-:Fat Chance:-Risk and Reward
Paul Taylor 2010
What is chance?
Why do we need chance?
• We balance risk / rewards in everyday life– What is the danger of a building collapsing?– A train being delayed?– Showing up to class vs Failing the Exam?
Roll of the Die...
• What are the odds?
http://www.edcollins.com/backgammon/diceprob.htm
http://www.extrabit.com/dice/d6-06.jpg
What are the odds?
http://www.extrabit.com/dice/d12-12.jpg
What do you do if you don’t have a 12 face die?
• Roll 2x 6 face die?• Roll 1x 6 face die and double the answer?• Roll 1x 6 face die and flip 1x coin?
http://www.serenapowers.com/img/dice.jpg
Rolling 2x 6 face diehttp://www.edcollins.com/backgammon/diceposs.gif
http://www.upscale.utoronto.ca/cgi-bin/ErrorAnalysis/HistogramExample.cgi
• 1x Die = 1-6• 1x Coin = H / T = +0 / +6
C# / XNA Randomness
Random randNumber;randNumber = new Random();int diceRoll = randNumber.Next(1, 7);
int dice12face = randNumber.Next(1, 7) + randNumber.Next(1, 7);
Complex Chance
• Suppose we have 184 different enemies for the player to face
• We want to be able to estimate the difficulty of the game without knowing the exact enemies chosen
A hierarchy of chance
• We have 184 different enemies– All must be easy, difficult, or normal– (We categorise the enemies)
• Now we can set probabilities for each category
Now what is the probability:
• That your game is fun?• That your game is too difficult?• That your game is too easy?
• Now to add some balance....
Adding some Balance
• We can’t just throw risk around without considering how it affects the balance of the game
http://blog.wineenthusiast.com/wp-content/uploads/2008/12/balance.jpg
Balancing Asymmetrical games
• Commonly achieved via Resource and Power balance– Vampire Guinea Pig Apocalypse
– Three main character classes:• Normal Guinea Pig• Vampire Guinea Pig• Exorcist Guinea Pig
Powers of Pigs
Exorcist Vampire GP Guinea PigDefence High Medium LowAttack Low High MediumAvoid Medium Low High
Checking the balance of powerExorcist Vampire GP Guinea Pig
Defence High Medium LowAttack Low High MediumAvoid Medium Low High
Exorcist Vampire GP Guinea PigDefence High (3) Medium (2) Low (1)Attack Low (1) High (3) Medium (2)Avoid Medium (2) Low (1) High (3)Total Power 6 6 6
Rock Paper Scissors
This is the circle of life version of fairnessUsed extensively by games such as Pokémon • There is no most powerful piece• For every power there is a weakness
Paper Scissors Rock has no probabilityPlayer: Paper Scissors Rock
Vs Paper Draw Win Lose
Vs Scissors Lose Draw Win
Vs Rock Win Lose Draw
When is probability a good choice?
• For small frequent challenges– Item Dropping– ??– ??
• When the player can estimate the risk
When is probability a bad choice?
• When the risk is high• When the player has no control over the
amount of risk• Irreversible actions
References
• Fundamentals of Game Design