6 ms·

Game Theory - Marginal Advantage

46 points by s_baar 16y ago

deleted 16y ago
[deleted]
lmkg 16y ago
For me, one of the reasons that the concept of Marginal Advantage is important for game design, is because you have to interact with, or at least react to, your opponent. In the Mancala example, the greedy AI was basically playing a single-player optimization game, and ignoring its opponent. Meanwhile, the clever AI paid attention to what its opponent could do and played around it. The Starcraft example continues the theme: amateurs concentrate on what's best for them in an absolute sense, while the pros consider their opponents. FYI, the author, Sean Plott, is better known as Day[9], one of the top-ranked Starcraft players in the United States. Also a mathematician, as it turns out. His podcasts on the SCII beta are really insightful.
Xurinos 16y ago
I cannot help but think that these examples share a different commonality -- that they are war simulations where the winners in these examples were the ones who did not overextend and instead fortified or played a better numbers game. This is not marginal advantage; it is fortification and resource consolidation. I forget the word for it... where you are trying to reduce your opponent's resources before yours... but that resource management skill is what makes good players good. Viewed that way, what is really going on is much less mystical.
- smallblacksun 16y ago
  Yeah. His examples didn't really show anything other than that experienced players make fewer mistakes.
- carbocation 16y ago
  The word is attrition, by the way.
  - Xurinos 16y ago
    That's it! War of attrition. Point for you.
snowbird122 16y ago
Insightful: all reasonably designed competitive games share three basic traits: 1. ambiguity of optimal play 2. diversity of play 3. allowance for skill
Terry_B 16y ago
I've had a really hard time finding writing of this quality and insight into good game design. There's lots of fluffy, high level stuff at one end of the spectrum and then lots of stuff that discusses the details of specific well trodden genres ad nauseum. There's not so much that's of direct use when you sit down and try and design an orginal type of game by applying principals like this it seems to me. I don't know how much of that is because the people with such insight haven't written it down, or they really just do it by feel and trial and error rather than by applying easy to describe techniques. Does anyone have any other recommendations like this?
- crystalis 16y ago
  Sirlin has written what seems to be the most commonly referenced piece whenever games and "thinking" come up. Playing to Win, available free at his website (www.sirlin.net/ptw/), doesn't directly deal with game design, but it comes up throughout. His blog generally trends on game design topics. (He's been a fighting game pro, rebalanced SF2 for the most recent version, and is in the process of releasing some physical games now.) Costikyan writes a lot of good stuff. http://playthisthing.com/randomness-blight-or-bane http://playthisthing.com/randomness-blight-or-bane is a great example, and you can find some other writings of his in various archives. PTT itself has him (and a few other contributors of varying flavors) writing on new (indie, board, etc.) games. Soren Johnson (Lead designer on Civ4) had a series going at http://www.designer-notes.com/ http://www.designer-notes.com/, but hasn't appeared to have posted recently. http://www.designer-notes.com/?p=132 http://www.designer-notes.com/?p=132 is a good example, discussing how easily players can perceive an AI to be "cheating". Brenda Braithwaite (Wizardry series, Train) has a similar, seemingly modestly defunct blog that is worth reading regardless. Edmund McMillen of Super Meatboy posted about difficulty: http://supermeatboy.com/13/Why_am_I_so____hard_/ http://supermeatboy.com/13/Why_am_I_so____hard_/. There's a similar post somewhere on the blog. Gama Sutra occasionally has useful things, but you need to filter a lot. Without endorsing it overly, Less Talk More Rock (http://boingboing.net/features/morerock.html http://boingboing.net/features/morerock.html) is worth consideration. (For balance, http://sinisterdesign.net/?p=457 http://sinisterdesign.net/?p=457).
  - 16y ago
michael_dorfman 16y ago
Third, a good competitive game should test a player’s skills and minimize the element of chance or luck. Ideally, the probability of a weak player defeating a good player should be as close to zero as possible. I'd disagree that this is the ideal. Personally, I enjoy games that mix luck and skill. Take Cribbage, for example-- the weaker player will still win about 45% of the time, by virtue of having been dealt better cards-- which is why tournaments consist of a number of games, to even out the luck. I think it's great if weaker players can defeat stronger players, on occasion. It helps keep the game interesting for everybody. Put another way: when I play chess with my children, I have to handicap myself-- otherwise, they'd lose every time, and quickly lose interest. When I play cribbage with them, they still win often enough to keep things interesting.
- derefr 16y ago
  That just means that the "real game" of Cribbage lasts for one tournament, not one session. If you only played chess openings, rather than entire games, they might win some of the time as well. Almost all games that adults play competitively are made to decisively rank their players' powers of strategy over their proper play-length. Games for children introduce progressively higher levels of chance, the younger and therefore less-equipped the child is to deal with real strategy. The maximum of this slope comes in early-childhood "games" such as Chutes and Ladders—not really a game at all, as there are no strategic choices made at any point. From this, you can take the idea that any game can be adapted for players of unequal strategic strength simply by adding chance components to it, or replacing some choice points with chance. What if, in Chess for example, you had to roll a die at the beginning of your turn to find out the maximum number of squares any of your pieces could move that turn? Or if, upon a bad roll, your opponent got to decide which of your pieces you must move?
jplewicke 16y ago
If you're interested in game theory and strategy and looking for a non-technical introduction, I'd heavily recommend the book Thinking Strategically by Dixit and Nalebuff ( http://www.amazon.com/gp/product/0393310353 http://www.amazon.com/gp/product/0393310353 ). I'd been exposed to a lot of the concepts before, but they hadn't completely clicked until reading their engaging examples.
JoeAltmaier 16y ago
Marginal Advantage implies looking one turn ahead, to determine how the opponent can react to your move. The Greedy approach doesn't have to look ahead at all. The difference is that simple - the more moves you look ahead, the better you play. Chess programs became "expert level" when there was enough CPU horsepower to look 6 moves ahead.

