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| Author | Luck calculation information |
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I have question about how luck is calculated. I read the information in help. It says
F^(1+[moves befallen so far]-[moves not befallen so far]*F/(1-F))
So, in case of wolf riders and wolf raiders. The move means a turn, or the move means the hits. Lets say, wolf raiders hit thrice, so will they get atleast 1 lucky hit in 10 hits.. or luck once in 10 turns they get.
Because if they get 1 luck in 10 turns, then they should perform 3 lucky hits.
Or is it, 1 lucky hit in 10 turns (1 lucky hit in 30 hits)?? | | Per hit for them | | http://eng.witchhammer.ru/viewpage.php?page_id=37 | If its per turn, then there is a bug. My wolf raiders hit 10 times in this battle, but didn't get any lucky hit.
https://www.lordswm.com/warlog.php?warid=495979728<=-1 | The [moves befallen so far] refers to turns.
But each hit is a separate calculation, so you can get 1 lucky hit, 2 lucky hits or even 3 lucky hits, just that the chances are recalculated each hit. | | Your wolf raiders didn't hit 10 times in that battle. I counted 7. | | So, in simple words, that would means wolfs get 1 lucky hit in 30 hits? | According to my deduction,
If you toss a coin, probability of heads is 1/2... But it is NOT necessary that out of 10 turns, 5 must be heads!
But eventually, it gets even, more or less..! | for imsunny:
It's counted per hit, not per turn.
for speed_dragon:
That is correct for mutually independent events, which is not the case for triggering of luck. Getting luck (or not) in any particular hit will affect the probability of getting luck (or not) in all subsequent hits for the battle.
https://www.lordswm.com/help.php?section=35
If you were to read and understand the formula, you will know that after 9 non-lucky strikes, you can be 100% confident the 10th will be a lucky strike (assuming you have 1 luck, as in imsunny's case). | Each strike is considered as "turn" in that formula, even if you strike several times in one turn.
For example, if Wolf Raiders make 2 attacks then they do 2*3=6 strikes (i.e. 6 "turns") or less strikes if the stack dies.
Let's look at your battle:
https://www.lordswm.com/warlog.php?warid=495979728<=-1
Wolf Raiders did 3+3+1=7 strikes there.
All 7 were unlucky strikes. Is it very rare event?
Let's calculate.
They had Luck = 1, so
F = Luck/10 = 0.1
The formula is this:
Prob_of_Luck = F^(1+Lucky_strikes-NonLucky_strikes*F/(1-F)) =
= F^(1+Lucky_strikes-NonLucky_strikes/9)
Probabilities of luck on each strike (if previous strikes were unlucky):
Prob_of_Luck on 1st strike = (0.1)^(1+0-0/9) = 0.1
Prob_of_Luck on 2nd strike = (0.1)^(1+0-1/9) = 0.1291549665
P(A or B) = 1-P(notA * notB) = 1-P(notA) * P(notB | notA)
Prob_of_Luck on either of 2 strikes = 1-(1-0.1)*(1-0.1291549665) = 0.2162394698
(it means that at least one lucky strike in any of 2 first strikes will be only 21.6% of times having Luck 1)
Prob_of_Luck on 3rd strike = (0.1)^(1+0-2/9) = 0.1668100537
Prob_of_Luck on either of 3 strikes = 1-(1-0.1)*(1-0.1291549665)*(1-0.1668100537) = 0.3469786059
(it means that at least one lucky strike in any of 3 first strikes will be only 34.7% of times having Luck 1)
Prob_of_Luck on 4th strike = (0.1)^(1+0-3/9) = 0.2154434690
Prob_of_Luck on either of 4 strikes = 1-(1-0.1)*(1-0.1291549665)*(1-0.1668100537)*(1-0.2154434690) = 0.4876678004
Prob_of_Luck on 5th strike = (0.1)^(1+0-4/9) = 0.2782559402
Prob_of_Luck on either of 5 strikes = 1-(1-0.1)*(1-0.1291549665)*(1-0.1668100537)*(1-0.2154434690)*(1-0.2782559402) = 0.6302272783
Prob_of_Luck on 6th strike = (0.1)^(1+0-5/9) = 0.3593813664
Prob_of_Luck on either of 6 strikes = 1-(1-0.1)*(1-0.1291549665)*(1-0.1668100537)*(1-0.2154434690)*(1-0.2782559402)*(1-0.3593813664) = 0.7631167043
Prob_of_Luck on 7th strike = (0.1)^(1+0-6/9) = 0.4641588834
Prob_of_Luck on either of 7 strikes = 1-(1-0.1)*(1-0.1291549665)*(1-0.1668100537)*(1-0.2154434690)*(1-0.2782559402)*(1-0.3593813664)* (1-0.4641588834) = 0.8730681903
It means that at least one lucky strike in any of 7 first strikes will be 87.3% of times having Luck 1, so you just were unlucky, but not too unlucky since 12.7% isn't very small chance of such bad luck. | | this wont help you,you are lucky or not :))) | Understanding this
- each stack has it's own luck/morale counter
- the more your stack had unlucky strikes the greater chance of lucky strike on the next hit
helped me a lot in battles (especially in some very hard hunts, where any wrong move means lost battle).
Example:
- when you know that your stack accumulated more than 80% probability of lucky strike on the next hit then you can plan your next movement accordingly (maybe it's worth to wait now, maybe you should attack bigger stack now, etc.).
Luck is random, but knowing probabilities sometimes helps a lot. |
This topic is long since last update and considered obsolete for further discussions.
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