Depth in Strategic Games Frank Lantz NYU Game Center Aaron Isaksen - - PowerPoint PPT Presentation

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Depth in Strategic Games Frank Lantz NYU Game Center Aaron Isaksen - - PowerPoint PPT Presentation

Jan 25, 2024 422 likes •1.22k views

Depth in Strategic Games Frank Lantz NYU Game Center Aaron Isaksen NYU Game Innovation Lab Alexander Jaffe Spry Fox Andy Nealen NYU Game Innovation Lab Julian Togelius NYU Game Innovation Lab Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth

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Frank Lantz NYU Game Center Aaron Isaksen NYU Game Innovation Lab Alexander Jaffe Spry Fox Andy Nealen NYU Game Innovation Lab Julian Togelius NYU Game Innovation Lab

Depth in Strategic Games

Frank Lantz NYU Game Center frank.lantz@nyu.edu

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Is there a well-defined property of game systems that corresponds to what designers and players mean when they refer to “strategic depth”?

The Question

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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Preliminary Observations

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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  • game design and computer science

Preliminary Observations

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 5
  • game design and computer science
  • tractable, but not currently known

Preliminary Observations

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 6
  • game design and computer science
  • tractable, but not currently known
  • existing research

Preliminary Observations

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 7
  • game design and computer science
  • tractable, but not currently known
  • existing research
  • laying a foundation

Preliminary Observations

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 8

Clarifying the Question

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 9
  • “deep” = “good”

Clarifying the Question

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 10
  • “deep” = “good”
  • a spectrum, not a binary

Clarifying the Question

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 11
  • “deep” = “good”
  • a spectrum, not a binary
  • psychology-independent

Clarifying the Question

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 12
  • “deep” = “good”
  • a spectrum, not a binary
  • psychology-independent
  • abstract, simplified strategic games

Clarifying the Question

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 13
  • “deep” = “good”
  • a spectrum, not a binary
  • psychology-independent
  • abstract, simplified strategic games
  • “d”

Clarifying the Question

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 14

Why Ask the Question?

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 15
  • conceptual tool to improve design discussions

Why Ask the Question?

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 16
  • conceptual tool to improve design discussions
  • suggest directions for design exploration

Why Ask the Question?

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 17
  • conceptual tool to improve design discussions
  • suggest directions for design exploration
  • pure curiosity and knowledge

Why Ask the Question?

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 18
  • conceptual tool to improve design discussions
  • suggest directions for design exploration
  • pure curiosity and knowledge
  • general questions about AI and “machine

aesthetics”

Why Ask the Question?

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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Our General Approach

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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  • strategic games as problem-solving tasks

Our General Approach

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 21
  • strategic games as problem-solving tasks
  • different “flavors” of hardness

Our General Approach

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 22
  • strategic games as problem-solving tasks
  • different “flavors” of hardness
  • complexity theory

Our General Approach

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 23
  • strategic games as problem-solving tasks
  • different “flavors” of hardness
  • complexity theory
  • existing properties:

Our General Approach

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 24
  • strategic games as problem-solving tasks
  • different “flavors” of hardness
  • complexity theory
  • existing properties:
  • state-space

Our General Approach

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 25
  • strategic games as problem-solving tasks
  • different “flavors” of hardness
  • complexity theory
  • existing properties:
  • state-space
  • branching factor

Our General Approach

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 26
  • strategic games as problem-solving tasks
  • different “flavors” of hardness
  • complexity theory
  • existing properties:
  • state-space
  • branching factor
  • “traditional” hardness

Our General Approach

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 27
  • strategic games as problem-solving tasks
  • different “flavors” of hardness
  • complexity theory
  • existing properties:
  • state-space
  • branching factor
  • “traditional” hardness
  • observing characteristics of real-world games

Our General Approach

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 28
  • strategic games as problem-solving tasks
  • different “flavors” of hardness
  • complexity theory
  • existing properties:
  • state-space
  • branching factor
  • “traditional” hardness
  • observing characteristics of real-world games
  • building a model

Our General Approach

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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Characteristics of Depth

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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  • Large community of dedicated players

Characteristics of Depth

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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  • Large community of dedicated players
  • Life-long learning with regular improvement

Characteristics of Depth

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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  • Large community of dedicated players
  • Life-long learning with regular improvement
  • Vast body of knowledge and strategic analysis

Characteristics of Depth

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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  • Large community of dedicated players
  • Life-long learning with regular improvement
  • Vast body of knowledge and strategic analysis
  • The Skill Chain (eg, Elo)

Characteristics of Depth

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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  • Large community of dedicated players
  • Life-long learning with regular improvement
  • Vast body of knowledge and strategic analysis
  • The Skill Chain (eg, Elo)
  • The Strategy Ladder

Characteristics of Depth

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

Perfect Play Solution Strength Computational Resources

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The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

Perfect Play Solution Strength Computational Resources

The capacity for a game system to allow for a ranked sequence of approximate solutions

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The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
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The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
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The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
  • when & how to evaluate
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SLIDE 41

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
  • when & how to evaluate
  • when & how to use heuristics
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SLIDE 42

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
  • when & how to evaluate
  • when & how to use heuristics
  • Computational Resources
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SLIDE 43

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
  • when & how to evaluate
  • when & how to use heuristics
  • Computational Resources
  • Number of operations
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SLIDE 44

