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Rydian wrote on 2013-08-02 01:44
Example Situation
- You have a bow with 0/10 durability. You want to repair it at Nerys, since she's cheap enough, 95%, and you blessed that beautiful thing anyways. You do 10 repairs, one point at a time (to preserve blessing).
Expectations
- "It has a 98% (I checked the wiki for once) chance of working with no issues!"
Result
- She nicks a point anyways, so you rage at the closest person to you.
"WHAT THE ***!?!? How can I be so unlucky! That should be 98% blessed, that means I had a 2% chance of failure for the whole thing!"
Reality
- Probability doesn't work that way. :( It's a 98% success rate per attempt. The more you repair, the more chances to fail. In this example we can calculate the chance as 0.98^10. So you actually have an ~81.7% chance of walking away from that repair job unharmed, not 98%.
Seeing as success chances in Mabi don't hinge on directly preceding successes (akin to dice rolls), the math is very simple. Assuming that you're just concerned with the chance of getting away without a failure, the formula is x^y, where x is the success rate per point (in decimal) and y is the number of attempts you want to make.
So here's some example success rates per number of attempts, rounded (nearest).
[Image: http://s16.postimg.org/6m440cvxx/success_chart.png]
So not only do the higher-success NPCs (and higher skill ranks for production) give you a better base chance,
the drop in success rate per attempt is less. For this reason it actually is worthwhile to use the more expensive NPCs to repair, but
that will only delay the inevitable. Even if you were able to get a 99.9% success rate, you'd still be down to a 90% chance of avoiding failure if you needed to repair 100 points total.
ADDITION:
As far as upgrade stones... it's bad because
you need to beat the odds. A success is +1 while a fail is -1, and with 50% success... this means that it'll try to be rank 0 or 1 (with the 100% success).
So you might as well try flipping coins to simulate it, and you'll need to get more heads than tails on average (and no, more heads
or tails won't work, as one is success and the other is just repeated fail, it has to skew towards
the same pre-selected side each time).
Assuming you have 15 stones to burn...
http://www.random.org/coins/?num=15&cur=60-usd.0025c-pa
Flip Again a few times and check your luck! Everybody's a [s]winner[/s] loser!
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Yoorah wrote on 2013-08-02 01:55
A good explanation for those who are clueless on basic probability. :) Cool table, too.
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Iyasenu wrote on 2013-08-02 04:32
Bring back perfect repairs, plix.
But for everything, woo woo.
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Gensokyou wrote on 2013-08-02 04:50
I can't rep you again. Thanks so much for explaining this to people. Now they might understand why i'm so anal about repair %s and protection pots. :U
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KomeijiSatori wrote on 2013-08-02 05:21
Nice chart.
Though Elen is weird for me. She hasn't failed once yet.
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Paradise wrote on 2013-08-02 05:23
that applies for "no fails at all" but doesn't apply for failures per try. That remains the same.
I mean this:
success rate for no failures (zero failures): success per point^points you are repairing (your formula)
Success rate for total durability (expected result): success per point
points expected to be repaired: points you are repairing * success rate/100
example:
repairing 10 points at 90%
success rate for no failures : rounded 35% (you need luck to get no failures, you will get at least 1 failure 65% of the time)
Success rate for total durability: 90% of your points should be repaired as average
Expected points to be repaired: 10*90/100= 9 points
More silly numbers on this example:
success rate for 1 failure : rounded 39% (90%^9)
success rate with 5 failures: rounded 59% (90%^5)
and so on....
Any way, good explanation on how success works, some people miss some facts there, this explain that well
btw this works the other way around to check for failure rates (like a total failure disaster).
under this example, you have a 0,00000001% prob of failing 10 dura.. pretty low huh?
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merrykitten wrote on 2013-08-02 05:31
heh, actually you should remember that those events are independent
i.e. for any given event the chance is the same and doesn't magically depend on the past. let's imagine we repair that bow with 97.5% rate, we successfully repaired 9 points of durability already and want to repair 10th, what chance of success do we have? no, it's not 77.6%, it's 97.5%. and if we want to repair 1000th point of durability after we succesfully repaired 999 of them? yes, it's the same 97.5%
those probabilities in the table it's probabilities of the chance of the series of repairs to end without any fails while for any single given repair in the series the chance is the same and doesn't magically decrease
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Paradise wrote on 2013-08-02 05:35
Quote from merrykitten;1130579:
heh, actually you should remember that those events are independent
i.e. for any given event the chance is the same and doesn't magically depend on the past. let's imagine we repair that bow with 97.5% rate, we successfully repaired 9 points of durability already and want to repair 10th, what chance of success do we have? no, it's not 77.6%, it's 97.5%. and if we want to repair 1000th point of durability after we succesfully repaired 999 of them? yes, it's the same 97.5%
those probabilities in the table it's probabilities of the chance of the series of repairs to end without any fails while for any single given repair in the series the chance is the same and doesn't magically decrease
Events that doesnt depend on the past still applies here, since the formula is not exclusive (doesn't make a subtraction of the past events, meaning we should subtract 1 time every time we repair or fail a point, and that includes other methods of past exclusive).
events that are exclusive are i.e., you have 10 boxes, one of them with a prize, every time you make a guess, you exclude that box and try to guess on another (meaning we have 9 boxes in the next try if we fail) and so on.
