Showing posts with label game studies. Show all posts
Showing posts with label game studies. Show all posts

18 December 2010

Lanchester's Game

I've been kicking ideas around about using Lanchester's Laws as a way to create a point-value system (1) for balancing sides in a game, and one of these involves designing a game around this mathematical principle. Usually point system seem to evolve after the game is created; I want to create the point system first, and build a game to fit the math. I'm not sure this is possible, but it should be interesting to try. So I set out to write out the rules for a simple game to demonstrate the difference between Lanchester's Linear, Square, and Logarithmic (see footnote 2) Laws, which I will abbreviate with L1, L2L0. This turned out to be a really good idea, because it gave me an insight about how these laws arise, and a simpler way to explain them.

[A note aside: I wrote most of this post two months ago, and it gave me many good ideas for other post in the process, but I never quite figured out how to finish this one. Now I need this basic discussion to go along with some new posts I'm working on, so I'm making a second effort to finish this one.]

The Game
This game is really very simple, actually more of a thought experiment that explains Lanchester's laws.


Map, Movement, and Range: There is no map, and so no movement, and no range. This is an abstract game, and attacking another unit depend on which Attack Rule is being played (see below). It would be a more interesting game with these elements, but they only complicate the discussion. Maybe I will try to add these back in for another post. (Also good discussion points.)


Forces: Two sides, Blue and Red, each side have a number of tokens (B or R tokens, respectively) or markers representing the strength of each force (These might represent soldiers, tanks, etc.). Each player should start with 20 to 30 tokens, but not necessarily the same number.

Lethality: an attack is resolved by rolling a die: success kills one enemy, remove that marker/token. Assume equal lethality for simplicity, or allow to be different for completeness. Each attack has a lethality, or probability of a kill equal to b for Blue and r for Red. Lethality does not have to be the same for each side, but it simplifies this discussion if it is. For a good demonstration this should be a fairly small probability, so that the game will last 10-20 turns. The following discussion will assume a lethality of b = r = 1/6, so a roll of 1 on 1d6 can be used to resolve this easily.

Attacks: Every turn each player makes one or more attacks. The number of attacks a player makes depends on the Attack Rule in play, and could depend on the current size of each force (B or R).

Sequence of play:
1) Set up the game, decide force sizes, lethality, and Attack Rule.
2) Begin turn: players make one or more attacks, as determined by the Attack Rule in play.
3) Resolve attacks for each player based on the size of their force at the beginning of the turn.
4) Remove destroyed forces.
5) If both played still have forces remaining, go back to step 2 and play another turn. Play continues until one side is eliminated.

Attack Rules:

L1: Each player makes one attack every turn. No matter what casualties occur over the course of the game, each player will have same same total number of attacks, and this number will be proportional to the small of the two forces. This is exactly what is expected under the Linear Law.

L2: Each player makes one attack for every 5 tokens they have remaining (round up or carry fractions o the next turn). Over the course of the game the total number of attacks will be larger for the player with the larger initial force. The ratio of total Blue attacks to Red attacks will be proportional to (B/R)^2 [the ratio B/R, quantity squared]. (It does not have to one attack for every 5 tokens, it only need be some small proportion of the current size of the force. 5 was just convenient).

L0: Each player makes one attack for every 5 (convenience again) of the other sides tokens. Here the number of attacks made against you is proportional to the size of your own force (see footnote 2 again). This seems like a strange rule, but war in unhealthy! Putting your army in the field makes if subject to direct and indirect threats. Starvation, disease, accidents, mules kicks, artillery and bombing, are all hazards that put the entire force at risk. Sometimes the more you bring, the more you lose.

Discussion:
Each of these "attack rules" will lead to distinctly different outcomes for the game. More importantly, a form of one or more of these rules is inherently present in all war games and combat simulations. Even if it is not written explicitly, but it will still arise from how the game plays.
Game combine these rules in interesting ways. For instance, terrain, stacking rules, and range limits will tend to restrict some units in a game to the L1 attack rule. Other units will have a clear field of fire to attack (and be attacked) will use the L2 rule. Some units might stay in relative safety and threaten the other force from afar (like artillery) and subject the other side to the L0 rule. A unit firing from a bunker might only be attacked under the L1 rule, may be able to attack other using the L2 rule. so it's not necessarily the same rule in effect for both sides.

