|
|
Post by sand20go on Apr 22, 2018 16:13:20 GMT
OK math guys.
Now lets ignore the other abilities on their respective cards. That is a debate for another day (and also matters because of other synergies in the list)
Trying to decide between Ellish and Sylss for Sorscha 1 SOLEY around which is better - Puppet Strings or Arcane Secrets for landing freezing grip. The tactical flexibility around puppet strings suggests STRONGLY that it would have the edge but wondering.
For purposes, lets say she (MG 6) is trying to land an unboosted FG on a Def 14 thing. Which is better - rerolls (I believe about 40% x 2 or about 80%) or roll 3 drop lowest? And how does the probability curve as we get into even higher defs and look at boosting?
PS. I think Ellish is strictly better. While upkeeping FG for Free is "nice" and Conduit is also great in situations Puppet master frees her up to go zipping around the battlefied - a KEY requirement for S. Plus the wording on Arcane secrets requires it to be the first spell cast to benefit. But just looking for the best "math" answer to the above.
|
|
|
|
Post by NephMakes on Apr 22, 2018 23:55:48 GMT
For purposes, lets say she (MG 6) is trying to land an unboosted FG on a Def 14 thing. Which is better - rerolls (I believe about 40% x 2 or about 80%) or roll 3 drop lowest? And how does the probability curve as we get into even higher defs and look at boosting? I've done a little of the math for attack rerolls. It's the same thing as getting at least one hit with two tries. You calculate it as the probability of not getting two misses. For your example that'd be around 1 - (0.6)(0.6) = 0.64. Rerolls on a 60% chance to hit isn't going to give you a 120% chance to hit. For higher defs see this plot. I haven't worked through any of the math for rolling an extra die and dropping the lowest value. |
|
|
|
Post by dogganmguest on Apr 23, 2018 2:17:33 GMT
It's easy enough to just make the computer do it for such a specific question. The chances of rolling an 8 goes from 42% on 2d6 to 68% on 3d6 drop lowest.
|
|
|
|
Post by dogganmguest on Apr 23, 2018 2:30:22 GMT
Forgot to add, that's just very slightly better than 1 - (1 - 0.416666667)^2... basically 66% for the reroll.
|
|
Cyel
Junior Strategist
Posts: 685 
|
Post by Cyel on Apr 23, 2018 6:01:31 GMT
Puppet Strings ?? ??  |
|
|
|
Post by greytemplar on Apr 23, 2018 6:22:29 GMT
Add a die drop the lowest is mathematically basically the same as +2 to the roll. That makes your probability of hitting Def14 with Focus 6 a cool 72%.
With rerolling, you take the probability of failure and multiply it by the probability of failure. The probability of rolling 7 or less on 2D6 is 58.333%. 58.3333%X58.333% is 34% chance of failure. Which makes the probability of success 66%.
So Arcane Secrets is straight up better in terms of modding your dice. Of course Puppet Master works on far more possible rolls, so its a question of flexibility vs a more focused benefit.
|
|
|
|
Post by 36cygnar24guy36 on Apr 23, 2018 6:25:44 GMT
I play in Mercs, so I get both  |
|
zich
Junior Strategist
Posts: 690
|
Post by zich on Apr 23, 2018 8:38:00 GMT
Puppet Strings ?? ?? The best rule that is not actually in the game. |
|
gordo
Junior Strategist
My star is green?
