CHANCE

GameDev Conference | 2015

Why Chance?

Chance is surprise…

…Surprise is FUN !

Why Chance?

Chance

Objects

Rules

SkillsSpace

Actions

Chance “concerns interactions between all of the other five mechanics”

A story…

First Game: In four rolls of a single dice, the Chevalier wins if at least one sixcomes up.

Success!

1

6

1

6

1

6

1

6

4

6+ + + =

66% of

24 ×1

6 × 6=24

3624 ×

1

6 × 6=24

36

A story…

Second Game: In twenty-four rolls of a pair of dice, the Chevalier wins if atleast one twelve comes up.

Success!66% of

Probability is…

#1. Probability is measure of chance that something will happen.

=number of “Looked For” outcomes

number of “Possible” outcomes

A story…

First Game:

1

6

1

6

1

6

1

6

Second Game:

1

6 × 6

Looked for: 6Possible: 1, 2, 3, 4, 5, 6

Looked for: 6 + 6Possible: 1+1, 1+2, 1+3, 1+4,

1+5, 1+6, 2+1, 2+2,… …36 results

Probability is…

#2. Probability is fractions=decimals=percents

#3. Probability is from Zero to One

24 ×1

6 × 6=24

36

1

6

1

6

1

6

1

6

4

6+ + + =

A story…

First Game: Second Game:

Looked for: 6Possible: 1, 2, 3, 4, 5, 6

Looked for: 6 + 6Possible: 1+1, 1+2, 1+3, 1+4,

1+5, 1+6, 2+1, 2+2,… …36 results

7

6= 117% ?

Enumerate!

OR means “+”

P(A) P(A)P(B)OR

More choices – more chances

𝑃 𝐴 𝒐𝒓 𝐵 = 𝑃 𝐴 + 𝑃 𝐵

For mutually exclusive events only.

A story…

First Game:

OR OR ×

AND means “”

More requirements – less chances

𝑃 𝐴 𝒂𝒏𝒅 𝐵 = 𝑃 𝐴 × 𝑃 𝐵

For NOT mutually exclusive events only.

P(B)P(A) AND

A story…

First Game:

1

6+

5

6×1

6+

5

6×5

6×1

6+

5

6×5

6×5

6×1

6= 𝟓𝟐%

100% – “Does” = “Doesn’t”

1 − 𝑃 𝐴 = 𝑃 𝐵

P(B)P(A)

A story…

Second Game:

35

36×35

36× ⋯ ×

35

36= 𝟓𝟏%×

24 times

1 − 𝟓𝟏% = 𝟒𝟗%

Sum effect

The Sum of

Multiple Linear Random Selections

is NOT a Linear Random Selection!

ZZZzzzz…

Sum effect

The Sum of Multiple Linear Random Selections is NOT a Linear Random Selection!

2…12

“…in the game Dungeons and Dragons, players generate (virtual) skill attributes with values ranging from 3 to 18 by rolling three six-sided dice. As a result, you see a lot of attribute values around 10 or 11, but very few at 3 or 18…”

Roll the Dice

Theoretical probabilityPractical probability

Monte Carlo Method - a problem solving technique used to approximate the probability of certain outcomes by running multiple trial runs.

Practice: Theory:

trialsMore

$ 100

$ 300

$ 1000$ 5000

63%25%

8%

4%

Expected Value

The expected value of a transaction in a game is the probability-weighted average of all the possible values that could result.

= $5000 × 4%+ $1000 × 8%+

+$300 × 25%+ $100 × 63% =

= $418

𝐸𝑉 = 𝑋 ∙ 𝑃 𝑋

Expected Value on practice

Example:

= 100%× 4 = 𝟒

Expected damage

= 80%× 5 + 20%× 0 = 𝟒

= 20%× 𝟒𝟎 + 80%× 0 = 𝟖

Lightning bolt is the best!

Yes!

No!

if HP is high enough

if HP low

e.g. HP = 15

Expected damage = 20%× 𝟏𝟓 + 80%× 0 = 𝟑

Human Element

Example:

= 66%× $2400 + 33% × $2500 + 1% × $0 = $𝟐𝟒𝟎𝟗

Expected value

Game B

But!

People are often willing to pay a price to eliminate the potential of regret

= 100%× $2400 = $𝟐𝟒𝟎𝟎

People are often willing to take a risk.

People like sure gain and probable loss.

How it works?

Example: Birthday Party

Option 1

Option 2

…

… …

JOB ?

Need Spices – Use Chance

“…Risk and randomness are like spices. A game without any hint of them can be completely bland, but put in too much and they overwhelm everything else. But get them just right, and they bring out the flavor of everything else in your game…”

Risk SuccessSurprise etc.Random

THANK YOU!