I have read many papers trying to model data from historical battles as if there is a new rule that somehow combines two or more of these rules. From a certain standpoint that is the wrong approach. These rules might mix, affecting different parts of armies in different ways, but there is no rule that says you will always get the same sort of mixture every time. In fact, you will almost certainly get a little different mixture in every battle. Lanchester's laws are not something over which either side has total control - they are something that happen to you during the battle. In a close fight, the army that is better able to exploit the rules is more likely to win.


Footnotes:
(1) Such as BattleValue in Battletech, which is the one I know the best. Ogre/GEV has a very simple point system. Warhammer 20K+/-20K has a point system but I know nothing about it other than it exists. If you can suggest other games that use point systems please post or email me about it so I can look into this topic further.
(2) The "Logarithmic" law arose from attempts to fit actual data of battle casualties to either the Square or Linear law, and finding that sometimes neither one is a very good fit. I have avoided mentioning it thus far in order to simplify discussion. The interpretation of the Logarithmic Law implies that the casualties suffered by one force are proportional to the size of one own force (not the opposing force). This seems unusual, but is sometimes observed in historical data describing large scale battles. See Fricken (1997) for the an excellent discussion and justification for the Logarithmic law.
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10 May 2010

Epic Win - Jane McGonigal on TED

If you are a gamer and don't already know who Jane McGonigal is, then you should watch this.

Jane McGonigal: Gaming can make a better world |
| Video on TED.com




Changing the world thru gaming is an ambitious goal, but it just might work. Could be try fun to try too.
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30 July 2009

Critical Mass of Ideas

What's the opposite of writer's block? It's one thing to be stuck with no ideas to write about, but is it possible to have too many ideas? That seems to be the situation I find myself in. So what's a blogger to do, except maybe write about it. Here's a summary of what's been going through my head lately, all of which I hope to come back to and write about when I can.

  • I have been trading comments with Steven Satak about some material from the TRO project. I think it's going to be really good.
  • (ai-yi-yi ... I'd better make shorter comments or I won't even be able to finish this post about having too much to write about.)
  • Lunch and conversation with Ken Burnside of Ad Astra Games has helped me focus my thoughts on some problems I was already working on, specifically how to value the offensive capability of weapons in a games. This lead to discussion of ...
  • ... Lanchester's Laws (something I keep meaning to write about), a formulation of the relative advantage of numerical superiority in combat ...
  • ... and a how it applies to the advantage of longer range individual combat. My intuition tells me this ought to be the same sort of relationship, but I'm trying to work through the math to verify this, and ...
  • ... this ties in nicely with what I've already been working on for the mathematics of Battletech.
  • My efforts in the Game Design Concepts class have been lacking recently. This has been a rich learning experience for me, and I need to make a serious effort to get caught up.
  • A game idea I've been kicking around for a while is starting to gel. It's high time for me to put together a prototype of this fast-paced air combat game, tentatively titled JINK!
  • My project with Tom of PhotonCutter Studios is coming along nicely. The guys in my Battletech group like the prototype I brought in last night, and there are indications it could be popular with a lot of serious miniatures gamers.
  • I got some comments about mt Crazy Climber game I wrote and blogged about for the Game Design Concepts class. Someone might actually give it a try! As a budding game designer, this sort of feedback is an incredibly inspiring experience. Saxywolf: If you are reading this, I haven't forgotten. I hope to repost a revised set of rules as soon as I get the time (but time is in short supply).
  • Finally, there are a few more ideas that came out of my time at ORIGINS that I haven't written about yet.
Time for work. If there are any of these topics you want to see sooner than later, let me know.
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26 June 2009

ORIGINS 2009: Day 3 - More Than Just Fun & Games

Friday evening, and I just over-napped the start of the sculpting class I wanted to sit in on (maybe next year). I whip out my convention schedule and look at the seminars I have marked earlier in the day:

Professional Gaming ? Modeling with Wargames
E160A -- An open panel discussion with audience participation, examining the state-of-the-art usage of wargames for modeling and decision support. Part of the Strategicorps event track. All ages / 50 seats. Run by Brant Guillory.

