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Author Topic: "Number Crunching"  (Read 1577 times)
Ramza
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« on: May 31, 2011, 05:52:26 PM »

I read Rob's editorial. Anyone else read it? I much enjoyed it, esp. cuz I like me some math.

http://www.rpgfan.com/news/2011/1653.html

My thoughts:

1) the problem isn't numbers (whether too few or too many). The problem is *always* hidden numbers. Which, if you're really freaking bored, you can approximate for yourself by testing something over and over (making sure you know as many possible factors as you can, esp if against different enemies with different attributes).

2) this idea on reverse-engineering a true hit/miss approximation is something we can take back to sports and their "Fantasy" equivalents. I am reminded of the opening chapters of Stephen Johnson's "Everything Bad Is Good For You," wherein he compares D&D to some of his favorite sports approximation statistics-games. Also, this: http://xkcd.com/904/ (be sure to read alt-text)

3) This statement needs further scrutiny:

Quote
Suppose we have a 5% chance to miss. Firing four times, we have a chance of missing all four shots equal to:

0.05^(4) = 6.25 E -6

Needless to say, that's an exceptionally small number. And yet these odds can happen repeatedly in games like Diablo and the aforementioned Fallout 3.

Outside of the very possible "hidden numbers" problem, this observation on Rob's part needs to be weighed heavily against human nature: that is, our ability to blow out of proportion the frequency of times things don't "go our way" compared to how often they do. How *repeatedly* in those games? And is it really so statistically unlikely as what you're expressing? Be sure to listen to the Radiolab episode on Stochasticity (that is, Randomness):

http://www.radiolab.org/2009/jun/15/

You flip a coin seven times and get eight heads in a row. OH MY GOSH! CRAZY! The likelihood of this (and, technically, any combination of eight that takes order into account) is 0.5 ^ 8, or 0.00390625. That's still about 200 times as likely as the scenario Rob lays out (.05^4). In any case, the eight in a row is a big deal if that happens on your first eight. You might think the coin is weighted. But out of 100 flips, how likely is it to get eight of the same thing in a row? How about out of 1000 flips?

And how many attack attempts do you make in any given game? 1000? 10000? 50000?

It's just important that we tend to focus on the frustrating aspects, when it feels like the numbers are "against" us.

I know people rant and rave on this when they have accuracy approximations in Strategy RPGs like FFT or Fire Emblem. But that's the thing about randomness: it's *random,* and unless you have a sufficient sample size, you can't very well go about disproving the odds displayed to you.

(I'm a HUGE fan of numbers!)

Pat
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« Reply #1 on: May 31, 2011, 06:46:35 PM »

I thought about starting a topic saying exactly what you said, Ramza.  But you beat me to it.

By the way, I've played D&D for years and there actually was an occasion when I rolled 4 natural 1s in a row on a d20.  That's the exact same probability the editorial mentioned.  But if you game enough something like that is bound to happen eventually.  Keep in mind that you're really looking at a much broader category that's "the probability of something unlikely happening that will stick in my head".  Rolling 4 natural 20s would have been remembered just as well, albeit in a different light.  And really it could have been anyone in the group, not just my rolls.

Even so, my bad luck is now legendary in my D&D group...
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Annubis
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« Reply #2 on: June 01, 2011, 09:57:45 AM »

1) the problem isn't numbers (whether too few or too many). The problem is *always* hidden numbers.

This.

Play The Last Remnant and you'll see why hidden numbers are complete bullshit. If that game had xp bars or semi-sensical happenings, it would have been a much better game. Instead, they tell you to go back to the kids table and let the math.random() sail the boat.
« Last Edit: June 01, 2011, 09:59:41 AM by Annubis » Logged
dyeager
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« Reply #3 on: June 01, 2011, 10:13:03 AM »

I'll say here what I said in the editor forums when we were discussing this particular editorial:

In this day and age, why play games that have an element of randomness if you don't like randomness? At this point there are so many games that borrow storytelling and character building elements from RPGs that if you don't want to ever miss something if you have enough skill to line up your shot, then you can play those games! They exist in abundance!

