Chris Hazard, CEO/Founder, Hazardous Software This presentation was given at the 2016 Serious Play Conference, hosted by the UNC Kenan-Flagler Business School. A serious game can be a useful tool to help understand a strategic problem to optimize solutions, manage risks, evaluate processes, and operationalize automation. The speaker will share broadly applicable techniques that have proven useful in designing and developing training games for solving strategic problems as well as company operations. The techniques include concepts from modeling and simulation, game theory, operations research, psychology, artificial intelligence and behavioral economics. The talk is intended for two audiences. The talk will show executives and managers possibilities for using serious games, how serious games overlap with what they may know from management science and how serious games can aid understanding, automating, training and operationalizing various aspects of games for strategic purposes. Serious game developers, will also learn share techniques that have worked for us at Hazardous Software.

1. Modeling, Math and Science
for Building Games that Improve
Organization Operation,
and Workforce Effectiveness
Christopher J. Hazard, PhD

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Hazardous Software Serious Games

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Image from user boysdean on Flickr.com
Image from user BLANCOBILL on TripAdvisor.com
Who is a Gamer?

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Play = immersion +
learning +
minimized actual risk +
time travel

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Simulation-Based Serious Games
Close Combat – Modern Tactics, Matrix Games
CyberCIEGE, NPS & Rivermind
EteRNA, CMU

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More Serious Games
With OR Aspects
Code of Everand, UK Department for Transport
MMORPG, 2009-2011
Cargo Dynasty, Serious Games Interactive,
TSU, TUR
Wildfire game, Lincoln Labs

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Not about
Virtual Worlds &
Chocolate Covered
Broccoli
Second Life

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How Different From M&S?
• Have human-centric interfaces
• Focus on usability
• Focus on exercise deployability
• Focus on creating & managing reusable
scenarios
• Focus on realistic communication &
controls
• Have AAR, AI, help, and tutorials
integrated/embedded

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Implicit Grinding
(and optimal downtime)
Just Cause 2
Niel de la Rouviere, Stellenbosch University

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Adaptive vs Choice vs Fixed
Content
Choice of content Adaptive content
D. Sharek PhD dissertation at NCSU, 2012. Investigating Real-time Predictors of
Engagement:
Implications For Adaptive Video Games and Online Training.

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Humans Are Rational*
*given limited computational bounds, strong
heuristics, poor probabilistic reasoning,
unfounded beliefs of others, inaccurate
capability assessments, inexplicable valuations,
and some level of [im]patience

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Utility & Currency
• Common currency: average-player time
– Skilled players & devoted players have most
• Find exchange rates for everything
– If items purchasable in $, find exchange
between player time and $
• Find amortization / discount rate

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Skill, Strategy, & Information Gain
• Skill
– Driven by capabilities, signaling, reputation
– Measured using statistics, hindsight
• Strategy
– Driven by preferences (valuations),
sanctioning, trust
– Solved using game theory, foresight
• Information Gain
– Driven by immersion, curiosity, relevance
– Provided via narrative, setting, instruction, cues

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Keynesian Beauty Pageant:
Guess 2/3 the average
• Everyone choose number [1,100]
• Closest to 2/3 the average wins
Image from thedigeratilife.com

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A Simple Game...
• Strategist
• Negotiator
• Artist
• Logician (e.g., programmer/lawyer)
• Impulsivist or risk seeker
• Risk avoider

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Bidding Game Rules
Card is cost:
A: 1
2: 2
3: 3
…
J: 11
Q: 12
K: 13
• Bid each round
• Winning bidder gets
price – cost
• Highest profit wins

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Bidding Game Results
• 3-4 rounds to "convergence"
• Generally considered "unfair"
• Bayesian Nash Equilibrium!
– Big reveal of same card: surprise
– Lack of reveal: anchoring and bias hook

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NASCAR: Drafter's Dilemma
• Red ahead, Blue behind, leave line together
• Payoff = number of cars passed
• Cooperate = allow other to jump back in line
• Defect = jump back in line without the other
Ronfeldt, First Monday J., '00
Cooperate Defect
Cooperate 3 3 -5 3
Defect 2 -5 1 1

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Mixed Strategy & Risk
• Intransitivity
• “Every unit overpowered”
• Forced risk
P S
R 0, 0 -1, 1 1, -1
P 1, -1 0, 0 -1, 1
S -1, 1 1,-1 0, 0
Street Fighter 4

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Payoff, Risk, Commitment
Stag Hare
Stag 10 10 0 8
Hare 8 0 7 7
Swerve Straight
Swerve 0 0 -1 +1
Straight +1 -1 -1000 -1000

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Creeping Sniper's Dilemma
Original image from ShadowShield.com

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Creeping Sniper's Dilemma
Single sniper position, σ, as a function of time:
• Multiple sniper: match quickest visible discount strategy
unless too risky
PositionofSniper
Near Target
Far Target

