. I was the first person the last time we discussed this to note that with a high enough pool that it goes back down again. So, yes, it's unlikely that this "problem" circumstance will even arise. And even less likely that anyone would care about it, as the actual odds are very small (<7%) in any case. And even if they do fumble, few people are aware of the aberration in question.

The other issue is one of perspective:

In all cases, while my odds of failing do decrease, my odds of fumbling if I do fail increases. The odds of fumbling with respect to the roll to begin with decrease, yes, but my chance of fumbling increases with respect to my chance of failing. Which is counterintuitive if you think about it as much as I have. Most have not, so it will not be a problem. Let me demonstrate what I think would be a better curve.

Code Select Expand

d10 success  Fail   fumble  ratio
1   10.00%   90.00% 45.00%  50.00%
2   19.00%   81.00% 28.64%  35.36%
3   27.10%   72.90% 21.04%  28.87%
4   34.39%   65.61% 16.40%  25.00%
5   40.95%   59.05% 13.20%  22.36%
6   46.86%   53.14% 10.85%  20.41%
7   52.17%   47.83%  9.04%  18.90%
8   56.95%   43.05%  7.61%  17.68%
9   61.26%   38.74%  6.46%  16.67%
10  65.13%   34.87%  5.51%  15.81%
11  68.62%   31.38%  4.73%  15.08%
12  71.76%   28.24%  4.08%  14.43%
13  74.58%   25.42%  3.52%  13.87%
14  77.12%   22.88%  3.06%  13.36%
15  79.41%   20.59%  2.66%  12.91%
16  81.47%   18.53%  2.32%  12.50%
17  83.32%   16.68%  2.02%  12.13%
18  84.99%   15.01%  1.77%  11.79%
19  86.49%   13.51%  1.55%  11.47%
20  87.84%   12.16%  1.36%  11.18%

Perhaps a bit high on the low end for fumbles. And completely fictitious, this doesn't represent any actual odds as produced by the game. But, you can see the trend that would be most intuitive (IMO). That being that failure decreases n all cases, but so do fumbles as a proportion of failures.

But again who but myself notices such things. So with all that, it's not an issue.

But that still doesn't mean that I don't find it a fun challenge to try and find a "solution" to the "problem".

I have now put far more effort into describing a non-problem than is probably healthy. But you keep asking about it. I'm not sure why all the concern. Does anyone out there hold the opinion that I think that this is some crippling feature of the game? I think that I've gone out of my way to tell people not to worry about it.

Mike

[Durgil]

Binomdist does not work in Works nor do any of the statistical distribution formulae. Just not included. That said, the Binomdist function can be worked out "manually" so to speak. That is, I think that using the FACT function and the formula in the Math Help thread that Jeff came up with that you can do just fine.

Sorry about that, Thirsty Viking.  You could always get the free Excel Reader for free if you would like to take a look at my speadsheet.

my odds of fumbling if I do fail increases.

This is what I'm trying to show you; you can not have a fumble if there are any successes, so these numbers or bogus.  To get ligitamate odds you have to look at both - the chance to roll two or more 1s and the chance of getting 0 successes.

But that still doesn't mean that I don't find it a fun challenge to try and find a "solution" to the "problem".

And I guess I just don't see the problem

[Mike Holmes]

my odds of fumbling if I do fail increases.

This is what I'm trying to show you; you can not have a fumble if there are any successes, so these numbers or bogus.  To get ligitamate odds you have to look at both - the chance to roll two or more 1s and the chance of getting 0 successes.[/quote]

To get the absolute odds, you need to combine them. Yes. I am well aware of that.

See I'm a statistician by trade. If I had to write up a report, there would be something in it that would say, While the increase in A does cause a decrease in B, B does increase relative to C.

This is, believe it or not a valid form of analysis.

What you are saying to me is that you are not concerned with the ratio of failures to fumbles. And you know what? That's a perfectly valid perspective. As I keep saying. Put from a different perspective, mine, which says that IRL, when you are given an advantage that there is a propensity not only to succeed, but for the margin of extreme failure to reduce at a proportional or greater rate, this is not an intuitive solution. It does not match natural curves of this sort. Really.

But if you cannot see that perspective, then comfort yourself in the fact that you are in the majority, and that they system will play "as is" satisfactorily. Why you have to persist in telling me that you don't have the same viewpoint as me is beyond me.

Look at my theoretical chart that represents my perspecutive of what would be correct. Is it the same as the other chart? No. Is there something non-intuitive about it from the perspective that I have described? No. So how is my statment incorrect.

People are of the belief that statistics is a science. Math is a science, statistics is an art.

Mike

[viktor_haag]

The reason I used the "must have more ones than any other single number" house rule is precisely as one of the posters described.

What I don't like is the increasing likelihood that a failure will be a fumble, as the test uses more dice.

