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

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Figure 2.1: A Tic-tac-toe board position, in which it is the “circles” player’s turn to play. The
labeling explains the indexing (left to right, bottom to top, starting at 1) of the grid.
account is described in Algorithm 1. The result of applying this algorithm to the Tic-tac-toe
situation of Fig. 2.1 is exhaustively represented in Fig. 2.2. For zero-sum games (as abstract
strategy games discussed here), there is a (simpler) Minimax variant called Negamax, shown in
Algorithm 7 in Appendix A.
Algorithm 1 Minimax algorithm
function mini(depth)
if depth ≤ 0 then
return −value()
end if
min ← +∞
for all possible moves do
score ← maxi(depth − 1)
if score < min then
min ← score
end if
end for
return min
end function
function maxi(depth)
if depth ≤ 0 then
return value()
end if
max ← −∞
for all possible moves do
score ← mini(depth − 1)
if score > min then
max ← score
end if
end for
return max
end function
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