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Operations Research: Lanchester's Laws
Gang of N units vs 1, all with sufficient
action range
X DPS, Y health
N each retain Y (1 – 1/N^2)
Original image from XCOM: Enemy Unknown

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Balancing With Game Theory: Strength and
Utility
Hammer Spear Curse
Hammer 1 3 0.5
Spear 0.33 1 0.5
Curse 2 2 1 Hammer Spear Curse
Hammer 0.000 -0.043 0.095
Spear 0.043 0.000 -0.070
Curse -0.095 0.070 0.000
Cost
Hammer 0.23
Spear 0.56
Curse 0.21
S (strength: # of player 1 to defeat player 2)
C (cost)
U (utility)
One player loses all utility, another fraction
Spear vs Hammer:
gain - loss
0.23 - (1/3 * 0.56)
Symmetric!

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Balancing With Game Theory:
Probabilities
Hammer Spear Curse
Hammer 0.000 -0.043 0.095
Spear 0.043 0.000 -0.070
Curse -0.095 0.070 0.000
U (utility)
Probability
Hammer 0.336
Spear 0.456
Curse 0.208
P (probability)
Probability
Hammer 0.333
Spear 0.334
Curse 0.333
P (probability)
Cost
Hammer 0.255
Spear 0.545
Curse 0.200
C (cost)
Hammer Spear Curse
Hammer 0.000 -0.073 0.073
Spear 0.073 0.000 -0.073
Curse -0.073 0.073 0.000
U (utility)

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Ambiguity as an Interestingness
Measure
• Find Nash equilibrium
– 20% sniper rifle, 30% machine gun, 50% shotgun
– 33% sniper rifle, 33% machine gun, 34% shotgun
• Control tightness
– Ambiguity vs predictability of next game states
(discounted)
• Difficulty of puzzles & optimal strategy
ascertainment
– Some ambiguity good, too much boring

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Learning & Information Gain
• Measure information gain between player
strategy and optimal
• Mixed strategy Nash equilibria
– 1/3 rock, 1/3 paper, 1/3 scissors
• How much information left to teach player?
– 1/4 rock, 1/4 paper, 1/2 scissors
– Info gain to achieve desired Nash equilibrium

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Complexity of Behavior

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Information Conveyance

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Corpse Party
Chapter 1 Infirmary

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Corpse Party
Chapter 1 Infirmary

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Infirmary Flow
take match from furnace
try door
try door
try match
try match
get rubbing alcohol
try door
exit
• Actual branching factor: 12
• Perceived branching factor: 11
• Exaggerated expectation
[Hilbert, PSYCHOL BULL '12]
– P(progress | revisit item) higher
than anticipated

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Infirmary Surprisal
• Player unsure of what to do, so assume
uniform distribution over new possibilities:
Q(X) ≈ 1/11, Q(Repeat) ≈ 0 => ~3.5 bits
• Correct distribution over possibilities,
minimizing assumptions: P(X) = 1/12
•
Q(repeat) ≈ 0 means
1/12 * ln( (1/12) / 0) = 1/12 * ln(∞) = ∞
Massive surprisal if assume no repeat actions
advance game

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Measuring Difficulty By Decision Information
Rate
X X
X
3 out of 6 paths lose
1
11
0
0 No loss, no information
Average 1 bit of information
Average 0.5 bits of information
1.5 bits of total information to win
1.5 bits / 2 steps = 0.75 bits per step to win

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Mutual Exclusion Between Mechanical and Social Reasoning
(Jack et al., Neuroimage, 2012)
Working Memory Capabilities & Affective Control
(Schweizer et al., J Neuroscience, 2013)

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Time Manipulation in Gaming
• Time zones • Reverse time
Chrono
Trigger Braid
• Fixed jump back• Time loop
Ratchet & Clank
Majora's
Mask

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Time Manipulation Transforms
Gameplay
Obstacle/Combat Course (FF12) Maze
Gran Turismo Sudoku (Optimization)
+Undo
+Timeline

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Time Manipulation & Causality
• Dynamically correct plans: blur hypothetical &
committed
• Long-term thinking about decisions
• Just in time vs redundancy
• Minmax & Nash equilibria
• Qualitative sensitivity analysis: plan fragility
• “Newton's Method” of strategy

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Time Manipulation Game Mechanics
• “Chronoenergy”: causality as a resource
– Locality & change magnitude
– What is a unit of causality?
• Player's intention vs low-level control
• AI to assist “when you're not then”
• Collaborative planning

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Desirability Index
• Desirability Index (geometric mean of
conflicting metrics) in multicriteria
optimization:
• Used for optimization in chemistry,
chemical engineering, mechanical
engineering
• Related to Shannon Entropy Maximization
• Easy to relate to output as a score, hard to
“game”

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Understanding Probability
Distributions

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Little’s Law, MDPs & More OR
• L = λW to measure
expected length of
queue by wait time
• MDPs for
modeling,
visualization into
process
• MILP, Pareto
Frontier

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Questions?
info@hazardoussoftware.com