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| Author | A question about morale and luck trigger probability |
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Hi
According to the game guide:
"The probability of morale/luck triggers = F^(1+[moves befallen so far]-[moves not befallen so far]*F/(1-F)), whence F is luck/10 or morale/10, each stack having its own independent counters for morale and luck; F∈[0;0.5]
In general, troops are befallen with morale/luck according to its normal probability. In case if it hasn't trigger for several consecutive turns, the odds of getting it on the next turn increase each time, and vice versa. In a hypothetical experiment with infinite amount of triggering, the general probability is still equal to 10% per morale/luck point."
What I'd like to know, is if someone knew in wich way this case: "In case if it hasn't trigger for several consecutive turns, the odds of getting it on the next turn increase each time, and vice versa." has an influence on the triggering probability.
Does it still take in account "moves befallen so far" and "moves not befallen so far" in the formula in any way? | "In case if it hasn't trigger for several consecutive turns, the odds of getting it on the next turn increase each time, and vice versa
is explanation of formula. It's accounted for in the moves befallen so far]-[moves not befallen so far part. | Alright, thanks.
So, if I got it, it means that it's considered that probability will increase because sooner or later because the creature will have reached the opponents one and, more likely, won't move anymore (or just a little bit), so that there isn't changes in the formula whatever happens?
And one more thing, that comes to my mind as I was written this reply:
let's fix F to F = 3/10
If the difference with moves befallens is equal to -1 (one "non used step"), I get something close to 0.5, wich is about 50% of triggering... That seems to be alright.
Now, let's say that this difference (the difference with moves befallens, and still with F = 3/10 as a reminder) is equal to -4, I get a result close to 2,4... 240%??
I think that I'm missing something here :) | wow, i wrote much about that, pressed the wrong button and now it's all gone!
so i have to write it down again (therefore parts you may need to understand may be missing due to my poor memory)
the first Question is:
When does morale trigger for the first time for shure?
to calculate that, F^(1+[moves befallen so far]-[moves not befallen so far]*F/(1-F)) has to be equal/bigger than 1
that is when (1+[moves befallen so far]-[moves not befallen so far]*F/(1-F)) becomes equal/smaller than 0 (because [any number]^0=1)
[moves befallen so far]=0 because we want to know the first time
for F^(1-[moves not befallen so far]*F/(1-F))>=0, [moves not befallen so far]*F/(1-F) has to be >=1 (because it is substracted from 1 at the formula)
and [moves not befallen so far]*F/(1-F)>=1 if [moves not befallen so far]*F>=(1-F)
so we have (with 3 morale):
[one move]*.3=.3
[seconde move]*.3=.6
[third move]*.3=.9 <- this is the first time where [moves not befallen so far]*F>=(1-F) and therefore the propability for morale to trigger is 100%/more (as explained above)
the real first-has-to-trigger-point is after 2.3333 not-triggered turns
so your calculating was correct, the only problem is that the unit can't move 4 times without triggering morale (but only at the start of the game!!!)
i hope you understand what i was trying to tell you
and you made 2 little mistakes:
[quote=Slust][b]Now, let's say that this difference (the difference with moves befallens, and still with F = 3/10 as a reminder) is equal to -4[/b]
(hope that quote works)
1. a difference can't be negative (as far as i know)
2. the difference with moves befallens - the point is, [moves befallen so far] and [moves befallen so far] are not treated equal. In fact, 0.43*[moves befallen so far]-1=[moves not befallen so far]
So it's a huge difference between for example 4*[moves befallen so far] and 8*[moves not befallen so far] compared to 17*[moves befallen so far] and 21*[moves not befallen so far]
well as i haven't studied anything yet (neither maths nor informatics nor something else) i can't assure that i'm 100% correct so take it as my humble opinion and prove it yourself | http://elfius.com/forum_new/index.php?showtopic=200
It has the info you're looking for (if I understood the Q correctly :) but good luck getting through text butchered by Google translator ;) | :)
Thank to both of you for all this.
Well, there is much to read, and I don't have enough time to think about all this right now, but I had a glance to it.
Translation is not great, but it still can be understood... But it works better in English than in French ^^
Well, anyway, may I ask someone to tell me what does those graphics are for, since it's not clealry explained on the text (and since text on images isn't translated :( )?
#4:
I was wrong considering that moves not befallen so far was equal to speed... And thus, moves befallen couldn't be bigger than moves not befallen. Just some stupid mistake, but in the end, it change much things (mainly considering negative numbers). | thx Shebali
i just worked myself through that page (translated by google into German - next time i'll better ask you to translate it for me into english so i won't have to guess 3 out of 4 sentences :p )
it exactly says what i tried to explain (although i'm in favour for my explanation)
all in all it worked out how big the propability is for the luck/morale to trigger based on turns with/without and how much you have
to make a long story short, here are the graphs:
http://elfius.com/forum_new/uploads/monthly_08_2008/post-19-1220095836.png
(chance to trigger for the first time in %, when the line ends it's the last possible turn to trigger. The lines are from above to bottom 5-1 luck/morale. So if you watch the red line you can see that at 50% of all cases luck/morale will trigger at the first turn and if it didn't it will definately trigger at the second turn)
chance to trigger for the second time:
http://elfius.com/forum_new/uploads/monthly_08_2008/post-19-1220097676.png
and third time:
http://elfius.com/forum_new/uploads/monthly_08_2008/post-19-1220098822.png
and the resumée:
http://elfius.com/forum_new/uploads/monthly_08_2008/post-19-1220099453.gif
(read that as:
from the left to to right at the top side you see luck/morale 1-5 listed. First line is the latest point of triggering (turn), second line is when it will trigger most of the time, followed by the latest point of triggering for the second time, again a line of where the chance is the biggest one to trigger and same goes for the last 2 lines)
and his final thoughts about that:
there isn't any advantage in quantity, so having (in theory) 2x 1 Luck is the same as having 1x 2 Luck.
