Target Numbers and probability

[ThrorII]

I found a One Ring die roller on the internet and decided to try some probabilities. Now, I have to assume that the math on the program is right, but it was very interesting. The website factors in G-runes, so they are factored in to the probabilities.

http://www.arcdream.com/tor/dice/index.php

I ran 40 die rolls for 2-success die, 3-success die, and 4-success die, with the following results:

2 Dice
TN12 65% success
TN14 40% success
TN16 35% success

3 Dice
TN12 80% success
TN14 75% success
TN16 40% success

4 Dice
TN12 99% success
TN14 97% success
TN16 80% success

While we have to assume the math is right on the website, and 40 rolls is not statistically a lot, it does give an indication of probabilities.

It seems that the success curve is way out of whack for the game. Most characters start with 2 die in most important skills, with 1 or 2 three-dice skills. They fail 60% of the time (which is weird that a "good" skill rank would fail 60% of the time on a "moderate" test). By 4 dice, they practically auto-succeed on even Hard tests.

Thoughts?

[Yusei]

These numbers seem off. My simulator gives me 80% success with 4 dice against a TN of 14, and 66% success against a TN of 16 (with 10,000 rolls). Here are the numbers I get:

Code: Select all

With 1 dice
 TN 12, normal: 25.6  weary: 20.9  diff: 81.67
 TN 14, normal: 13.3  weary: 13.3  diff: 100.00
 TN 16, normal: 7.8  weary: 7.8  diff: 100.00
 TN 18, normal: 8.8  weary: 8.8  diff: 100.00
 TN 20, normal: 8.5  weary: 8.5  diff: 100.00
With 2 dice
 TN 12, normal: 49.9  weary: 32.5  diff: 65.06
 TN 14, normal: 34.1  weary: 22.7  diff: 66.50
 TN 16, normal: 19.7  weary: 13.4  diff: 67.95
 TN 18, normal: 11.3  weary: 10.7  diff: 94.27
 TN 20, normal: 8.7  weary: 8.7  diff: 100.00
With 3 dice
 TN 12, normal: 74.2  weary: 46.9  diff: 63.19
 TN 14, normal: 58.7  weary: 34.3  diff: 58.48
 TN 16, normal: 41.1  weary: 22.3  diff: 54.36
 TN 18, normal: 27.3  weary: 16.8  diff: 61.71
 TN 20, normal: 16.5  weary: 11.5  diff: 69.44
With 4 dice
 TN 12, normal: 90.8  weary: 57.2  diff: 63.05
 TN 14, normal: 80.3  weary: 45.2  diff: 56.27
 TN 16, normal: 66.3  weary: 32.8  diff: 49.42
 TN 18, normal: 51.0  weary: 24.9  diff: 48.82
 TN 20, normal: 34.4  weary: 16.9  diff: 49.11

This is the simulator I quickly wrote for Protection rolls, for another thread, but the results are applicable here too, right?

[Rich H]

Here are some further probabilities around TN14.

Default Rolls Comparison

Roll Type SL 0 SL 1 SL 2 SL 3 SL 4 SL 5 SL 6
Normal + Bonus: 15.972 28.356 62.153 85.629 95.944 99.138 99.860
Normal: 8.333 16.667 41.898 69.483 88.567 96.932 99.396
Normal + Penalty: 0.694 0.116 0.019 16.207 55.634 84.800 96.412
Wearied + Bonus: 15.972 28.356 47.415 63.657 76.005 84.694 90.493
Wearied: 8.333 16.667 31.250 47.724 62.635 74.518 83.242
Wearied + Penalty: 0.694 0.116 0.019 10.651 27.547 45.370 60.995

Bonus = reroll d12 and keep highest
Penalty = reroll d12 and keep lowest

... but not 100% sure of these results as I dug them out of some old notes I have - think they were originally from a post on RPGnet when TOR first came out.

Three posts all with different results - awesome.

[Evening]

I found a One Ring die roller on the internet and decided to try some probabilities. Now, I have to assume that the math on the program is right, but it was very interesting. The website factors in G-runes, so they are factored in to the probabilities.

http://www.arcdream.com/tor/dice/index.php

I ran 40 die rolls for 2-success die, 3-success die, and 4-success die, with the following results:

2 Dice
TN12 65% success
TN14 40% success
TN16 35% success

3 Dice
TN12 80% success
TN14 75% success
TN16 40% success

4 Dice
TN12 99% success
TN14 97% success
TN16 80% success

While we have to assume the math is right on the website, and 40 rolls is not statistically a lot, it does give an indication of probabilities.

Thoughts?

2d
TN14 40% success

3d
TN12 80% success
TN16 35% success

These are low. The dice roller is factoring in 0 (zero) for the Eye?

These numbers seem off.
This is the simulator I quickly wrote for Protection rolls, for another thread, but the results are applicable here too, right?

Did your simulator factor the feat die '12' (G rune) as a success and 11=0 (zero)?

Here are some further probabilities around TN14.

Default Rolls Comparison

Roll Type SL 0 SL 1 SL 2 SL 3 SL 4 SL 5 SL 6
Normal + Bonus: 15.972 28.356 62.153 85.629 95.944 99.138 99.860
Normal + Penalty: 0.694 0.116 0.019 16.207 55.634 84.800 96.412
Wearied + Bonus: 15.972 28.356 47.415 63.657 76.005 84.694 90.493
Wearied + Penalty: 0.694 0.116 0.019 10.651 27.547 45.370 60.995

Bonus = reroll d12 and keep highest
Penalty = reroll d12 and keep lowest

I'm not understanding how the +Bonus/+Penalty results are meaningful in any way. Shouldn't +Bonus(G) be 100% autosuccess and why replace the Penalty(0) with a bonus of +1-12 to the skill dice sum?

[Yusei]

Did your simulator factor the feat die '12' (G rune) as a success and 11=0 (zero)?

Yes. I'll check tomorrow that I haven't made a mistake somewhere, but the results seem consistent with what I've experienced in play (4 dice isn't an automatic success against a high TN).

[Evening]

I only asked because the numbers look a little low, but the Eye might explain that.

[Glorelendil]

Here's an app that rolls dice 25,000 times for each skill level and displays the results by TN 12 through 20:

http://powerful-fortress-2839.herokuapp.com/

And for weary:

http://powerful-fortress-2839.herokuapp.com/weary

Here's the source code if you want to double-check my work. Please do. (I lifted it from my simulator so it's more complicated than it needs to be for this app):

https://docs.google.com/document/d/1xpq ... sp=sharing

[Yusei]

I think your feat dice never roll a Sauron, seeing as you draw rand(12)+1 and Sauron is 0.

And I made a mistake in my simulations... I stupidly rolled rand(5)+1 instead of rand(6)+1 for success dice. I've edited my post with the new results.

[Glorelendil]

I think your feat dice never roll a Sauron, seeing as you draw rand(12)+1 and Sauron is 0.

And I made a mistake in my simulations... I stupidly rolled rand(5)+1 instead of rand(6)+1 for success dice.

My code? After rolling feat dice it does this:

@feats = @feats.map{|d| d == 11 ? 0 : d }

Which turns 11's into zeroes. Then when testing whether the roll beat the TN, it first looks to see if the feat is a zero and if so returns false.

P.S. The other hint that Saurons are working is that skill of 6 vs. TN of 12 still fails over 8% of the time.

[Yusei]

Oh, OK, I didn't notice that line, my bad. Was there a reason not to draw from 0 to 11 and consider 11 as a gandalf?