Ігор Антонов “Короткий курс теорії ймовірності для ігрових дизайнерів.” http://gamedev.lviv.ua https://www.facebook.com/startuplviv https://twitter.com/gdlviv

1. CHANCE
GameDev Conference | 2015

2. Why Chance?
Chance is surprise…
…Surprise is FUN !

3. Why Chance?
Chance
Objects
Rules
SkillsSpace
Actions
Chance “concerns interactions between all of the other five mechanics”

4. A story…
First Game: In four rolls of a single dice, the Chevalier wins if at least one six
comes up.
Success!
1
6
1
6
1
6
1
6
4
6
+ + + =
66% of

5. 24 ×
1
6 × 6
=
24
36
24 ×
1
6 × 6
=
24
36
A story…
SecondGame: In twenty-four rolls of a pair of dice, the Chevalier wins if at
least one twelve comes up.
Success!66% of

6. Probability is…
#1. Probability is measure of chance that something will happen.
=
number of “Looked For” outcomes
number of “Possible” outcomes

7. A story…
First Game:
1
6
1
6
1
6
1
6
Second Game:
1
6 × 6
Looked for: 6
Possible: 1, 2, 3, 4, 5, 6
Looked for: 6 + 6
Possible: 1+1, 1+2, 1+3, 1+4,
1+5, 1+6, 2+1, 2+2,…
…36 results

8. Probability is…
#2. Probability is fractions=decimals=percents
#3. Probability is from Zero to One

9. 24 ×
1
6 × 6
=
24
36
1
6
1
6
1
6
1
6
4
6
+ + + =
A story…
First Game: Second Game:
Looked for: 6
Possible: 1, 2, 3, 4, 5, 6
Looked for: 6 + 6
Possible: 1+1, 1+2, 1+3, 1+4,
1+5, 1+6, 2+1, 2+2,…
…36 results
7
6
= 117% ?

10. Enumerate!

11. 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.

12. A story…
First Game:
OR OR
×

13. 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

14. 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%

15. 100% – “Does” = “Doesn’t”
1 − 𝑃 𝐴 = 𝑃 𝐵
P(B)P(A)

16. A story…
SecondGame:
35
36
×
35
36
× ⋯ ×
35
36
= 𝟓𝟏%
× 24 times
1 − 𝟓𝟏% = 𝟒𝟗%

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

18. ZZZzzzz…

19. 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…”

20. 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

21. $ 100
$ 300
$ 1000
$ 5000
63%
25%
8%
4%
ExpectedValue
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

22. ExpectedValue 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

23. 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.

24. How it works?
Example: Birthday Party
Option 1
Option 2
…
… …
JOB ?

25. 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

26. THANK YOU!