house rules ... that page error is madening

[Thirsty Viking]

Mike i saw a theoretical post where you had raised the fumble percentages for low dice with TN 10  ...  did you have a method you were proposing that generated those numbers ...  or was that just a this would be nice if we could figure out how to do it?

[Mike Holmes]

Yopu know there were a few methods floating about, and I can't remeber if I'd applied one or not. I'll check and get back to this thread tomorrow.

Meanwhile does anyone happen to remember a good one? I know that I came up with a couple that were absurdly complicated, just for theory's sake. But I'm not remenbering a playable one.

-Edited in later-Oop. Just checked that other thread. You were refering to what I had in there. No, that was purely theoretical, as I said in the post. The numbers for success and failre were even just made up. I ws just tring to demonstrate the curve I was looking for there. But, again, as I ws saying above, if you look at earlier threads, people had quite a few ideas about how it might be done.

Mike

[Thirsty Viking]

your right there were some threads bandied arround...  i thought you were putting forward the idea of more 1's than any other failed number...  thus making fumbles rarer as TN increases.   I'm sorry that post shouldn't have been addressed to you.

[Durgil]

Revised, Updated, and Corrected.  The latest and the Greatest for a TN of 10.

Code Select Expand

Target Number of 10
# of Dice Chance of Failure Chance of two 1s Odds of Fumbling Fumbles/Failures Ratio
1 90.00% N/A N/A N/A
2 81.00% 1.00% 1.00% 1.23%
3 72.90% 2.80% 2.52% 3.46%
4 65.61% 5.23% 4.24% 6.46%
5 59.05% 8.15% 5.94% 10.06%
6 53.14% 11.43% 7.50% 14.11%
7 47.83% 14.97% 8.84% 18.48%
8 43.05% 18.69% 9.93% 23.07%
9 38.74% 22.52% 10.77% 27.80%
10 34.87% 26.39% 11.36% 32.58%
11 31.38% 30.26% 11.73% 37.36%
12 28.24% 34.10% 11.89% 42.10%
13 25.42% 37.87% 11.88% 46.75%
14 22.88% 41.54% 11.73% 51.28%
15 20.59% 45.10% 11.46% 55.67%
16 18.53% 48.53% 11.10% 59.91%
17 16.68% 51.82% 10.67% 63.98%
18 15.01% 54.97% 10.19% 67.87%
19 13.51% 57.97% 9.67% 71.57%
20 12.16% 60.83% 9.13% 75.09%


Now, Mike and Thirsty Viking, how do these numbers match-up?

Man, I wish I code get this code thingy to work the way I want it to!

Sorry, I forgot this discussion moved.

[Thirsty Viking]

Revised, Updated, and Corrected.  The latest and the Greatest for a TN of 10.

Code Select Expand

Target Number of 10
#d Chance of Failure Chance of two 1s Odds of Fumbling Fumbles/Failures Ratio
1 90.00% N/A N/A N/A
2 81.00% 1.00% 1.00% 1.23%
3 72.90% 2.80% 2.52% 3.46%
4 65.61% 5.23% 4.24% 6.46%
5 59.05% 8.15% 5.94% 10.06%
----SNIP-----

Now, Mike and Thirsty Viking, how do these numbers match-up?

Your close,  you never differ from me more than a % now...  I know i have some rounding errors as i get into huge numbers  so lets just look at the first 5 dice.   My table is wider so you can verify my method.

Code Select Expand


TN = 10
#d  Fail%    # Fail   NO 1's   1 1's    2+ 1's  FUMBLE%
1 90.00% 000009 000008 000001 00000 0.00%
2 81.00% 000081 000064 000016 00001 1.00%
3 72.90% 000729 000512 000192 00025 2.50%
4 65.61% 006561 004096 002048 00417 4.17%
5 59.05% 059049 032768 020480 05801 5.80%

ok i only track the failures... and the rolling of 1's without a success.

Forgive the Leading Zeros, but it made things much easier to align.
You can see our Failure numbers are identincal.  Where my numbers are not percentages they represent the total number of combinations of dice that meet the given criteria
1d values are obvious --- I calculate my columns as follows starting with 2d:

Code Select Expand


%Fail = ((TN-1)/10)^#d
#Fail  = (TN-1)^#d
NO 1's = (TN-2)^#d
1 1's = ((the # failures with 1 1's at (#d-1))*(TN -2))+(the # of NO 1's at (#d-1))
2+ 1's = ((the # failures with 2+ 1's at (#d-1))*(TN -1))+(the # of NO 1's at (#d-1))
Fumble%  =   (2+1's)/(10^#d)

Note: by changing formula to TN-2 in the 2+ 1's   it becomes exactly 2 1's...  but for our purposes we don't care about exactly 2..  or more than 2 1's


I hope this is clear...  If not ask...  but i am 100% sure that @ 3 dice you have exactly 25 out of 1000 combinations that are fumbles.  not 25.2 combinations....  
at  12d   My fumble % from these formulas is 11.1 % instead of your higher value.. darn i clipped it,  think you were running 11.9?%  i used to have numbers in this range till i found an error in my sheet.   when i found this error my old formula for calculating failurers with no 1's =((#failures - failures with 1 1's)-(failures with 2 1's))  showed me that it was really (TN-2)^#d  ...   I hadn't thought of that till then...   thats when i knew my sheet was right.   In my current sheet I don't get an error large enough to make these numbers different (as whole numbers) until 16 dice  when 281474976710658   - 281474976710656 = 2

Obviously excell works with 15 digits.   Starting at 17 dice i get trailing 0's  because WORKS doesn't track anymore.  I think this is more than sufficent accuracy for out purposes however  :-)