I'm curious if any mathematically inclined Ironlanders could tell us regular Ironlanders the odds regarding 'reroll...
I'm curious if any mathematically inclined Ironlanders could tell us regular Ironlanders the odds regarding 'reroll but count a weak hit as a miss' type moves.
edit: Those moves allow you to reroll any/all the dice in one roll.
edit: Those moves allow you to reroll any/all the dice in one roll.
As I understood the question, you want the percentage of: when a weak hit becomes a miss after the reroll. Rerolling is by nature a human choice depending on the situation, so we must settle some rules first. A "reroll AI" if you will. In this scenario:
ReplyDelete- On a strong hit, we don't reroll.
- On a miss, we reroll based on this logic:
+ If the action die brought a value less than 3 without the bonuses, we reroll it.
+ If the action die isn't rerolled, we reroll both challenge dice
+ If a challenge die has greater value than an acceptable value based on our bonuses that apply on the action die(I made this value 4 + bonuses - (bonuses/2) ), we reroll it.
- On a weak hit, we reroll based on this logic:
+ We focus on the challenge die that we didn't pass:
> If this challenge die has greater value than the acceptable value based on our bonuses, we reroll that challenge die.
> If this challenge die has less or equal than our acceptable value, we check the action die. If the action die value without the bonuses is less than 3, we reroll the action die. If not, we do not reroll anything.
A little complicate I know, but human decisions aren't always predictable and can't always be applied. So. Based on this logic, and after running some tests, here are some resuts:
Action Die + 0 :
Miss -> Miss: 28276 (28.276%)
Miss -> Weak hit: 22028 (22.028%)
Miss -> Strong hit: 8941 (8.941%)
Weak hit -> Miss: 650 (0.65%)
Weak hit -> Weak hit: 19250 (19.25%)
Weak hit -> Strong hit: 11846 (11.846%)
Strong hits: 9009 (9.009%)
Number of tests: 100000
Action Die + 1 :
Miss -> Miss: 17132 (17.132%)
Miss -> Weak hit: 18110 (18.11%)
Miss -> Strong hit: 9981 (9.981%)
Weak hit -> Miss: 568 (0.568%)
Weak hit -> Weak hit: 21127 (21.127%)
Weak hit -> Strong hit: 18082 (18.082%)
Strong hits: 15000 (15.0%)
Number of tests: 100000
Action Die +2 :
Miss -> Miss: 9465 (9.465%)
Miss -> Weak hit: 14111 (14.111%)
Miss -> Strong hit: 9794 (9.794%)
Weak hit -> Miss: 319 (0.319%)
Weak hit -> Weak hit: 20183 (20.183%)
Weak hit -> Strong hit: 23093 (23.093%)
Strong hits: 23035 (23.035%)
Number of tests: 100000
Action Die +3 :
Miss -> Miss: 5064 (5.064%)
Miss -> Weak hit: 9109 (9.109%)
Miss -> Strong hit: 8996 (8.996%)
Weak hit -> Miss: 230 (0.23%)
Weak hit -> Weak hit: 16419 (16.419%)
Weak hit -> Strong hit: 26770 (26.77%)
Strong hits: 33412 (33.412%)
Number of tests: 100000
Action Die +4 :
Miss -> Miss: 2253 (2.253%)
Miss -> Weak hit: 5615 (5.615%)
Miss -> Strong hit: 7418 (7.418%)
Weak hit -> Miss: 154 (0.154%)
Weak hit -> Weak hit: 12083 (12.083%)
Weak hit -> Strong hit: 27310 (27.31%)
Strong hits: 45167 (45.167%)
Number of tests: 100000
Action Die +5 :
Miss -> Miss: 984 (0.984%)
Miss -> Weak hit: 2801 (2.801%)
Miss -> Strong hit: 5550 (5.55%)
Weak hit -> Miss: 100 (0.1%)
Weak hit -> Weak hit: 7456 (7.456%)
Weak hit -> Strong hit: 23915 (23.915%)
Strong hits: 59194 (59.194%)
Number of tests: 100000
Hope I somewhat answered your question.
Wow, yeah, that's great. Thanks for your rather exhaustive response! So, if I understand correctly, it looks like it's only worth using such a move if you have a +3 or higher to your roll.
ReplyDeleteRichard Robertson Ah, sorry I misunderstood your question. Now that I read it a couple of times I think I got it. So, a move lets you reroll, but if you choose to do so, then your weak hits count as a miss. Ok. Then there is the only one additional devastating scenario of Weak Hit -> Weak Hit, but now your Weak Hit is a miss since you rerolled. So we focus only to the Weak Hits, since the rest is a general probability to the reroll mechanic in general(using thhe above fixed logic). So, we already scored a Weak Hit. At +3 we have a roughly 62% to turn it into a Strong Hit, and 38% to turn it into a miss(Weak Hit / Miss). At +2 this becomes 53% to turn it to a Stron Hit and 47% to turn it to a Miss, etc.
ReplyDeleteSo, in the end, it still is a human decision to choose when the chances are worth attempting it. Some people may attempt it at a +2 where it's somewhat a 50-50, others may be extremly cautious and decide that a 62% at +3 isn't worth the risk.