Same goes for D&D really. Why, games like Sorcerer, Dogs in the Vineyard, etc. - these are games built by people who enjoyed the storytelling and creative elements of D&D but hated the randomness. They were built to cater to exactly the audience Rob is representing here. So why not play those instead?

I think that the point of view is perfectly valid (even if I think the math in the editorial is terribly misleading for reasons already pointed out) - the author likes games where SKILL is rewarded consistently. There are a massive pile of games like that. It seems strange to me to criticize a game for having an element of randomness when it was designed specifically to have randomness.
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« Reply #4 on: June 01, 2011, 10:15:45 AM »

It seems strange to me to criticize a game for having an element of randomness when it was designed specifically to have randomness.

I hate eating strawberry ice cream because it doesn't taste of mint. :[
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dyeager
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« Reply #5 on: June 01, 2011, 10:25:35 AM »

A little bit, yeah. :-)

As for the math - the human brain is notoriously terrible at interpreting randomness. I particularly recommend the book The Drunkard's Walk for anybody interested in the topic. The human mind is actually SO bad at randomness that typically when you are doing it EXACTLY right, you will be accused of doing it WRONG. I remember way back when iTunes had to release an update to its shuffle algorithm to make it LESS random because people were accusing it of playing the same songs too often!

EDIT: http://www.amazon.com/Drunkards-Walk-Randomness-Rules-Lives/dp/0375424040
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« Reply #6 on: June 01, 2011, 10:44:04 AM »

Good posts thus far. What are the benefits of randomness in a game?

To me, it opens the possibility of unexpected things happening. Skill becomes more about predicting rather than planning. You run probability of failure and do everything possible to ensure you succeed. Honestly, the most entertaining moments are when things don't go as planned and something awesome or terrible happens.
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« Reply #7 on: June 01, 2011, 10:55:15 AM »

It's certainly true that numbers can be used to validate nearly any argument.  Pat's analysis of my math is 100% valid.  This is more of a minor annoyance in video games that causes me to roll my eyes.  I can live with it.  It may piss me off on occasion, but I understand that it can happen.  

My bigger issue is when the numbers present a completely insurmountable obstacle for me as a gamer.  There are points in Borderlands that I simply cannot get through until my character has reached a certain level.  It doesn't matter that I can beat Modern Warfare on veteran.  My skill as a gamer is not going to get me through some of the hardest battles.  I love how one fat, bald, overweight guard at the end of Witcher 1 can kill me in three hits simply because his numbers behind the scenes are designed to crush me.  At least Zeus looks intimidating in God of War.  This guy looked like a white Carl Winslow, and he was strong as a titan.

One of the things I pointed out on the editor's board is my love of character development.  This was an aspect almost exclusive to RPGs for years.  This type of gameplay has found its way to shooters, survival horror games, action titles, etc.  The best RPGs allow me to completely customize my character and style, while the worst force me to play a certain way to overcome the design of the game.  Dragon Age was brutal when I tried to play the game as a JRPG and focused on damage.  It wasn't until I played the game the way the designers intended that I was able to succeed.  Is that proper player choice and character development?  Am I supposed to follow what the designers intended or should I be able to succeed in other ways?  Why offer choice if there's only one correct way to play?  My favorite games offer choice and success, even if the choice is a simple one between a shotgun and a sniper rifle.    

I'm glad people enjoyed the article and it has created some awesome discussion.  That was purely the intent.  I love to talk and debate games from a scientific and analytical standpoint.  I think that's the only way the medium advances.  
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dyeager
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« Reply #8 on: June 01, 2011, 12:07:58 PM »

The wrong numbers lead to the wrong conclusions. The right numbers, properly interpreted, lead to correct conclusions. Poorly interpreted, yet more wrong conclusions.

So from a "scientific" or "analytical" perspective, you of all people should know that the notion "you can use numbers to prove anything" is the purview of the person who doesn't actually want to give the numbers their full critical analysis.

