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| Thread: empty pandora's box |  This thread is pages long: 1 2 · NEXT» |
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demarest
Known Hero
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posted October 12, 2007 05:38 AM |
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empty pandora's box
I had read that if a hero opens a pandora's box and it is empty, that that means it was going to give spells that that hero couldn't understand. Well, I just opened one (random map) with a hero that had Expert Wisdom and it was empty. Anybody have any ideas why?
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Homer171
Promising
Supreme Hero
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posted October 12, 2007 05:44 AM |
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Well Pandora's boxes can be empty sometimes. It can give: Experience, Spell Points, Morale, Luck, Resources, Primary Skills, Secondary Skills, Artifacts, Spells and even Creatures but if the number is 0 it dosen't give anything. Rare but happens sometimes.
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Don't be too proud of this technological terror you've constructed. The ability to destroy a planet is insignificant next to the power of the Force.
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angelito
Honorable
Undefeatable Hero
proud father of a princess
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posted October 12, 2007 12:22 PM |
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Edited by angelito at 12:23, 12 Oct 2007.
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An empty pandora's box can only have THREE reasons:
1. There were spells inside, and your hero didn't carry a spellbook.
2. There were high level spells (level3 and/or higher) inside and your hero didn't have wisdom (basic for lev3, advanced for lev4, expert for lev5 spells).
3. There were spells inside which the hero already had knowledge of. (all level 1 spells for example)
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Better judged by 12 than carried by 6.
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Xarfax111
Bad-mannered
Supreme Hero
The last hero standing
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posted October 12, 2007 04:26 PM |
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4. The pan box can be simply empty
@sorry Angelito, that was no joke. A pan box can be simply empty too.
Best regards Xarfax1
PS: Geez, cant you take a small joke about being a Drillmaster?
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angelito
Honorable
Undefeatable Hero
proud father of a princess
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posted October 12, 2007 04:38 PM |
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Edited by angelito at 16:40, 12 Oct 2007.
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On a random map, you will never find an empty box (to my knowledge). Not sure on what map you discovered that.
A pandora box is nothing else than a "value", and the AI doesn't set a value of "0" on a map. Would be same to see a neutral stack of monsters on the map, and when u attack them, they disappear all of a sudden.
I don't know how many hundreds of random maps I have looked up to check values (value of utopia guards, value of high level 7 guards, value of specific pandora box guards, etc...) and I have yet to see an empty box.
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Better judged by 12 than carried by 6.
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SAG
Promising
Supreme Hero
WCL owner
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posted October 12, 2007 05:32 PM |
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Edited by SAG at 17:33, 12 Oct 2007.
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Quote:
Well Pandora's boxes can be empty sometimes. It can give: Experience, Spell Points, Morale, Luck, Resources, Primary Skills, Secondary Skills, Artifacts, Spells and even Creatures but if the number is 0 it dosen't give anything. Rare but happens sometimes.
not correct because:
1) on random maps pandora can't give Spell Points, Morale, Luck, Secondary Skills, Artifacts
2) value can't be 0.
Angelito is correct as always 
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Binabik
Responsible
Legendary Hero
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posted October 12, 2007 08:32 PM |
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Quote:
I don't know how many hundreds of random maps I have looked up to check values (value of utopia guards, value of high level 7 guards, value of specific pandora box guards, etc...) and I have yet to see an empty box
I haven't gotten to values that high in my testing. Are you saying you actually looked inside the boxes?
I was thinking I read somewhere there was a 5% chance of getting nothing. But it doesn't say that in the editor, so I don't know where I heard that. But if that's true I think you would need to open at least 100-200 boxes to conclude it can't happen.
Maybe one of the statistics people can give the probability of how many need to be opened to be "pretty damn sure" (that's technical terminology that stats people use.).
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angelito
Honorable
Undefeatable Hero
proud father of a princess
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posted October 12, 2007 10:07 PM |
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Edited by angelito at 22:07, 12 Oct 2007.
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Yes, I opened all the boxes. Otherwise it wouldn't give me any information about the guards value.
Like: a box with 5k exp. points has about the same value as 5k gold or all level 1 spells.
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Better judged by 12 than carried by 6.
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Binabik
Responsible
Legendary Hero
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posted October 12, 2007 10:14 PM |
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So different treasure values made different boxes. I guess I assumed that when a treasure value makes them appear, that the contents was completely random. I think I've only tested up to around 3000.
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted October 12, 2007 10:24 PM |
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Edited by dimis at 22:55, 12 Oct 2007.
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Number of boxes to be opened.
Quote:
I was thinking I read somewhere there was a 5% chance of getting nothing. But it doesn't say that in the editor, so I don't know where I heard that. But if that's true I think you would need to open at least 100-200 boxes to conclude it can't happen.
Maybe one of the statistics people can give the probability of how many need to be opened to be "pretty damn sure" (that's technical terminology that stats people use.).
Direct Approach
I don't know much about statistics, but we can observe the following:
Say that something happens with probability x on each trial and all trials are independent. Then, it does not happen with probability (1-x) on each trial. Since this is the case for every of our trials, (by the multiplication principle) it follows that after N tries something does not occur not even once with probability p = (1-x)^N. So, if you want to be pretty much sure, say at least 99% = 0.99 confident, I assume this means that the probability of your claim being correct is at least 99% = 0.99; or in other words, the probability that you are not correct is less than or equal to 1% = 0.01.
This forms the following inequality:
(1-x)^N <= 0.01
Now, taking the logarithms (say base 10) the inequality is preserved, since log(x) is "1-1" and strictly increasing (monotone):
log( (1-x)^N ) <= log(0.01)
or equivalently
N log(1-x) <= log(0.01)
Now, 0 < x < 1, therefore -1 < -x < 0, therefore 0 < 1 - x < 1, therefore log(1-x) < log(1) = 0.