It's not a big deal for me, and the house rule seemed to fix the problem nicely. Yes, I do realize that it lowers the chance of fumbling, and thanks for the suggestion about amending: I will amend my rule to say "to avoid fumbling on a failed roll, you must produce a group of matched dice that has more dice in it than the number of ones you rolled in the failure".

[viktor_haag]

For some reason, my last post to this thread seems to have been weirdly formatted (massively indented to the right).

If that makes your eyes hurt, I apologize....


--
Viktor

[Thirsty Viking]

As for the Thirsty Viking, MS Works or Excel, I don't know the difference, but if you use the formula =BINOMDIST(# of Successes,# of Dice, % of Rolling a Success Per Dice,FALSE), you will get the odds of getting that many successes while rolling that many dice with that Target Number.  Just Like my post back on Math Help says, I've developed a couple of Excel Spreadsheets that have all of the work done for you, you just have to pick the Target Number, and it gives you the odds for all of this stuff.  All you need to tell me is where to send it to.

ok ...  just for verification sake.  could you run your sheet for TN 10
and compare your results to mine?  I can't do that. cause i can't use your fancy function...   Even if you send it to me, works can't execute those functions.

Code Select Expand


TN 10

d10 % success %failure % fumble
01     10.000% 90.000% 00.000%
02     19.000% 81.000% 01.000%
03     27.100% 72.900% 02.500%
04     34.390% 65.610% 04.170%
05     40.951% 59.049% 05.801%
06     46.856% 53.144% 07.269%
07     52.170% 47.830% 08.508%
08     56.953% 43.047% 09.492%
09     61.258% 38.742% 10.221%
10     65.132% 34.868% 10.709%
11     68.619% 31.381% 10.980%
12     71.757% 28.243% 11.063%
13     74.581% 25.419% 10.988%
14     77.123% 22.877% 10.782%
15     79.411% 20.589% 10.474%
16     81.470% 18.530% 10.086%
17     83.323% 16.677% 09.640%
18     84.991% 15.009% 09.155%
19     86.491% 13.509% 08.645%
20     87.842% 12.158% 08.122%
21     89.058% 10.942% 07.598%
22     90.152% 09.848% 07.081%
23     91.137% 08.863% 06.576%
24     92.023% 07.977% 06.088%
25     92.821% 07.179% 05.621%
26     93.539% 06.461% 05.177%


If our numbers match then we are both probably correct.  Mine disagree slightly with Mikes.  His agree with an earlier version of my sheet I decided was in error after cranking out the probabilites by hand with a flow chart for the first 4 dice.

Lastly On the issue of higher target numbers have a higher chance of fumbling...   If we addopt the rule variant suggested then the higher the target number the less likely a fumble on a failure is at all dice levels. the math for this hurts my head to contemplate but it should be obvious...  this is true at all dice levels.  so to fumble less all you need to do is try something harder... say what?   you are trading one  possible inconsistancy for a clear inconsistancy.  

Here is my rationale to leave the system alone.  People who know they are doing something they aren't very good (few dice) at  tend to be more careful at what they are doing. People with mediocre ability for the dificulty they are attempting often push beyond thier limits and fail more spectacularly(they no longer know how much they don't know).  Masters of the art have passed over top of that bell curve....   sure you occasionally get the rank neophyte who with overzealous application roayally screws up...  he must have had passion dice involved  :-)

Again, unless you are at TN 10+ it never climbs above
4.5%@TN9@7d    ex.    Parrying a sword with rondel (Cheap dagger)
2.6%@TN8@5d    ex.    Parrying with a mace or a rapier(against swung)
1.7%@TN7@4d    ex.    Parying with Poinard (better dagger)vs Swung sword
1.3%@TN6@3d    ex.    Parrying with a sabre
1.0%@TN5@2d    ex.    Parying a rapier with a rapier/poinard

Out of combat the fumble results make as much sense as long as target numbers are selected appropriately.  Just chose appropriate fumble results.

What you are saying to me is that you are not concerned with the ratio of failures to fumbles. And you know what? That's a perfectly valid perspective.

On the Contrary...  I relish it,  I celebrate,  I shout it from the roof tops. The beter you are the further out on the ledge you go..  the more spectacular your failures become.   Case in point?  Mountain Climbing in the Himalayas(sp)  whats the stat of deaths on K2?  1 in 3?  one in 5?  These are climbers with lots of dice...  the problem is that thier difficulty number is high  How high would be a nicely modeled question.  Sure there are some who give up and come back down.   Little peon 3-4d mountain climber that I am...  I don't try it.  The primary tie is to difficulty number not dice.  Yes normal failures disappear.  when the best of the best fail...  it's almost always a fumble.

[Thirsty Viking]

numbers you have for the chance to fumble are good until you get up to rolling 5 dice, then our numbers don't match.  Here's what I've got:

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# of Dice     Fumble
1              N/A
2              1.0%
3              2.7%
4              4.9%
5              7.3%
6              9.8%
7             12.4%
8             14.9%
9             17.2%
10            19.4%


I agree with you to this point,  but then i think rounding errors may creep in.  I seperated out all the 3+ 1  from my calculations,  but they shouldn't be ignored,  they are still fumbles a weakness in your formulae.