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
  • when & how to evaluate
  • when & how to use heuristics
  • Computational Resources
  • Number of operations
  • Working memory
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SLIDE 45

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
  • when & how to evaluate
  • when & how to use heuristics
  • Computational Resources
  • Number of operations
  • Working memory
  • K-complexity “footprint”
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SLIDE 46

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
  • when & how to evaluate
  • when & how to use heuristics
  • Computational Resources
  • Number of operations
  • Working memory
  • K-complexity “footprint”
  • Strength
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SLIDE 47

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
  • when & how to evaluate
  • when & how to use heuristics
  • Computational Resources
  • Number of operations
  • Working memory
  • K-complexity “footprint”
  • Strength
  • Win rate
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SLIDE 48

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
  • when & how to evaluate
  • when & how to use heuristics
  • Computational Resources
  • Number of operations
  • Working memory
  • K-complexity “footprint”
  • Strength
  • Win rate
  • Quality of move selection
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SLIDE 49

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
  • when & how to evaluate
  • when & how to use heuristics
  • Computational Resources
  • Number of operations
  • Working memory
  • K-complexity “footprint”
  • Strength
  • Win rate
  • Quality of move selection
  • Steps
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SLIDE 50

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Strategies - complete algorithmic descriptions
  • when & how to search
  • when & how to evaluate
  • when & how to use heuristics
  • Computational Resources
  • Number of operations
  • Working memory
  • K-complexity “footprint”
  • Strength
  • Win rate
  • Quality of move selection
  • Steps
  • What is the model’s output?
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SLIDE 51

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 52

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

Perfect Play Solution Strength Computational Resources

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SLIDE 53

The Strategy Ladder

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

Perfect Play Solution Strength Computational Resources

The shape of this curve reveals something important about the game’s underlying structure

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Applications of the Model

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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Applications of the Model

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Conceptual tool for speculation
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Applications of the Model

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Conceptual tool for speculation
  • Direct observation of real games at low CR levels
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Applications of the Model

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Conceptual tool for speculation
  • Direct observation of real games at low CR levels
  • Complete analysis of small games, toy games
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Applications of the Model

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Conceptual tool for speculation
  • Direct observation of real games at low CR levels
  • Complete analysis of small games, toy games
  • Research tool for observing how d changes as you

change aspects of the rule set

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Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 60

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
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SLIDE 61

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
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SLIDE 62

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
  • pure search
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SLIDE 63

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
  • pure search
  • one weird trick
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SLIDE 64

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
  • pure search
  • one weird trick
  • Games of pure search
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SLIDE 65

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
  • pure search
  • one weird trick
  • Games of pure search
  • don’t “feel” deep
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SLIDE 66

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
  • pure search
  • one weird trick
  • Games of pure search
  • don’t “feel” deep
  • don’t support life-long learning
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SLIDE 67

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
  • pure search
  • one weird trick
  • Games of pure search
  • don’t “feel” deep
  • don’t support life-long learning
  • don’t allow for multiple skill levels
slide-68
SLIDE 68

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
  • pure search
  • one weird trick
  • Games of pure search
  • don’t “feel” deep
  • don’t support life-long learning
  • don’t allow for multiple skill levels
  • Complex strategies
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SLIDE 69

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
  • pure search
  • one weird trick
  • Games of pure search
  • don’t “feel” deep
  • don’t support life-long learning
  • don’t allow for multiple skill levels
  • Complex strategies
  • knowledge
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SLIDE 70

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
  • pure search
  • one weird trick
  • Games of pure search
  • don’t “feel” deep
  • don’t support life-long learning
  • don’t allow for multiple skill levels
  • Complex strategies
  • knowledge
  • explanation
slide-71
SLIDE 71

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
  • pure search
  • one weird trick
  • Games of pure search
  • don’t “feel” deep
  • don’t support life-long learning
  • don’t allow for multiple skill levels
  • Complex strategies
  • knowledge
  • explanation
  • insight
slide-72
SLIDE 72

Observations: Search vs. Heuristics

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Games of low d fail by having simple best avail strats
  • Simple strategies
  • pure search
  • one weird trick
  • Games of pure search
  • don’t “feel” deep
  • don’t support life-long learning
  • don’t allow for multiple skill levels
  • Complex strategies
  • knowledge
  • explanation
  • insight
  • Semi-ordered game structure allows for heuristics as

a form of search-compression

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SLIDE 73

Next Steps

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

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SLIDE 74

Next Steps

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Further refinement of the model
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SLIDE 75

Next Steps

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Further refinement of the model
  • Application to simple games
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SLIDE 76

Next Steps

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Further refinement of the model
  • Application to simple games
  • Development and analysis of toy games
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SLIDE 77

Next Steps

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Further refinement of the model
  • Application to simple games
  • Development and analysis of toy games
  • Full Analysis of toy versions of real games
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SLIDE 78

Next Steps

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Further refinement of the model
  • Application to simple games
  • Development and analysis of toy games
  • Full Analysis of toy versions of real games
  • Partial analysis of real games
slide-79
SLIDE 79

Next Steps

Frank Lantz NYU Game Center frank.lantz@nyu.edu Depth in Strategic Games

  • Further refinement of the model
  • Application to simple games
  • Development and analysis of toy games
  • Full Analysis of toy versions of real games
  • Partial analysis of real games
  • Further exploration of search vs. heuristics