So, dividing the last inequality, since log(1-x) < 0, we have:
N >= log(0.01)/log(1-x) [useful for scientific calculators one may use].
Or the more neat formula:
N >= log_{1-x}(0.01) [Logarithm in base (1-x)]
Hence, say that the claim is that x = 5% = 0.05, then by substitution one gets:
N >= -2/log(0.95) <==> N >= -2/-0.022276395 <==> N >= 89.78...
or equivalently N >= 90.
Hence, after 90 trials, with probability >= 99% you verify your claim; i.e. after 90 trials the probability that at least one of the boxes you opened is empty, is >= 99%.
Note, that if you wanted to be just 90% sure, the same formula would yield:
N >= -1/log(0.95) <==> ... <==> N >= 45 trials.
Or if you wanted to be even more sure, say 99.9% = 0.999, then:
N >= -3/log(0.95) <==> ... <==> N >= 135.
What's going on with x?
Now, assume that you make a constant number of trials, say N. But we want to figure out what's going on with x.
Then, again, we have (99% to be sure):
N log(1-x) <= log(0.01) <==> 1 - x <= 10^{log(0.01)/N} <==> 1 - 0.01^{1/N} <= x
or equivalently:
x >= 1 - root[N](0.01) [The N-th root of 0.01].
So, if you perform say N=100 trials, then root[100](0.01) = 0.95499.., i.e:
x >= 0.045 or x >= 4.5%.
Meaning, that you are at least 99% sure after 100 trials, that if no box among the 100 opened is empty, then the probability of assigning zero value to that box, should be less than 4.5%.
Similarly, 90 trials, guarantee with probability 99% that the box is assigned a value of zero (meaning empty) with probability less than 5% (assuming that in all of your experiments you did not encounter a single empty box; otherwise, you know that there is at least one such box, which seems to be the case of misunderstanding in the previous posts).
Do I make sense?
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The empty set
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Binabik
Responsible
Legendary Hero
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posted October 12, 2007 10:30 PM |
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Edited by Binabik at 22:32, 12 Oct 2007.
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LOL Dimis, just tell us the answer. How many need to be opened? I'll let you decide the definition of "pretty damn sure".
edit: Has anyone else heard that there's a 5% chance for nothing, or am I imagining things?
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demarest
Known Hero
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posted October 12, 2007 10:48 PM |
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Quote:
3. There were spells inside which the hero already had knowledge of. (all level 1 spells for example)
Thanks
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted October 12, 2007 11:08 PM |
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Tester's Choice may be?
Quote:
LOL Dimis, just tell us the answer. How many need to be opened? I'll let you decide the definition of "pretty damn sure".
edit: Has anyone else heard that there's a 5% chance for nothing, or am I imagining things?
I 've never heard, but perhaps I am not the most typical person to ask!
As for the answer, it seems that 90 trials can make you 99% confident that the probability of assigning zero (0) to one of the boxes is less than or equal to 5% (i.e.: you do not encounter a single one of them being empty!). Moreover, 135 trials make you 99.9% confident for exactly the same thing (probability of assigning zero to the boxes is less than or equal to 0.05 = 5%). Of course, if the assumed non-zero probability is more than 5%, in the same number of steps you are now much more confident.
So, it's the tester's choice. Even 45 trials can give a good indication since they guarantee 90% on your confidence level that x <= 0.05 = 5%, where x is the probability of assigning zero to the value of the boxes.
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The empty set
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dimis
Responsible
Supreme Hero
Digitally signed by FoG
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posted October 12, 2007 11:12 PM |
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Edited by dimis at 23:15, 12 Oct 2007.
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That's my idea
So what am I trying to say?
That the variables are two. Hence there is a trade-off between "how high x can be" and "how confident one (person) can be".
Now a certain number of trials gives let's say some "potential" to your observations. You can be more confident that x is not something large, or less confident (but still up to a good amount ) but x is assigned a smaller value.
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The empty set
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Binabik
Responsible
Legendary Hero
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posted October 12, 2007 11:13 PM |
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OK, cool
We just need to find out how many Angelito opened. Or I can do it when I test whatever value makes boxes.
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Xarfax111
Bad-mannered
Supreme Hero
The last hero standing
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posted October 12, 2007 11:43 PM |
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A pan box can be empty cause the map designer did so, means it doesnt have to be anything in there.
Im sorry that i gave the impression that it referred to random generator.
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angelito
Honorable
Undefeatable Hero
proud father of a princess
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posted October 13, 2007 12:29 AM |
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Quote:
OK, cool
We just need to find out how many Angelito opened.
Hundreds...at least. Especially when I made my RMG testing.
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Better judged by 12 than carried by 6.
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SAG
Promising
Supreme Hero
WCL owner
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posted October 13, 2007 10:17 AM |
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i've played about 500 randoms during last 4 years. Each game opening 2-6 pandora boxes. Was never surprised. That means's testing of ~1500 boxes
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PyroStock
Adventuring Hero
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posted March 29, 2015 10:08 PM |
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Empty
I know I'm  necromancing this thread, but I am playing a RMG game with a hero who has Expert Wisdom yet missing multiple spells from each level (some L1, some L2, some L3, some L4 & one L5 spells). This hero just opened 2 empty Pandora Boxes.
Perhaps the difference is generating a random map with the editor produces different Pandora Boxes than the in game random map generator? Nevertheless, you can get empty boxes from the in game random map generator, so:
4.Box is empty.
is correct.
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PyroStock
Adventuring Hero
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posted March 29, 2015 10:32 PM |
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Additionally, the hero does not have all spells of any elemental school either, so no it's not that either.
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