Simulations: Evaluating game system behavior

Petri Lankoski Södertörn Univeristy

SimulationsEvaluating game system behavior


SimulationsGame systems with random component are

complex

Simulations can help to understand how a part of the system behaves One does not need ready game for simulation

Does not replace playtesting But simulation can show the features work in the

long run

Balancing weapons & troops non-symmetrical things are hard to balance


Simulating a game systemModel

sum of two six sided dice -> sum of two random numbers between 1 to 6

Weapon: change to hit, damage dealt & fire rate

Simulating system Run model many times to learn how the system

behaves Run 50000 times and calculate distribution or

averages, average damage per minute, etc.

Settlers of Catan


Simulation How the players gain resources

Simplified Robber vs no robber discard Only resource amount simulated, not types

Assumptions Four player game 0-3 resources at hand when ones turn ends

Model for using resources One specific board set-up

The results does not vary much board to board The results can vary with not optimal settlement placements

50 000 iterations used


Simulation set-up• 4 victory point set-up

• Settlements -> cities• 6 victory point sim• 1&2) 8 victory point sim


Model#!/usr/bin/python import randomfrom collections import Counter

# board model (2 victory points) field1 = { 2: {'white': 0, 'blue':0, 'red': 0, 'orange': 0}, 3: {'white': 0, 'blue':0, 'red': 1, 'orange': 1}, 4: {'white': 1, 'blue':1, 'red': 0, 'orange': 0}, 5: {'white': 0, 'blue':2, 'red': 1, 'orange': 0}, 6: {'white': 1, 'blue':1, 'red': 1, 'orange': 1}, 8: {'white': 1, 'blue':1, 'red': 1, 'orange': 1}, 9: {'white': 1, 'blue':0, 'red': 0, 'orange': 1}, 10: {'white': 1, 'blue':0, 'red': 1, 'orange': 1}, 11: {'white': 0, 'blue':0, 'red': 1, 'orange': 1}, 12: {'white': 0, 'blue':0, 'red': 0, 'orange': 0}}

The above model does not contain handling for robber The code for simulating this model is bit more complicated


Resource gain


Robber Effect


Balance of set-up1 2 3 4

White 2.0553 2.6120 3.1700 3.7267

Blue 2.0761 2.6593 3.2396 3.8224

Red 2.0808 2.6661 3.2496 3.8348

Orange 2.0892 2.6745 3.2605 3.8454

• Resource gain for each color is very similar• White might have small disadvantage


What can one learn?

Easy to run what if scenarios Robber -> discard all Discard if more than four resources

Estimating the costs for building

Balance of the the initial set-up


Monopoly

Board & Movement


Chance to end Up In a square1/40 = 2,50%?

3 doublesin a row

1/16 Card takesto Jail

A player can increaseprobability to land to These squares(out with doubles)


Chance to Land at a Square


Break Even Times


What we learnedStaying in prison strategy alters changes to

land other squares Long prison stay good at the end game

Break even time downward trend is good

Breakeven times are long Slow start Note that one cannot build before owning all

squares with that color


Thank You!

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Design

Simulations: Evaluating game system behavior