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

• The probability that the ith units is losing hit points (∆HPi = minus) is higher for
foes (Ai = false) with vulnerable classes (Ci = healer) that are more susceptible to be
targeted (T = i), and also for allies (Ai = true) whose role is to take most of the damages
(Ci = tank). As for Ai, the probability of IDi is driven by our
• Obviously, the usage of skills depends on their efficiency on the target (R, resistances),
and on their class. As a result, we have P(Ri|Ci, S, T ) as the conditional distribution on
“resists”. The probability of the resist to “nature based effects” (Ri = nature) for skills
involving “nature” damage (s ∈ {nature_damage}) will be very low as it will be useless
to use spells that the receiver is protected against.
• The probability that the ith character will die soon (IDi) will be high if i is targeted
(T = i) with a big heal or big instant damage (S = big_heal or S = big_damage,
depending on whether i is an ally or not).
Parameters
• P(T t−1 ) is unknown and unspecified (uniform). In the question, we always know what was
the previous target, except when there was not one (at the beginning).
• P(T |T t−1 ) is a probability corresponding to the propensity to switch targets. It can be
learned, or uniform if there is no previous target (it the prior on the targets then).
• P(S) is unknown and so unspecified, it could be a prior on the preferred skills (for style
of for efficiency).
• P(HPi|Ai, Ci, S, T ) is a 2×4×m×2 probability table, indexed on if the ith character is an
ally or not, on its class, on the skills (#S = m) and on where it is the target or not. It can
be learned (and/or parametrized), for instance P(HPi = x|ai, ci, s, t) = 1+count(x,ai,ci,s,t)
10+count(ai,ci,s,t) .
• P(Di|Ai, S, T ) is a 4 × 2 × m × 2 (possibly learned) probability table.
• P(Ai|S, T ) is a 2 × m × 2 (possibly learned) probability table.
• P(∆HPi|Ai, S, T ) is a 3 × 2 × m × 2 (possibly learned) probability table.
• P(Ri|Ci, S, T ) is a 8 × 4 × m × 2 (possibly learned) probability table.
• P(Ci|Ai, S, T ) is a 4 × 2 × m × 2 (possibly learned) probability table.
Identification
In the following Results part however, we did not apply learning but instead manually specified
the probability tables to show the effects of gamers’ common sense rules and how it/they can
be correctly encoded in this model.
About learning: if there were only perceived variables, learning the right conditional probability
tables would just be counting and averaging. However, some variables encode combinations
of perceptions and passed states. We could learn such parameters through the EM algorithm
but we propose something simpler for the moment as our “not directly observed variables” are
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