46 points by s_baar 16y ago

deleted 16y ago

[deleted]

lmkg 16y ago

For me, one of the reasons that the concept of Marginal Advantage is important for game design, is because you have to interact with, or at least react to, your opponent. In the Mancala example, the greedy AI was basically playing a single-player optimization game, and ignoring its opponent. Meanwhile, the clever AI paid attention to what its opponent could do and played around it. The Starcraft example continues the theme: amateurs concentrate on what's best for them in an absolute sense, while the pros consider their opponents. FYI, the author, Sean Plott, is better known as Day[9], one of the top-ranked Starcraft players in the United States. Also a mathematician, as it turns out. His podcasts on the SCII beta are really insightful.

Xurinos 16y ago

I cannot help but think that these examples share a different commonality -- that they are war simulations where the winners in these examples were the ones who did not overextend and instead fortified or played a better numbers game. This is not marginal advantage; it is fortification and resource consolidation. I forget the word for it... where you are trying to reduce your opponent's resources before yours... but that resource management skill is what makes good players good. Viewed that way, what is really going on is much less mystical.

smallblacksun 16y ago
Yeah. His examples didn't really show anything other than that experienced players make fewer mistakes.
carbocation 16y ago
The word is attrition, by the way.
- Xurinos 16y ago
  That's it! War of attrition. Point for you.

snowbird122 16y ago

Insightful: all reasonably designed competitive games share three basic traits: 1. ambiguity of optimal play 2. diversity of play 3. allowance for skill

Terry_B 16y ago

I've had a really hard time finding writing of this quality and insight into good game design. There's lots of fluffy, high level stuff at one end of the spectrum and then lots of stuff that discusses the details of specific well trodden genres ad nauseum. There's not so much that's of direct use when you sit down and try and design an orginal type of game by applying principals like this it seems to me. I don't know how much of that is because the people with such insight haven't written it down, or they really just do it by feel and trial and error rather than by applying easy to describe techniques. Does anyone have any other recommendations like this?

