Possible number of passive tree combinations
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In terms of game building, you always do want to keep it as simple as possible, while still maintaining the complexity you require for variety. Complexity != variety however.
At the end of the day, there is no variety between taking +2% damage vs. +2% accuracy when you've already taken 30 other nodes which are similar. Those choices are ultimately not build-making. Likewise, the same applies to fire damage vs. lightning damage, IFF those damage types do nothing else special. Therefore, in order to count a build as meaningful, you have to divvy everything up into categories of mechanics, and then use combinatorics on the modularized mechanics to determine the amount of variety in the game you actually have. (ie. If you have two passive skill distributions that are roughly similar but one has 10% higher accuracy and the other has 10% higher damage... I would not consider those mechanically different builds.) The only problem with counting there is categorization, and sets that have mechanics that overlap. POE strives to make each skill gem, each elemental effect, and each keystone significantly different in terms of mechanics, and each of those mechanics imparts replayability and real choice in build creation. I feel that is its strongest point. Their biggest weakness is probably that they can never add another class to the game, but they can offer skins on the existing classes instead. If you have account problems please [url="http://www.pathofexile.com/support"]Email Support[/url]
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So just to clarify, 1 + 1 = 3 right?
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" Only if Big Brother tells you it is so. "Minions of your minions are your minion's minions, not your minions." - Mark
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" Sure, but you need complexity to have variety. This is why most games these days have no depth. Certainly, POE could have infinite complexity and in the end not be complex, because complexity requires more than complexity, but if you don't even have a base complexity to start with, you'll never have it. That's why most games will never have it. I'm not saying that POE, with 2^116 or more possible builds, is more or less complex than game X BECAUSE of the number 2^116. My analysis is not quantitative - it's just to show that most games, especially most new RPGs, do not even have a BASE complexity of 2^116. Diablo 3 has room for 3 passives. Even if there were 50 passive skills to choose from among those 3, it will only mean D3 has 19600 passive trios (and this isn't even unique combinations). 2^116 vs 19600, one of these numbers is enormous, right? 116 vs 3? I mean, yes, this isn't a quantitative analysis, and even such basic comparisons as 116 vs 3, should be enough, but that comparison isn't shocking enough for some people. Good balance and design take complexity and deepen it. Simple complexity with good balance and design is going to create a simple game, no matter what. I can't think of a deep game which is simple - even checkers has 10^40 possible boards. I mean. Dragon Age 2 complexity vs POE complexity 1350 choose 116 / 60 choose 20 = 5.701962e+154 Path of Exile is 154 zeros more complex than Dragon Age 2, which is supposed to be a single player rpg. Really, I should do total complexity actually, just to demonstrate my point further... DA2's passive and active skill system are intertwined. You spend skill points to raise both active and passive skills. So it's only fair to compare POE's active skills against that... 81 active gems 46 support gems 24 max sockets 6(1350 choose 116 * 127 choose 24) / (270* choose 80) = 7.31254e+126 POE is 10^126 more complex than a SP RPG. It'll probably be even more daunting when I do BG2's total complexity. *270 comes from the fact DA2 has 4 party members, 3 of them have 20 skill points to use against 60 passive/active skills to choose from, the main character has 90 skills to choose from with 20 points. My Keystone Ideas: http://www.pathofexile.com/forum/view-thread/744282 Last edited by anubite#0701 on Nov 28, 2012, 8:00:13 AM
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" This is a pretty good point and most likely the biggest factor as without considering this you are calculating the number of routes you could take not the number of builds you could end up with. I think the easiest way to estimate this is to only consider new nodes that can be reached with each passive point and ignoring any node that could have been reached earlier and also ignoring the fact that 2 different branches could easily collide. As very rough guesstimation I would say the average number of new nodes that can be reached with each point is 2 (realistically I think it will actually be a bit lower than this but since I am ignoring nodes that could have been taken earlier I think it will approximately balance out) then just math 2^100 ~ 1x10^30 seems considerably lower than the first post but this method considers both the fact that the passive points have to be linked to each other and gives a very rough consideration to the possibility of multiple routes ending with the same end result. However I think this only works as a low end estimate for a better estimate you need to consider taking old nodes and ending up with the same build. This is pretty simple way to get a guess I have another idea which I may try, if it is any good I will make a separate post for it. IGN --- Grizdale Last edited by Grizdale#2543 on Nov 28, 2012, 12:17:30 PM
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" This is exactly the post I hoped you wouldn't make, because it's senseless. I agree so far that you need some complexity to make the game interesting, but at some point it doesn't matter anymore how high the number is. Let's just assume there is a game that offers 10000 different build options and 1000 of those builds are noticeable different from each other and are viable. This game would beat every other game without any problems when it comes to build options. And you can't really compare Diablo 3 and PoE when it comes to passives... Diablo 3 passives bring a huge bonus and difference to the character, in PoE on the other hand most passives will give you +10 dex or something like that. And I think 1350 over 116 doesn't really mean what you tihnk it means, because the result is the number of different 116-sized-groups you can pick from 1350 unqiue nodes. This is obviously not the case with the PoE skill web. Saying something like: " is just so wrong. It doesn't say anything about the complexity of the game, or not at least in the way I would define the "complexity" of a game. And I really don't know what this number " is supposed to say? The math is so way off here. Anyway, I just want to stress that while I agree that offering a lot of options is important, the number doesn't say anything.. it just doesn't matter if it is 10^5 or 10^50. Just as an example.. possible combinations of the Wizard in D3: You chose 6 active skills out of 25 and 3 passives out of 15. => 80.580.000 possible combinations.. and that is without skillrunes |
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Just a couple of questions that come to mind -
How do you take into account that some of the possible passive combinations are, in reality, not viable build option? In terms of end game survivability the build choices become more prohibitive, that is, some skill combinations are undesirable because they are basically unplayable. Perhaps this consideration falls outside the scope of your thesis, yet in a practical sense it does effect the number of 'playable' build options. How do you define complexity in your study? Is it simply variety? Is a game complex simply because it presents you with many possible choices? Does complexity have to with the underlying strategy by which these choices are presented to the player? Any game that causes you to think beyond the moment has a certain amount of complexity inherent in its design. Does randomness further add to complexity, because things don't go according to plan and you have to rethink your strategy? Does you study have a way of expressing randomness as an element of complexity? I have enjoyed this thread and all its contributors, the source of complexity in game design is a timely subject considering the indie trend of returning to the old school emphesis on game play, as opposed to big studios eye candy orientation. I completely agree with your premise that a game must have, atleast a statistical, underlying complexity in order to any chance of real complexity. GL with your study, let me know where you post it when you are finished. Bring me my bow of burning gold
Bring me my arrows of desire..... If i am a troll who is no troll who then is the troll? http://www.pathofexile.com/forum/view-thread/53626 }:) 'I rise from the ashes of my own defeat, only to be smitten down again...' - Some poor soul. |
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1) Checkers has something like 10^21 combinations, not 10^40
2) Checkers has been solved! (meaning every combination has been calculated and win conditions can be achieved after the very first move) 3) One has to define complexity and what it means to have a significant build 4) It's hard or even impossible to take into account passive combinations that result in the same build (taking 2 nodes of the same type as your last node) or builds that are not viable 5) In any game that has huge numbers of possible raw combinations, only a handful of 'categories' are truly meaningful... even games with the largest build diversities still only perhaps have 1000's of meaningful builds that significantly change tactics or mechanics If you have account problems please [url="http://www.pathofexile.com/support"]Email Support[/url]
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