Minimax

**Minimax ([[Ián-sǹg-hoat|ián-sǹg-huat]])**, ia̍h **ki̍k-sió ki̍k-tāi ti̍t** (), ū-tang-sî-á mā siá-tsò **Minmax**, **MM** hi̍k-tsiá **an-tiám** (鞍點; saddle point)), sī jîn-kang tì-huī, kuat-tshik lí-lūn, tsoo-ha̍p phok-ī lí-lūn, thóng-kè ha̍k í-ki̍p thiat-ha̍k tang-tiong sú-iōng ê kuat-tshik kui-tsik; iōng teh siōng-hāi ê tsōng-hóng (khó-lîng ū siōng-tuā ê sún-si) tsi-hā siōng-sió huà ê khó-lîng sún-sit. Tng-teh tshú-lí siu-ik ê sî-tsūn, Minimax mā hőng kiò-tsò "maximin" (tsuè-tuā ki̍k-sió ti̍t), ì-sù tio̍h-sī tsuè-tuā huà tsuè-sió siu-ik. Minimax thâu-á sī-tio̍h to-hong ī-tsiá lîng-hô (多方奕者零和; several-player zero-sum) hâm phok-ī lí-lūn (game theory) jî-lâi thê-tshut, hâm-kài ī-tsiá (player) tshái-tshú lûn-liû hîng-tōng kah tông-sî hîng-tōng nn̄g-tsióng tsōng-hóng. Āu--lâi mâ-hőng khok-tián kàu koh-khah ho̍k-tsa̍p ê phok-ī í-ki̍p tsûn-tsāi bô khak-tīng sìng ê it-puann kuat-tshik būn-tê.

## Tsoo-ha̍p sài-kio̍k lí-lūn
### Hi-gí-bé
Ē-bīn sī tshim-tōo siū-hān ê minimax ián-sǹg-huat tsi guī-tài-bé (hi-gí tîng-sik bé; pseudocode):

 **function** minimax(node, depth, maximizingPlayer) **is**
     **if** depth = 0 **or** node is a terminal node **then**
         **return** the heuristic value of node
     **if** maximizingPlayer **then**
         value := −∞
         **for each** child of node **do**
             value := max(value, minimax(child, depth − 1, FALSE))
         **return** value
     **else** *(* minimizing player *)*
         value := +∞
         **for each** child of node **do**
             value := min(value, minimax(child, depth − 1, TRUE))
         **return** value

 *(* Initial call *)*
 minimax(origin, depth, TRUE)

Minimax hâm-sòo uî hio̍h tsiat-tiám (tsiong-tuan tsiat-tiám hâm siōng-tuā tshiau-tshuē tshim-tōo tshù ê tsiat-tiám ) thuân-huê tsi̍t-ê "khé-huat sik ê ti̍t" (heuristic value). Hui hio̍h tsiat-tiám ê ti̍t kè-sîng uì i-ê āu-tāi ê hio̍h tsiat-tiám. Tsit-ê "khé-huat sik ê ti̍t" (heuristic value) sī tsi̍t-ê hun-sòo, iōng-teh hîng-liông tsiat-tiám tuì siōng-tuā huà ê sńg-ī-tsiá ê iú-lī tîng-tōo. In-tshú, tuì siōng-tuā huà sńg-ī-tsiá iú-lī (pí-jû tit-tio̍h sìng-lī) ê tsiat-tiám tit-hun kuân-kuè tuì siōng-tsió huà sńg-ī tsiá iú-lī ê tsiat-tiám. Tsiong-tuan (sńg-ī kiat-sok) hio̍h tsiat-tiám ê khé-huat sik ti̍t (heuristic value) tuì-ìng siōng-tuā huà sńg-ī tsiá ê iânn, su hi̍k-tsiá pênn-tshiú. Tuì-tio̍h tsuè-tuā tshiau-tshuē tshim-tōo sóo-tsāi ê hui tsiong-tuan hio̍h tsiat-tiám, phîng-kóo hâm-sòo ē kóo-kè tsit-ê tsiat-tiám ê "khé-huat sik ti̍t" (heuristic value). Tsit-ê phîng-kóo ti̍t ê phín-tsit hâm tshiau-tshuē tshim-tōo kuat-tīng tsuè-tsiong minimax kiat-kó ê phín-tsit hâm tsún-khak sìng.

Minimax ián-sǹg-huat teh i-ê tîng-sū bé lāi-té kā nn̄g-ê ī-tsiá (tsuè-tuā huà ī-tsiá hâm tsue-sió huà ī-tsiá) hun-khui tshú-lí. Khiā-tī tsit-ê kuan-tshat \ \max(a,b) = -\min(-a,-b), minimax ián-sǹg-huat sòo-siông ē-tàng kán-huà tsò negamax ián-sǹg-huat.

## Tsù-kái

## Tsham-ua̍t
 
* Alpha–beta pruning
* Expectiminimax
* Maxn algorithm
* [Computer chess
* Horizon effect
* Lesser of two evils principle
* Minimax Condorcet
* Regret (decision theory)
* Monte Carlo tree search
* Negamax
* Negascout
* Sion's minimax theorem
* Tit for Tat
* Transposition table
* [Wald's maximin model
* Gamma-minimax inference
* Reversi Champion
*Artificial intelligence in video games

## Guā-pōo liân-kiat

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*  — A visualization applet
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