|
2 years ago ::
Jun 12, 2008 - 3:28PM
#1
|
|
|
Um, because I did? Where do you think my numbers came from?
At 10 difference, for instance, you're looking at DS losing 3.5625% of the time versus II losing 3.375% of the time.
Ok.. those figures don't match the ones you posted earlier or anyone else's (except mine) ..but I have 3.75% for II.
The whole range of difference values doesn't matter. What matters is the difference values which you are likely to encounter and which is better across those values.
True.. but that depends on your modifier as well as the ones you are likely to meet.
So overall, you're better off with Danger Sense if you have at least an initiative bonus at least +3 higher than theirs, and at most +10 higher than theirs. And I think someone else (you maybe?) have already said that.
I have DS better by 0.44% at +2.
If I typically have an advantage within that range over my foes, I'm better off with Danger Sense. Otherwise, I'm better off with Improved Initiative. So the answer of which is better is: It depends on the character.
For our next trick, we could actually tell people which you should take depending on what your initiative bonus is, based on the range of monster initiative modifiers at various levels.
Monster initiatives allegedly mostly lie around 3/4level+1.somthing.
You'd have to have very high Dex to get ahead of that -especially when you fight higher level monsters. Basically you need Improved Initiative to get into the zone where Ds would be better.. at which point you already have II anyway.
Even if you get high enough that some/many of the enemy have -2 to your initiative modifier, the benefit form II on those that don't will be much higher than the loss it suffers compared to DS on the ones you do beat by that much.
|
|
|
|
2 years ago ::
Jun 12, 2008 - 3:33PM
#2
|
|
|
Wow Seeker, nice work.
So if you are facing monsters with higher base init than you, II is clearly better. If you have the higher, DS offers a very slight advantage, diminishing to none.
Since monsters with higher base init are generally those that represent greater threat, I think II pulls ahead here again.
Edit: Seeker, would you be able to add a third element to the graph: QD(+2) + DS?
|
|
|
|
2 years ago ::
Jun 12, 2008 - 3:34PM
#3
|
|
|
Updated graph to a column graph as line graph was too hard to read when margins were small.
|
|
|
|
2 years ago ::
Jun 12, 2008 - 3:36PM
#4
|
|
|
Column 1: PC's Initiatve modifier - monster's initiative modifier Column 2: Danger Sense absolute increases in chance of winning inititatives: Spoiler:
Show
[code]+20 0.00%
+19 0.00%
+18 0.24%
+17 0.69%
+16 1.32%
+15 2.12%
+14 3.06%
+13 4.11%
+12 5.25%
+11 6.45%
+10 7.69%
+9 8.94%
+8 10.18%
+7 12.15%
+6 12.51%
+5 13.56%
+4 14.50%
+3 15.30%
+2 15.94%
+1 16.39%
0 14.37%
-1 16.39%
-2 15.94%
-3 15.30%
-4 14.50%
-5 13.56%
-6 12.51%
-7 11.38%
-8 10.18%
-9 8.94%
-10 7.69%
-11 6.45%
-12 5.25%
-13 4.11%
-14 3.06%
-15 2.13%
-16 1.33%
-17 0.69%
-18 0.24%[/code]
Are these the figures you're using?
|
|
|
|
2 years ago ::
Jun 12, 2008 - 3:49PM
#5
|
|
|
Incidentally, there must presumably be a way to directly calculate the odds, rather than relying on seeing the results of thousands of trials in Excel or Matlab, right? Anyone know how to do that?
|
|
|
|
2 years ago ::
Jun 12, 2008 - 3:52PM
#6
|
|
|
Incidentally, there must presumably be a way to directly calculate the odds, rather than relying on seeing the results of thousands of trials in Excel or Matlab, right? Anyone know how to do that?
Uh, we aren't doing "thousands of trials". We're calculating them directly.
|
|
|
|
2 years ago ::
Jun 12, 2008 - 4:02PM
#7
|
|
|
I'm not the only one who was doing 10000 =randbetween(1,2) in Excel.  So how do you do the math?
|
|
|
|
2 years ago ::
Jun 12, 2008 - 4:09PM
#8
|
|
|
Uh, we aren't doing "thousands of trials". We're calculating them directly.
 I actually wasn't sure of my math so I populated 8000 rows of a spreadsheet with every possible combination of 3 d20 rolls. My Math-fu is weak.
|
|
|
|
2 years ago ::
Jun 12, 2008 - 4:17PM
#9
|
|
|
That's actually smarter than doing it randomly, since you know 1-20 will each come up 5% of the time, in an ideal universe.
|
|
|
|
2 years ago ::
Jun 12, 2008 - 4:20PM
#10
|
|
|
Column 1: PC's Initiatve modifier - monster's initiative modifier
Column 2: Danger Sense absolute increases in chance of winning inititatives:
Spoiler:
Show
[code]+20 0.00%
+19 0.00%
+18 0.24%
+17 0.69%
+16 1.32%
+15 2.12%
+14 3.06%
+13 4.11%
+12 5.25%
+11 6.45%
+10 7.69%
+9 8.94%
+8 10.18%
+7 12.15%
+6 12.51%
+5 13.56%
+4 14.50%
+3 15.30%
+2 15.94%
+1 16.39%
0 14.37%
-1 16.39%
-2 15.94%
-3 15.30%
-4 14.50%
-5 13.56%
-6 12.51%
-7 11.38%
-8 10.18%
-9 8.94%
-10 7.69%
-11 6.45%
-12 5.25%
-13 4.11%
-14 3.06%
-15 2.13%
-16 1.33%
-17 0.69%
-18 0.24%[/code]
Are these the figures you're using?
I wasn't sure that was directed at first. Your numbers don't really make sense to me.
I generated my own numbers, and because my math skills are weak I began by populating 8000 rows of my spreadsheet with all of the possible results to get on 3d20. I then counted up all the times each feat would lose initiative for different relative bonuses and subtracted the percentage from 1. I Divided all the calculations into 3 similar groups, PC Wins Ties, PC Loses Ties, and 50/50 on ties.
It's a brute force inelegant solution, but I'm 100% confidant in the results as the math is very simple.
|
|
|
