Simulations
Evaluating game system behavior

Petri Lankoski

Södertörn Univeristy
Simulations
 Game systems with random component are
complex
 Simulations can help to understand how a part of
the system...
Simulating a game system
 Model
 sum of two six sided dice -> sum of two random
numbers between 1 to 6
 Weapon: change ...
Settlers of Catan
Simulation
 How the players gain resources
 Simplified
 Robber vs no robber discard
 Only resource amount simulated, n...
Simulation set-up
• 4 victory point set-up
• Settlements -> cities
• 6 victory point sim
• 1&2) 8 victory point sim

Petri...
Model
#!/usr/bin/python
import random
from collections import Counter
# board model (2 victory points)
field1 = {
2: {'whi...
Resource gain

Petri Lankoski

Södertörn Univeristy
Robber Effect

Petri Lankoski

Södertörn Univeristy
Balance of set-up
1

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....
What can one learn?
 Easy to run what if scenarios
 Robber -> discard all
 Discard if more than four resources

 Estim...
Monopoly

Petri Lankoski

Södertörn Univeristy
Board & Movement
A player can
increase
probability to
land to
These squares
(out with doubles)

Chance to end
Up In a squa...
Chance to Land at a
Square

Petri Lankoski

Södertörn Univeristy
Break Even Times

Petri Lankoski

Södertörn Univeristy
What we learned
 Staying in prison strategy alters changes to land
other squares
 Long prison stay good at the end game
...
Thank You!

 http://petrilankoski.wordpress.com

Petri Lankoski

Södertörn Univeristy
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Simulations: Evaluating game system behavior

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Global Game Jam Stockholm Presentation some additional slides & bullets (that I removed to fit the presentation in 20 minutes)

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Simulations: Evaluating game system behavior

  1. 1. Simulations Evaluating game system behavior Petri Lankoski Södertörn Univeristy
  2. 2. Simulations  Game 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 Petri Lankoski Södertörn Univeristy
  3. 3. Simulating a game system  Model  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. Petri Lankoski Södertörn Univeristy
  4. 4. Settlers of Catan
  5. 5. 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 Petri Lankoski Södertörn Univeristy
  6. 6. Simulation set-up • 4 victory point set-up • Settlements -> cities • 6 victory point sim • 1&2) 8 victory point sim Petri Lankoski Södertörn Univeristy
  7. 7. Model #!/usr/bin/python import random from 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 Petri Lankoski Södertörn Univeristy
  8. 8. Resource gain Petri Lankoski Södertörn Univeristy
  9. 9. Robber Effect Petri Lankoski Södertörn Univeristy
  10. 10. Balance of set-up 1 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 Petri Lankoski Södertörn Univeristy
  11. 11. 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 Petri Lankoski Södertörn Univeristy
  12. 12. Monopoly Petri Lankoski Södertörn Univeristy
  13. 13. Board & Movement A player can increase probability to land to These squares (out with doubles) Chance to end Up In a square 1/40 = 2,50%? 1/16 Card takes to Jail 3 doubles in a row
  14. 14. Chance to Land at a Square Petri Lankoski Södertörn Univeristy
  15. 15. Break Even Times Petri Lankoski Södertörn Univeristy
  16. 16. What we learned  Staying 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 Petri Lankoski Södertörn Univeristy
  17. 17. Thank You!  http://petrilankoski.wordpress.com Petri Lankoski Södertörn Univeristy

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