This will give you the following odds of rolling a fumble:

Code Select Expand

# of Dice          Fumble
1               N/A
2               0.8%
3               2.0%
4               3.2%
5               4.3%
6               5.2%
7               5.9%
8               6.4%
9               6.7%

Serious i can niether tell what Target number your modeling, nor your errors...  but obviously on 2d the chance to fumble is 1% exactly.
assuming you are modeling TN10 your numbers should be  Ah i found it,  you hard coded the modifier .9 into an equation...  when it was already compensated for you.  Your numbers should be close to collumn 1 or 3

Code Select Expand


#d % 2 %2 *.9 % 2+
1 0.0% 0.0% 0.0%
2 1.0% 0.9% 1.0%
3 2.4% 2.2% 2.5%
4 3.8% 3.5% 4.2%
5 5.1% 4.6% 5.8%
6 6.1% 5.5% 7.3%
7 6.9% 6.2% 8.5%
8 7.3% 6.6% 9.5%
9 7.5% 6.8% 10.2%
10 7.5% 6.8% 10.7%
11 7.4% 6.6% 11.0%
12 7.1% 6.4% 11.1%
13 6.7% 6.0% 11.0%
14 6.3% 5.6% 10.8%
15 5.8% 5.2% 10.5%


1st collum is the % of total rols that are failures with exactly 2 1's
2nd collumn closely models your number  withing  call it rounding.
3rd collumn is all fumbles without a success..  These are I believe the true numbers we need.

I don't know whats wrong with your math...  But I've become sure of mine...  we can try to solve this if you want..  or drop it.

[Thirsty Viking]

Look at my theoretical chart that represents my perspecutive of what would be correct. Is it the same as the other chart? No. Is there something non-intuitive about it from the perspective that I have described? No. So how is my statment incorrect.

People are of the belief that statistics is a science. Math is a science, statistics is an art.

Mike

LOL  there have been so many charts  I'm not sure the one you mean.  The counterintuitive thing that I saw was having the % of fumbles for the same number of dice rolled  go down as the TN goes up....   If that isn't counterintuitive i don't know what is.  For arguments sake lets stick to TN above 4 where all reasonable TN's exist  ...  Yes i have specialized people to a 3 at startup...  but thats the extreme  takes a fumble to fail freak.

If your variant addressed this as well,  i'll have to reread the entire thread to find it.

[Mike Holmes]

"Or if you have a rationale that points out why this makes sense" to quote myself from the last thread. Which you now have. Great. You have a rationale, to add to TROS, the poster has an optional rule to address the same issue. And I'm still looking at it.

How many times do I have to repeat this that all of these are only a "problem" if you see it the way I do. It's a matter of opinion, not fact. Get it people? So, why you keep on harping on this is really beyond me. As I've now written five times on this thread, it's nothing anyone should be concerned about if they don't want to be. It's nothing that can possibly damage game play in any serious fashion.

It's just a weird part of the way the system works that a few of us are interested in looking at alternate ways to do. It's like a math excercise. We do it more to see it it can be done than anything else. This thread was supposed to be about optional rules. Well, the neat thing about optional rules is that they're optional. If it doesn't make sense to you, do not use it.

I can't say it any more clearly than that.

Mike

[Thirsty Viking]

on one post you had 50% of failures on 1 d being a fumble for TN 10
I must have missed something in another thread, cause i never saw how you were generating these numbers.

[Durgil]

I’m sorry to drag this on with one more post, but I goofed.  The odds of rolling two 1s was just that, not two or more.  The chart below is for a TN of 10, and it shows the number of Dice rolled, The odds of getting no successes, the odds of getting two OR MORE 1s, and the final overall odds of rolling a fumble.

Revised Chart

Code Select Expand

# of Dice 0 Successes Two or More 1s Chance of Fumble
1               90.0%       N/A           N/A
2               81.0%       1.0%         0.8%
3               72.9%       2.8%         2.0%
4               65.6%       5.2%         3.4%
5               59.0%       8.1%         4.8%
6               53.1%          11.4%         6.1%
7               47.8%       15.0%       7.2%
8               43.0%       18.7%       8.0%
9               38.7%       22.5%       8.7%
10             34.9%       26.4%       9.2%
11             31.4%       30.3%       9.5%
12             28.2%       34.1%       9.6%
13             25.4%       37.9%       9.6%
14             22.9%       41.5%       9.5%
15             20.6%       45.1%       9.3%
16             18.5%       48.5%       9.0%
17             16.7%       51.8%       8.6%
18             15.0%       55.0%       8.3%
19             13.5%       58.0%       7.8%
20             12.2%       60.8%       7.4%


Sorry for the overtime and the mistake.

PS-The speadsheet that I made has been fixed, so I'll try to get the updated sheets to you if I still have your email.