crystalis 16y ago
Sirlin has written what seems to be the most commonly referenced piece whenever games and "thinking" come up. Playing to Win, available free at his website (www.sirlin.net/ptw/), doesn't directly deal with game design, but it comes up throughout. His blog generally trends on game design topics. (He's been a fighting game pro, rebalanced SF2 for the most recent version, and is in the process of releasing some physical games now.) Costikyan writes a lot of good stuff. http://playthisthing.com/randomness-blight-or-bane http://playthisthing.com/randomness-blight-or-bane is a great example, and you can find some other writings of his in various archives. PTT itself has him (and a few other contributors of varying flavors) writing on new (indie, board, etc.) games. Soren Johnson (Lead designer on Civ4) had a series going at http://www.designer-notes.com/ http://www.designer-notes.com/, but hasn't appeared to have posted recently. http://www.designer-notes.com/?p=132 http://www.designer-notes.com/?p=132 is a good example, discussing how easily players can perceive an AI to be "cheating". Brenda Braithwaite (Wizardry series, Train) has a similar, seemingly modestly defunct blog that is worth reading regardless. Edmund McMillen of Super Meatboy posted about difficulty: http://supermeatboy.com/13/Why_am_I_so____hard_/ http://supermeatboy.com/13/Why_am_I_so____hard_/. There's a similar post somewhere on the blog. Gama Sutra occasionally has useful things, but you need to filter a lot. Without endorsing it overly, Less Talk More Rock (http://boingboing.net/features/morerock.html http://boingboing.net/features/morerock.html) is worth consideration. (For balance, http://sinisterdesign.net/?p=457 http://sinisterdesign.net/?p=457).
- 16y ago

michael_dorfman 16y ago

Third, a good competitive game should test a player’s skills and minimize the element of chance or luck. Ideally, the probability of a weak player defeating a good player should be as close to zero as possible. I'd disagree that this is the ideal. Personally, I enjoy games that mix luck and skill. Take Cribbage, for example-- the weaker player will still win about 45% of the time, by virtue of having been dealt better cards-- which is why tournaments consist of a number of games, to even out the luck. I think it's great if weaker players can defeat stronger players, on occasion. It helps keep the game interesting for everybody. Put another way: when I play chess with my children, I have to handicap myself-- otherwise, they'd lose every time, and quickly lose interest. When I play cribbage with them, they still win often enough to keep things interesting.

derefr 16y ago
That just means that the "real game" of Cribbage lasts for one tournament, not one session. If you only played chess openings, rather than entire games, they might win some of the time as well. Almost all games that adults play competitively are made to decisively rank their players' powers of strategy over their proper play-length. Games for children introduce progressively higher levels of chance, the younger and therefore less-equipped the child is to deal with real strategy. The maximum of this slope comes in early-childhood "games" such as Chutes and Ladders—not really a game at all, as there are no strategic choices made at any point. From this, you can take the idea that any game can be adapted for players of unequal strategic strength simply by adding chance components to it, or replacing some choice points with chance. What if, in Chess for example, you had to roll a die at the beginning of your turn to find out the maximum number of squares any of your pieces could move that turn? Or if, upon a bad roll, your opponent got to decide which of your pieces you must move?

jplewicke 16y ago

If you're interested in game theory and strategy and looking for a non-technical introduction, I'd heavily recommend the book Thinking Strategically by Dixit and Nalebuff ( http://www.amazon.com/gp/product/0393310353 http://www.amazon.com/gp/product/0393310353 ). I'd been exposed to a lot of the concepts before, but they hadn't completely clicked until reading their engaging examples.

JoeAltmaier 16y ago

Marginal Advantage implies looking one turn ahead, to determine how the opponent can react to your move. The Greedy approach doesn't have to look ahead at all. The difference is that simple - the more moves you look ahead, the better you play. Chess programs became "expert level" when there was enough CPU horsepower to look 6 moves ahead.