BUT: The more luck/morale you have, the better you can calculate the point of triggering. If you have 5 Luck and your attack wasn't a lucky one you can bet on getting a lucky one next time! As the curve is expotentionally decreasing according to your amount of luck/morale, having at least 3-4 is much better than having 2 luck not only because of damage but because of calculation too.
->Well if you don't count you turns of (not) triggering of every single stack you have it won't affect you anyway. But if you do count it, you may get an huge advantage out of this (knowing when the last point is where luck/morale HAS to happen). And more luck/morale increases your ability to predict that exponentionally. | weird - didn't read you asked for explanation for those graphs (but did it anyway by myself and took enough time for you to ask first during the time i was writing)
i will ask Shebali if she knows a page too that shows the efficiency of morale compared to luck (only in dmg) | looks like no one is interested in those calculations
i'll do the maths as soon as i've got time (have to become lvl 1 thief guild first) | Honestly I got some strange luck and morale triggers .. At level 3 - 4 with +1 luck I just got max 2 lucks in a battle .. :)
But at level 5 and up .. I got ALMOST ALWAYS 3 - 7 lucks with only +1 luck .. :)
Also for arts, Thieve amulet gives us more lucks than amulet of luck in this case the luck is just +1 :)
I knew it from Thieves Guild .. :) | for RandhyTheDarks:
Luck counter is separate for each stack -_- What you're describing is just random. And 1 luck from Thief Ammy is exactly the same as 1 luck from Ammy of luck >_> | To #10 : At higher levels, battles are usually harder. This makes them longer wich gives more chances to trigger luck/morale.
A battle duration is irrevelant for this sort of calculation. you need to count in turns.
To #8 : About pure dmg, morale is better because it stacks. When a morale trigger hit, the chance to trigger a second one comes twice faster.
But imo, the biggest difference between morale and luck is "tactical", and that is very situational. | A lot to read, and a lot to say :)
# 4:
When does morale trigger for the first time for shure?
to calculate that, F^(1+[moves befallen so far]-[moves not befallen so far]*F/(1-F)) has to be equal/bigger than 1
that is when (1+[moves befallen so far]-[moves not befallen so far]*F/(1-F)) becomes equal/smaller than 0 (because [any number]^0=1)
If I remember well my maths lessons... That is true about x^0 = 1, but I think that you are wrong about the x^0,y that would be equal / bigger than 1.
In this case, x is F in this formula, and F is a fraction (? I'm not sure about mathematical vocabulary :P); well, it's something like x/y, and 0 <= F < 0.5
In the case of a number that belongs to ]0 ; 1[, this number power ( ^ ) an other number of ]0 ; 1[ will be < 1.
so we have (with 3 morale):
[one move]*.3=.3
[seconde move]*.3=.6
[third move]*.3=.9
Unfortunately, it's not that easy with probability.
I'd say that, in order to calculate this, you should consider the probability to don't have a triger (0.7 if you consider the 0.3 trigger probabilty).
In this case, you should multiply probabilities among themselves, so it would be: 0.7*0.7*0.7 = 0.343 for the third turn, not to get a trigger.
So that the probability to get a trigger would be of 1 - 0.343 = 0.657 (considering that you wouldn't get any before ^^ If not, it's more complicated :P). This is why, on the graphs, you don't have something linear, wich would be the graph for the formula you used :)
Once again... About all this, that's if I remember well my maths... I haven't any probability classes for several years.
Anyway, Shebali's link makes me think that there something that makes all this more complicated too, but I can't get the file to download, that should contain more informations :(
One last thing: all those informations are interesting indeed, and I didn't expected to find out such (the sure luck for exemple ^^); but what I was thinking about, when writting this thread, was the influence of steps on trigger probability; would it be non used steps, or the total amount of steps.
It may seems useless to you, but as a wiz, I was trying to figure it out, in order to see what could be the influence of a speed mini art on luck / morale, since I'm thinking of using on some of my units. A better triggering probability may be a good plus to a greater speed.
I'll try to figure out what was wrong about this:
Now, let's say that this difference (the difference with moves befallens, and still with F = 3/10 as a reminder) is equal to -4, I get a result close to 2,4... 240%??
Without the difference mistake, I may find a correct result, but I don't have enough time anymore for this today ^^ | i guess you kind of misunderstood it
so we have (with 3 morale):
[one move]*.3=.3
[seconde move]*.3=.6
[third move]*.3=.9
was just calculated for [moves not befallen so far]*F
in search for the point when [moves not befallen so far]*F/(1-F) >=1
the real propability to trigger itself for each move is indeed calculated differently
usually you would expect something like that:
0,7^[moves not befallen so far +1]
but unfortunately the exponential function hasn't got a linear exponent so you get that weird curve as a result |
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