This sounded like something that might really be interesting, and since I paid for that Strategicorps ribbon so I really ought to use it. This might have been the best decision I made all week.

I arrived just as things were about to get started. With more panel members than audience, Brant decided to have us all pull our chairs into a circle to facilitate discussion. Good call Brant. Introductions ensued:

The Panel:
Brant Guillory (Moderator, former US Army Captain, PhD candidate in Communications, Bayonet Games) 1,2,3


Col. Matthew Caffery (Chief, Wargaming Plans & Programs Directorate, Air Force Research Laboratory) See 1,2


John Tiller, PhD (independent game developer with Matrix Games and HPS Simulations) See 1,2,3




James SterrettJames Sterrett, PhD (Simulations Instructor, U.S. Army Command and General Staff College (Northrup Grumman), Military Historian, Ad Adstra Games {Attack Vector : Tactical}) 1,2,3



Joseph Miranda (Editor Strategy & Tactics Magazine, MCS Group) 1,2,3



Maj. Michael Martin (CGSC graduate, soon-to-be PhD candidate in Modeling and Simulations at ODU in Norfolk.)

The audience (as best I recall):
Col. Ken Guillory (MLRS commanders in Desert Storm I: a man of vast military experience and father of Brant Guillory) 1

Robert Crandall (Programmer and Games Developer, Core Talent Games, Matrix Games)

Jim Snyder (Matrix Games, Lock and Load Games) 1,

Myself (DE)

Several others joined in as well, including a number of avid gamers, but I didn't get any more names.
---------------------------------------

The following is my (pitiful) attempt to summarize some of the discussion, more-or-less stream-of-consciousness style. I will attempt to attribute comments where I can. All quotations are approximate.

BG: This discussion is intended to be about the use of games and simulation to model warefare, rather than as a training tool.
JT: The modeling process is "legitimate but not realistic.
MM: Modeling guys get good data on the physical aspects, but not data on psychological aspects. A favorite tactic: "suppression fire and sneak around" works because it distracts the enemy.
KG: (on adjudication of information) personalities matter. Not all leaders are equally about to pass on important information.
MM: Try a search on "Correlation of Forces and Means".
MC: Air Force Command structure is nearly Theater to Pilot. This is necessary because functional groups (bombers, ECCM, refueling tankers) are not based together.
[DE: the discussion turned to data representing units - like maximum road speed - and what that means]
JT: A tank platoon moves at the speed of its most confused Sergeant.
BG: Average speed means more than maximum speed (says the man who rode an abramsM1A1 tank down the road at 60+ mph!).
JT: Mission is more important than the vehicle. Recon units will be faster because that is their mission, not (entirely) because their vehicles are faster.
KG: Not the maxumum speed OR the average, but what you need when you need it.
RC: Maximums are useful for specific instances (what you need when you need it again).
MC: [drew a chart dipicting the relationship between granulatity, completeness, and interpretability in simulations, which I did not capture adequately. The essence was that you cannot have all three at the same time.]
JM: CRTs (combat results tables) based on data resresenting actual outcomes.
??: Logistics controls movement
BG KG: [pointed out some physical limitations to logistics] Navy loads by tonnage and like items, so all humvees from different units will be transported together, rather than by organizational group.
??: "Generals study logistics"
??: different levels and aspects of simulation
??: Outcome of simulation may be affected by the agenda of those creating it.
DE: [summarizing] There was additional discussion of whether there could be a game simply about logistics [there are many examples] or if there needs to be direct conflict [something to go BOOM at the end].
JM?: [a good story on why a simulation cannot contain all possible outcomes] "Under what circumstances can a Calvary unit capture a ship at sea?" [and it actually happened!]
??: Does "resting" units get rewarded in games?
MC: [modestly described what has been called the "Caffrey Loop"] What can we learn from history that can make better games?
--------------------------------------------
The official discussion concluded, but 7-8 of us adjorned to the bar across the street. The evening concluded with several very pleasant rounds of beer, and (among many other things) a discussion of the merits of weaponized Silly-Putty (I get the strangest ideas sometimes).