Repairs are the same as flipping a coin, but the weight on the coin is different for each face, in those cases, what i said, and what its on the OP applies. (scratch what i said in this line before, im sleepy sorry)
Any way, success rates on mabi = LOL
do not use logic, it wont work, mabi doesn't use logic most of the time, i have many funny numbers about failing i can throw here.
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Exkalamity wrote on 2013-08-02 05:41
Hmm here's a harder question for those mathematically inclined: What is the average number of upgrade stones needed to reach step 5? I've pondered this one lightly on and off and now I propose it to you. (I don't know the answer.) I guess for simplicity sake treat the probability of a step succeeding at any given step to be 50%. This question then boils down to the following game: if you score 1 point for every heads, and -1 points for every tails, how many coin flips on average does it take to get 4 points assuming you can never go below 0 points?
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Paradise wrote on 2013-08-02 05:46
you have to multiply each success rate for every try
remember that % are numbres divided by 100, so 10% is 0.1.
In your case , to reach lvl 3 it is: 100%*50%*50%=25% (1*0.5*0.5)
0.25 of your stones will success, meaning that you need 1/0.25 times the stones you need at 100% success (you need 3 stones to get lvl 3 if you ever fail)
1/0.25=4 then 4*3 =12 stones (As average!)
Just add the following success rates and you can get an idea.
success rate lvl "N"= lvl 1 success * lvl 2 success....... .* lvl N success
Stones needed with no failures: N stones
Stones needed (expected): (1/(success rate lvl "N"/100))*N /// OR /// N*100/(success rate lvl "N")
(please do not take the OR as a logic operator, geek joke)
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merrykitten wrote on 2013-08-02 05:51
>What is the average number of upgrade stones needed to reach step 5
too lazy to think :3
>The first upgrade success rate is 100%, 2~3 is a 50%, and 4~6 have a 45% success rate.
i.e. 0.5*0.5*0.45*0.45 = 0.05 chance to get it from the first try. if every fail moved you back to lvl 1 it would take 20*4 = 80 stones on average, actually the number is somehow smaller
edit
20*4 = 80, lol
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Paradise wrote on 2013-08-02 06:00
Quote from merrykitten;1130583:
>What is the average number of upgrade stones needed to reach step 5
too lazy to think :3
>The first upgrade success rate is 100%, 2~3 is a 50%, and 4~6 have a 45% success rate.
i.e. 0.5*0.5*0.45*0.45 = 0.05 chance to get it from the first try. if every fail moved you back to lvl 1 it would take 20*4 = 80 stones on average, actually the number is somehow smaller
edit
20*4 = 80, lol
yea now that i think about it, making it going back a lvl needs to consider past events, since they affect the success rate for every try if the success rate changes. None of our formulas covered it but its somehow near
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merrykitten wrote on 2013-08-02 06:20
it's one of those tasks which you should just run simulation for
10000 tries give 29, rarely 30 stones
[code]
av_stones, tries = 0, 10000
tries.times do
step, stones = 1, 1
while 1
stones += 1
if step == 0
step = 1
elsif step == 1 or step == 2
rand > 0.5 ? step -= 1 : step += 1
elsif step == 3 or step == 4
rand > 0.45 ? step -= 1 : step += 1
end
break if step == 5
end
av_stones += stones
end
p av_stones/tries
[/code]
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wildk wrote on 2013-08-02 06:32
Let %N be the chance of success at step N;
xN be the expected number of stones required to reach step N;
xN = xN-1 + %N + (1-%N) * (xN - xN-2)
Given initial condition
x0 = 0
x1 = 1
x2 = x1 + 50% + 50% * (x2 - x0)
x2 = 1 + 0.5 + 0.5 * x2
x2 = 3
x3 = x2 + 50% + 50% * (x3 - x1)
x3 = 3 + 0.5 + 0.5 * x3 - 0.5
x3 = 6
x4 = x3 + 45% + 55% * (x4 - x2)
x4 = 6 + 0.45 + 0.55 * x4 - 1.65
x4 = 32/3 ~= 11
x5 = x4 + 45% + 55% * (x5 - x3)
x5 = 32/3 + 0.45 + 0.55 * x5 - 3.3
x5 = 469/27 ~= 18
x6 = x5 + 1 = 496/27 ~= 19
In summary
Step 0: 0
Step 1: 1
Step 2: 3
Step 3: 6
Step 4: 11
Step 5: 18
Step 6: 19
Don't think I made any mistakes here but please check and also rep because I hate maths.
Quote from merrykitten;1130596:
it's one of those tasks which you should just run simulation for
10000 tries give 29, rarely 30 stones
You can't do a simulation because it's an open loop. You'll never get a result, only maths will work here :<
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Gensokyou wrote on 2013-08-02 06:35
On this one...
Let X be the number of stones you need to get to Step 5, and P1, P2, P3, etc... Be the success rates per step.
X = (P1 * P2 * P3 * P4 * P5) * 100
= 1*0.5*0.45*0.45*0.4*0.4 * 100
= OVER 9000!!!!!!!!!!!!
That number is fairly accurate, by the way. I think.
Inb4 someone says i dunno how to math lel