Outside the bounds of what we're talking about here, but let's just say computers wouldn't work and ergo video games wouldn't exist if you could "use numbers to prove anything". From the perspective of the software designer. ;-)

As to the design issue of artificial barriers based not on skill but on time commitment, which now that we've discussed it farther seems to be the real crux of the matter: I think it is perfectly okay for these things to be a matter of taste, but these design decisions often come down to very real cost issues. Perhaps dollars are not a legitimate excuse, but in the end it's a business and sometimes you need to make decisions on where you want your money spent.

Finally, as for wanting to play the game in ways aside from the way the designers intended - the difference between video games and other media is that there is a limit to how much FREEDOM one has to explore. You can let your imagination wander past those hills on the horizon for example, but if a designer didn't build anything beyond them to actually see yourself, you can't actually go there. Same thing with a boss battle. If a battle is designed a certain way (and the more complex the battle and AI, the more money required), trying to do things a different way may in fact prove frustrating (or ridiculously easy or otherwise unbalanced). That doesn't always mean it's a failure on the part of the devs or the designers. Your choice between the sniper rifle and the shotgun still had to be put there and accounted for in some way by the devs to even be possible, let alone fun.

Dragon Age is actually a really good example of what you are talking about. As a story, I thought Dragon Age: Origins soared. As a GAME however, something I play within the bounds of tactile input and mechanics, I thought it was pretty awful precisely because of the way choice was such a transparent illusion, exacerbated greatly at higher difficulty settings.

In the end internet forums are probably the most imperfect place possible to have a conversation like this. It would be better to discuss it with a bottle of cognac and some cigars.
« Last Edit: June 01, 2011, 12:17:21 PM by dyeager » Logged
PaleRobbie
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« Reply #9 on: June 01, 2011, 12:41:36 PM »

Quote
In the end internet forums are probably the most imperfect place possible to have a conversation like this. It would be better to discuss it with a bottle of cognac and some cigars.

Totally agree!

Video games are all about illusion.  You have the illusion of choice, but you can never work outside of what the designers program.
« Last Edit: June 01, 2011, 12:44:53 PM by PaleRobbie » Logged
dyeager
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« Reply #10 on: June 01, 2011, 12:55:59 PM »

I don't know that I necessarily agree that video games are entirely about illusion of choice though. I think games like Pac Man for example are still great (especially the Championship editions), but they do not weave any kind of illusion of choice. You control a yellow thing that eats dots and stays away from ghosts. The only choices you have are where to turn. That's not illusion of choice. That's legit choice but in a very very tiny box.

Despite this the game is still ridiculously fun. Nobody ever criticizes Pac Man for the things we criticize RPGs and other games for. Granted the goals of RPG design and Pac Man are very different, but they are also more complex and loftier - in many ways unattainable.

EDIT: Also I apologize as that may have been an incorrect reading of what you meant by "video games".
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« Reply #11 on: June 01, 2011, 01:16:29 PM »

You end up working within in the confines of the rules set and structure provided by the designers and programmers when you play a video game.  Pac Man turning left or right at the fork in the road is certainly one example of player choice.  I was more speaking to the "freedom" developers talk about in current generation games.  The illusion of freedom comes from the restrictions put in place by the game makers.  Bethesda RPGs offer a great deal of choice in where to go and how to carry out missions.  But I'm never given an option like, say, challenging the leader of the super mutants to one-on-one combat, skinning him alive and wearing his head as a crown and testament to my unholy army of death raiders.  The developers lay out several options and choices for me to make, but I have to work within the confines of what they dictate.  Now, I'm not suggesting that this is problem in video games or something that needs to drastically change (not to mention the fact that it would be practically impossible to give total and complete freedom within the structure of a video game).  I'm merely pulling back the curtain a little bit so I can see The Wizard and understand how the game works and how these choices and decisions impact my own personal experience with the game.

*puffs cigar*
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Ramza
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« Reply #12 on: June 01, 2011, 06:16:54 PM »

Cigar-puffing aside, I think this forum, unlike so many others, is a great place to discuss this sort of thing.

Read all. Love it all.
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