I would like to thank the entire group, and especially Brant for moderating a great session.

[7/6/09 -- Thanks to the active responses of many of the panel members, I have been able to update and correct this post.]
[7/8/09 -- I now recall there was discussion of how people with particular agendas might influence the simulation results, and how this might be overcome. I commented that we were now talking about modeling the simulation process itself. At this point, Brant threatened "that if I got any more analytical, I would be require to buy the first round of beer". For the record, I bought the first round. :-) ]
[This post has been back-dated to approximately the actual time it occurred.]
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11 May 2009

Understanding Comics

This book is one of the optional texts for Ian Schreiber's Game Design Concepts class I signed up for this summer.
Ian Writes: Understanding Comics: The Invisible Art, by McCloud. While this book claims to be about comics, many of the lessons within can be applied to game design and other forms of art. It also happens to be a comic book itself, and fun to read.
[image scottmccloud.com]
Ian is correct, it's a great little book and I can easily see how most of it can be applied to games as well as comics. I did a little web searching on Scott McCloud and quickly came up with even more good stuff: Scott McCloud's Web Site including a blog and much more, Scott McCloud's TED lecture, and of course you can pick up your own copy Understanding Comics for $16.55 + shipping at Amazon.

Here is the Scott McCloud video from TED:


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27 April 2009

Game Design Class

How would you like to take a class in game design? Ian Schreiber is offering a class called Game Design Concepts, and it's free [except for the optional books, which are not at all expensive].

[From Game Developers Conference 2009 Speakers] Ian Schreiber has been in the industry for eight years, first as a programmer and then as a game designer. He has worked on five published game titles and two serious game projects. Ian has taught game design and development courses at Ohio University, Columbus State Community College, and Savannah College of Art and Design.
Ian also has a blog: Teaching Game Design.

So I signed up for the class, my books should arrive via Amazon tomorrow, and I'm looking forward to meeting Ian at ORIGINS is summer. Maybe this will help me get some of my game ideas into a form where they could actually be played.

[Found on Applied Game Design]
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05 April 2009

The Greatest Game, EVER

Question: What is the greatest game, ever?

The answer, of course, is that there is no best spaghetti sauce.

That link will take you to 17 minute TED video with Malcolm Gladwell (and his hair) explaining how market researcher Howard R. Moskowitz realized that offering more variety allowed more people to be happier with the product they chose. It wasn't that one type of spaghetti sauce was better than any other, it was that people have differing preferences.

I think the same sort of argument can be made for games. Once you get past the basic mechanics of how the game is presented, it comes down to what the player wants. Simple or complex. Platform type (computer,box,tabletop,etc.). Solo or social. Stand alone or "collectible".
I could probably list a lot of other aspects of games, but I think you get the idea.

This post is inspired by a comment someone made to my November post about Netrek being the greatest Star Trek game ever. This might tell you something about how long I tend to sit on ideas, and that I am a terrible procrastinator.

25 February 2009

Language and Games

Found at Paperpools:

Suppose I grow up in a family where people obsessively play Hearts. We switch around between different versions of the game - sometimes we play Black Maria, where the Queen of Spades costs you 13 points and you pass on three cards to the left before you begin play, sometimes we invent twists of our own. I also have four friends: A lives in a family of chess fanatics, B lives in a family of bridge fanatics, C lives in a family of go fanatics, D lives in a family of poker fanatics.