Posts: 548
|
Post by gordo on Apr 23, 2018 13:30:57 GMT
Add a die drop the lowest is mathematically basically the same as +2 to the roll. That makes your probability of hitting Def14 with Focus 6 a cool 72%. With rerolling, you take the probability of failure and multiply it by the probability of failure. The probability of rolling 7 or less on 2D6 is 58.333%. 58.3333%X58.333% is 34% chance of failure. Which makes the probability of success 66%. So Arcane Secrets is straight up better in terms of modding your dice. Of course Puppet Master works on far more possible rolls, so its a question of flexibility vs a more focused benefit. I've heard the whole "Signs and Portents is basically +2" schtick before and it's not that accurate. I don't care to do the math on it, so I brute forced it and wrote a program to simulate the die rolls several million times and averaged the results. This what was rolled: Threshold: 2 2d6 Success %:100.0 2d6 with a re-roll Success %:100.0 3d6 drop lowest Success %:100.0 Threshold: 3 2d6 Success %:97.2107 2d6 with a re-roll Success %:99.9248 3d6 drop lowest Success %:99.53450000000001 Threshold: 4 2d6 Success %:91.6857 2d6 with a re-roll Success %:99.3105 3d6 drop lowest Success %:98.142 Threshold: 5 2d6 Success %:83.3189 2d6 with a re-roll Success %:97.2148 3d6 drop lowest Success %:94.9227 Threshold: 6 2d6 Success %:72.2461 2d6 with a re-roll Success %:92.2964 3d6 drop lowest Success %:89.3263 Threshold: 7 2d6 Success %:58.4106 2d6 with a re-roll Success %:82.6323 3d6 drop lowest Success %:80.5392 Threshold: 8 2d6 Success %:41.5785 2d6 with a re-roll Success %:65.89620000000001 3d6 drop lowest Success %:67.9569 Threshold: 9 2d6 Success %:27.7721 2d6 with a re-roll Success %:47.8379 3d6 drop lowest Success %:52.2783 Threshold: 10 2d6 Success %:16.6647 2d6 with a re-roll Success %:30.5991 3d6 drop lowest Success %:35.6571 Threshold: 11 2d6 Success %:8.321000000000002 2d6 with a re-roll Success %:15.9967 3d6 drop lowest Success %:19.9085 Threshold: 12 2d6 Success %:2.7732 2d6 with a re-roll Success %:5.459499999999999 3d6 drop lowest Success %:7.439500000000001 Average 2d6 roll: 7.000962727272727 Average 3d6 drop lowest roll: 8.458471636363637 The "+2" analogy is only right when you need to roll an average number. It's not that useful when you are trying to figure out how much damage you will do vs whether you will hit, since rolling "to hit" is a pass/fail scenario vs a "every point counts" scenario. |
|
|
|
Post by NephMakes on Apr 23, 2018 16:37:16 GMT
I'd say those numbers mean that 2d6 with rerolls and 3d6 drop lowest are basically the same. Rerolls are slightly better at making probable things more probable and 3d6 drop lowest is slightly better at hitting less-likely rolls, but those 2-5% differences probably don't outweigh the other differences between the models.
|
|
|
|
Post by dogganmguest on Apr 23, 2018 21:03:13 GMT
There's no need to simulate rolls, or do any complicated math. The probability of a result is the number of ways to get that result divided by the number of total possibilities. With three dice, you only have 216 possibilities so just check them all. Takes less time and effort than simulating thousands of rolls and gives precise results.
|
|
gordo
Junior Strategist
My star is green?
Posts: 548
|
Post by gordo on Apr 23, 2018 22:08:17 GMT
There's no need to simulate rolls, or do any complicated math. The probability of a result is the number of ways to get that result divided by the number of total possibilities. With three dice, you only have 216 possibilities so just check them all. Takes less time and effort than simulating thousands of rolls and gives precise results. I think you over estimate how long it took me to write and run this (about 20 minutes). |
|
|
|
Post by dogganmguest on Apr 24, 2018 0:06:29 GMT
But it only took me five minutes to recreate your output with the correct values.
|
|
Fang
Junior Strategist
Posts: 117
|
Post by Fang on Apr 24, 2018 20:43:53 GMT
I'd say those numbers mean that 2d6 with rerolls and 3d6 drop lowest are basically the same. Rerolls are slightly better at making probable things more probable and 3d6 drop lowest is slightly better at hitting less-likely rolls, but those 2-5% differences probably don't outweigh the other differences between the models. NephMakes pretty much nailed it with this, but for those who are more graphically inclined, I dug out my dice excel sheet and made a graph. For the specific example, hitting 14 with a stat of 6 means you need an 8, which is right when 3d6 drop low takes the lead over reroll. EDIT: Sorry to any colorblind people, I am tired and didn't pull out my handy color choices chart to check if the differences are clear enough for everyone.. If anyone want to see it but can't because of my lazy default color scheme, let me know and I'll fix it.  EDIT2: Second graph is colorblind friendly. If anyone still has an issue, please let me know so I can improve my colorblind friendly graph making in the future.  |
|
|
|
Post by NephMakes on Apr 24, 2018 22:51:04 GMT
EDIT: Sorry to any colorblind people, I am tired and didn't pull out my handy color choices chart to check if the differences are clear enough for everyone.. Can't speak for the colorblind, but I'm pretty sure yellow lines on a white background are, like, a graphic design sin. It reminds me of how back in the day high school cheerleaders used to draw signs in bubbly letters, each a different color, and it'd always end up reading "G O O D U C K!" or "G O T E A !" |
|
