Simulation and Game Design

Daniel “Delta” Collins

CUNY/Kingsborough

www.superdan.net

Part I: Problem Statement

Strategic Dominance

• One strategy is better than another in all cases• So: One player option decisively beats another• Dominated option will practically never get played• Wasted design & world-building effort• Game should be “balanced”• All player choices should have some utility and

actually get used from time to time• Modern concern (old-school: “Realism vs. playability”)

Rock-Paper-Scissors?

• Result of balancing may be “rock-paper-scissors”

• Three main options that beat others in cycle– History: Swords-Pikes-Cavalry

– Original D&D: Fighters-Clerics-Wizards

– Starcraft: Protoss-Terrans-Zerg

• Or any other odd number

• Criticisms, feasibility: even this difficult!

• See Simon, et. al.: Understanding Video Games

Ad-Hoc Point Systems

• Point system with “best guess” values

• Always inherently flawed

• Overlooks interactions between pieces in play

• Play is inherently irreducible

• Examples:– Warhammer army points

– Character ability point-buys

– D&D War Machine mass combat

– 3E D&D magic item price formulas

Traditional Playtesting

• Paper prototyping

• Play on the tabletop

• Person-vs-person

• Small sample size (time constraint)

• Unreliable gauge of true balance level

Part II: Solve by Simulation

Large-Scale Simulation

• Simulate core mechanic in a program

• Use computing power not available in 70's

• Testbed to run encounters automatically

• Play game thousands or millions of times

• Get more accurate view of different game options

Generate Data

• Have each piece fight against all others

• Or each character type vs. stock encounters

• Run large number of fights (how many?)

• Compute win percents– A beats B 45% or 80% of the time, etc.

• Scan results for dominance

• Count number of opposed strategies one beats

Iterations

• If results unacceptable, modify pieces– Reduce dominant type's strength

– Increase weakest type's power

– Modify prices or points

• Most intense part of game design process

• Iterated Elimination of Dominated Strategies (IEDS)– If one piece loses to all others, consider removing it, repeat

– May greatly reduce pieces this way

Advantages

• Much more time efficient

• Modifications don't take months or years to assess

• Rebalance before game is released

• Not perfectly balanced, but raises awareness

Limitations

• Don't recreate entire game

• Core mechanic will suffice

• Simplify or eliminate tactical movement

• Possibly single types, not mixed parties

• Perfect simulation would require strong AI– Tactics, strategy, meta-game analysis

– Beyond current capacities

• Prioritize!

How Long? Do The Math

• Our win percents will be estimates

• But accurate to some confidence and margin of error

• Statistics says sample size is: n = (z∙σ/E)2

• For 95% confidence, normal score z = 1.96 ≈ 2

• Because win percents are proportions (0 to 1), max standard deviation σ = 0.5

• Exercises: Find desired run cycles at 95% CL.– (a) Margin of error 5%

– (b) Margin of error 1%

• Times all the combinations in game & iterate

Part III: Examples

Book of War (2011)

• Old-school wargame

• Simplified for casual players

• Statistics make results same as D&D en masse

• Each figure represents 10 creatures

• Hardest part: Pricing figures for point-buy (80%?)

• Input: Figure types, budget, terrain, weather

• Output: Matrix of win percents

Book of War (2011)

Book of War (2011)

Book of War (2001)

Star Frontiers (1983)

• Science-fiction RPG

• Knight Hawks spaceship combat supplement

• Game comes with 4 stock scenarios

• No rules for setting up custom games

• Add pricing point-buy?

• Limitation: Game fixed, some dominance

• Input: Ship types, budget, squadron combos

• Output: Matrix of win percents, averages

Star Frontiers (1983)

Star Frontiers (1983)

Star Frontiers (1983)

3E D&D Challenge Ratings

• Every monster has a CR

• Indicates balanced party level to challenge

• As usual: Creating monster easy, CR hard!

• Simulate core fight against stock NPC fighters

• Binary search for closest to 50% win rate

• Input: Full D&D stat block, number of monsters, combats, melee or ranged

• Output: Most balanced level to fight

3E D&D Challenge Ratings

3E D&D Challenge Ratings

3E D&D Challenge Ratings

Part IV: Open Questions

Are We In a Simulation?

• Plato's Allegory of the Cave

• Descartes' Evil Demon (deus deceptor)

• Recent philosophical writings

• The Matrix

How Can We Know?

• Beane, Davoudi, Savage: “Constraints on the Universe as a Numerical Simulation” (2012)

• Looking for quantum & astrophysical tests to support or deny such a possibility (aliasing?)

• Article in New York Times last week (2/14/14)

How Can Code Know?

• Security vs. malware: run incoming code on an emulation (simulation)

• Malware now developed to detect if it's in a simulation & avoid revealing behavior

• Run-time differences, etc.

• Kang, Yin, Hanna, McCamant, Song: “Emulating Emulation-Resistant Malware” (2009)

• Thanks to Richard Lipton for this point: http://rjlipton.wordpress.com/

Thank You!

Links

• Example details & code: http://www.superdan.net/gaming/jhu/

• My regular D&D game blog: http://deltasdnd.blogspot.com/

• OED Games website: http://www.oedgames.com/