What I see at once is something remarkable. Languages are translatable, more or less; it may be more or less tricky, but it's intelligible to speak of Chinese being translated into Turkish AND Arabic AND English. Games are not translatable. Chess is a game for two players with complete information; you can't "explain" what's going on in a chess game in terms of bridge, which is a game for two sets of partners with imperfect information, a mixture of skill and chance which depends on skilful sharing of information between partners. And you can't "explain" either in terms of poker, which is a game for an indeterminate number of players, a mixture of skill and chance in which sharing of information between players would in fact be collusion and outlawed. A game is intelligible on its own terms - which means, paradoxically, that you can play a game with someone whose language you don't know, provided you both know the rules of the game.

You don't understand a game in terms of some other game, you understand it by learning to play it - but the more games you play, the more you will understand about the radical otherness of games.


Read the entire post and comments at Paperpools.

Hat Tip: Andrew Gelman at Statistical Modeling, Causal Inference, and Social Science, which also adds some insightful and mathy comments.

23 December 2008

The Mathematics of ... Candyland???

Candyland game math statistics Markov chainI mentioned Markov-chains a while back (not to be confused with Markov Chaney), and I though that might make an interesting topic to relate to games. It seems though that several many others have beaten me to the punch, and written very well on this subject, so instead I'm going to point out one or two other fine efforts, review, and comment.

[Image taken from lscheffer.com, who also has a nice analysis.]

In my own words, a Markov-chain is a series of random states. A trivial example might be flipping a coin; the coin is either in a state of "heads" or "tails" and has a 50% chance of changing state with each flip. It can get more complicated, with the probabilities of changing to a different state dependent on the current or even (correct me if I am wrong) previous states. A state which ends the series (if any) is called an absorbing state. In my recent Netrek post the number of planets a team controls would be the state, and the absorbing state would be one team conquering all the planets, thus ending the series and the game (oversimplified, but true).

Candyland is a Markov-chain if you reshuffle the deck of cards after every draw. Each square (rhomboid?) on the board represents a state, and players advance randomly towards the end of the game. Reshuffling is required so that the probability of changing states remains independent of previous card-draws (if you were wondering). There is a nice summary and history of the game itself here.

Speaking of fine work, Greg Costikyan wrote about this a few weeks back, and it has traveled far in the blogosphere. The really interesting part here is (for me) the discussion of whether or not it really is a game; all moves are random, so if the player doesn't actually do anything is it really a game? My answer: Yes. Not the most interesting game we may ever play by any means, but most definitely a game. Games where players make decisions and enact strategies are more difficult, and for most, more interesting.

I should not end without mentioning an older game that is a Markov-chain to start with - no reshuffling required - known to most as Snakes and Ladders.

[Image from DKimages]

20 December 2008

Fear of Failing

Jesper Juul Video game theory reader 2
Jesper Juul has a book out, or rather a chapter he wrote which is collected in this book which is coming out soon.

Juul writes:

Winning isn’t everything

It is quite simple: When you play a game, you want to win. Winning makes you happy, losing makes you unhappy. If this seems self-evident, there is nonetheless a contradictory viewpoint, according to which games should be “neither too easy nor too hard”, implying that players also want not to win, at least part of the time. This is a contradiction I will try resolve in what follows.


I read the Fear of Failing article, and recognized his "Snake" game and the accompanying survey. I don't know if was one of his study participants or if I encountered it at some later time, but I recall play this game and completing the survey (some years ago). Now that I'm trying to write about games on my own, it is particularly interesting to have this particular research come back to me in this way.
-----
fear of failing game difficulty player skill progression Introduction Game Development Steve RabinBut back to the article: Mr. Juul gives an excellent account of the balance between game difficulty and player skill/ability, and that the proper balance is what make a good game. He is writing about video games in particular, but this easily applies to the sort of tabletop games as well.
Before I forget, the image to the right (© 2004 Noah Falstein, reference: Falstein, Noah. 2005. "Understanding Fun—The Theory of Natural Funativity". In Introduction to Game Development, ed. Steve Rabin, 71-98. Boston:Charles River Media.),

Then I got to thinking, and although I still think this applies to tabletop games, is not so simple to describe what is going on you add in the dynamics of human players, either in tabletop games or multiplayer video/computer games. I touched on this briefly when I wrote about The Mathematics of Netrek, and I intend to spend some more time on this in future posts.