Bayesian Programming and Learning for Multi-Player Video Games ...

• Class: C i∈�1...n ∈ {T ank, Contact, Ranged, Healer} is the class of the ith player. Class
(C) is simplified over 4 values: a Tank can take a lot of damages and taunt enemies,
a Contact class which can deal huge amounts of damage with contact weapons (rogue,
barbarian...), Ranged stands for the class that deals damages from far away (hunters,
mages...) and Healers are classes that can heal in considerable amounts.
• Resists: R i∈�1...n� ∈ {Nothing, F ire, Ice, Nature, F ireIce, IceNat, F ireNat, All} informs
about the resistances of the ith player. The resist variable is the combination of binary
variables of resistance to certain types of (magical) damages into one variable. With 3
possible resistances we get (2 3 ) 8 possible values. For instance “Ri = F ireNat” means
that the ith character resists fire and nature-based damages. Armor (physical damages)
could have been included, and the variables could have been separated.
• Skill: S ∈ {Skill1 . . . Skillm}. The skill variable takes all the possible skills for the given
character, and not only the available ones to cast at the moment to be able to have reusable
probability tables (i.e. it is invariant of the dynamics of the game).
Decomposition
The joint distribution of the model is:
P(S).P(T t |T t−1 ).P(T t−1 ).
P(S, T t−1,t , HP1:n, D1:n, A1:n, ∆HP1:n, ID1:n, C1:n, R1:n) = (3.5)
n� �
P(HPi|Ai, Ci, S, T ).P(Di|Ai, S, T ).P(Ai|S, T ) (3.6)
i=1
P(∆HPi|Ai, S, T ).P(Ri|Ci, S, T ).P(Ci|Ai, S, T )P(IDi|T ) �
We want to compute the probability distribution on the variable target (T ) and skill (S), so
we have to consider the joint distribution with all variables on which target (T ) or skill (S) are
conditionally dependent: the previous value of target (T t−1 ), and all the perceptions variables
on each character.
(3.7)
• The probability of a given target depends on the previous one (it encodes the previous
decision and so all previous states).
• The health (or hit) points (HPi) depends on the facts that the ith character is an ally (Ai),
on his class (Ci), and if he is a target (T ). Such a conditional probability table should be
learned, but we can already foresee that a targeted ally with a tanking class (C = tank)
would have a high probability of having low hit points (HP ) because taking it for target
means that we intend to heal him.
• The distance of the unit i (Di) is more probably far if unit i is an enemy (Ai = false) and
we target it (T = i) as our kind of druid attacks with ranged spells and does not fare well
in the middle of the battlefield.
• The probability of the ith character being an ally depends on if we target allies of foes
more often: that is P(Ai|S, T ) encodes our propensity to target allies (with heals and
enhancements) or foes (with damaging or crippling abilities).
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