Black Jack Hybrid Decision Network
An object of class HydeNetwork establishing a graphical model for a game
of Black Jack.
BlackJack
A HydeNetwork object constructed using the code shown in
the example. The network has seven random nodes, three ten deterministic
nodes, three decision nodes, and one utility node. This is (almost) the same
network used in 'vignette("DecisionNetworks", package="HydeNet")'.
## Not run:
BlackJack <-
HydeNetwork(~ initialAces | card1*card2
+ initialPoints | card1*card2
+ highUpcard | dealerUpcard
+ hit1 | initialPoints*highUpcard
+ acesAfterCard3 | initialAces*card3
+ pointsAfterCard3 | card1*card2*card3*acesAfterCard3
+ hit2 | pointsAfterCard3*highUpcard
+ acesAfterCard4 | acesAfterCard3*card4
+ pointsAfterCard4 | card1*card2*card3*card4*acesAfterCard4
+ hit3 | pointsAfterCard4*highUpcard
+ acesAfterCard5 | acesAfterCard4*card5
+ pointsAfterCard5 | card1*card2*card3*card4*card5*acesAfterCard5
+ playerFinalPoints | initialPoints*hit1*pointsAfterCard3
*hit2*pointsAfterCard4*hit3*pointsAfterCard5
+ dealerFinalPoints | dealerUpcard
+ payoff | playerFinalPoints*dealerFinalPoints)
cardProbs <- c(rep(1/13,8), 4/13, 1/13) # probs. for 2, 3, ..., 9, (10-K), A
BlackJack <- setNode(BlackJack, card1, nodeType="dcat",
pi=vectorProbs(p=cardProbs, card1))
BlackJack <- setNode(BlackJack, card2, nodeType="dcat",
pi=vectorProbs(p=cardProbs, card2))
BlackJack <- setNode(BlackJack, card3, nodeType="dcat",
pi=vectorProbs(p=cardProbs, card3))
BlackJack <- setNode(BlackJack, card4, nodeType="dcat",
pi=vectorProbs(p=cardProbs, card4))
BlackJack <- setNode(BlackJack, card5, nodeType="dcat",
pi=vectorProbs(p=cardProbs, card5))
BlackJack <- setNode(BlackJack, dealerUpcard, nodeType="dcat",
pi=vectorProbs(p=cardProbs, dealerUpcard))
#Note: node dealerFinalPoints will be defined below, following some discussion
# about its conditional probability distribution.
#####################################
# Deterministic Nodes
#####################################
BlackJack <- setNode(BlackJack, highUpcard,
"determ", define=fromFormula(),
nodeFormula = highUpcard ~ ifelse(dealerUpcard > 8, 1, 0))
BlackJack <- setNode(BlackJack, initialAces,
"determ", define=fromFormula(),
nodeFormula = initialAces ~ ifelse(card1==10,1,0) +
ifelse(card2==10,1,0))
BlackJack <- setNode(BlackJack, acesAfterCard3,
"determ", define=fromFormula(),
nodeFormula = acesAfterCard3 ~ initialAces + ifelse(card3==10,1,0))
BlackJack <- setNode(BlackJack, acesAfterCard4,
"determ", define=fromFormula(),
nodeFormula = acesAfterCard4 ~ acesAfterCard3 + ifelse(card4==10,1,0))
BlackJack <- setNode(BlackJack, acesAfterCard5,
"determ", define=fromFormula(),
nodeFormula = acesAfterCard5 ~ acesAfterCard4 + ifelse(card5==10,1,0))
BlackJack <- setNode(BlackJack, initialPoints,
"determ", define=fromFormula(),
nodeFormula = initialPoints ~ card1+card2+2)
BlackJack <- setNode(BlackJack, pointsAfterCard3, "determ", define=fromFormula(),
nodeFormula = pointsAfterCard3 ~
ifelse(acesAfterCard3 == 3,
13,
ifelse(acesAfterCard3 == 2,
card1 + card2 + card3 + 3 - 10,
ifelse(acesAfterCard3 == 1,
ifelse(card1 + card2 + card3 + 3 > 22,
card1 + card2 + card3 + 3 - 10,
card1 + card2 + card3 + 3),
card1 + card2 + card3 + 3
)
)
)
)
BlackJack <- setNode(BlackJack, pointsAfterCard4, "determ", define=fromFormula(),
nodeFormula = pointsAfterCard4 ~
ifelse(acesAfterCard4 == 4,
14,
ifelse(acesAfterCard4 == 3,
ifelse(card1 + card2 + card3 + card4 + 4 > 38,
card1 + card2 + card3 + card4 + 4 - 30,
card1 + card2 + card3 + card4 + 4 - 20
),
ifelse(acesAfterCard4 > 0,
ifelse(card1 + card2 + card3 + card4 + 4 > 22,
card1 + card2 + card3 + card4 + 4 - 10,
card1 + card2 + card3 + card4 + 4
),
card1 + card2 + card3 + card4 + 4
)
)
)
)
BlackJack <-
setNode(BlackJack, pointsAfterCard5, "determ", define=fromFormula(),
nodeFormula = pointsAfterCard5 ~
ifelse(acesAfterCard5 == 5,
15,
ifelse(acesAfterCard5 == 4,
ifelse(card1 + card2 + card3 + card4 + card5 + 5 > 51,
card1 + card2 + card3 + card4 + card5 + 5 - 40,
card1 + card2 + card3 + card4 + card5 + 5 - 30
),
ifelse(acesAfterCard5 == 3,
ifelse(card1 + card2 + card3 + card4 + card5 + 5 > 51,
card1 + card2 + card3 + card4 + card5 + 5 - 30,
card1 + card2 + card3 + card4 + card5 + 5 - 20
),
ifelse(acesAfterCard5 == 2,
ifelse(card1 + card2 + card3 + card4 + card5 + 5 > 31,
card1 + card2 + card3 + card4 + card5 + 5 - 20,
card1 + card2 + card3 + card4 + card5 + 5 - 10
),
ifelse(acesAfterCard5 > 0,
ifelse(card1 + card2 + card3 + card4 + card5 + 5 > 22,
card1 + card2 + card3 + card4 + card5 + 5 - 10,
card1 + card2 + card3 + card4 + card5 + 5
),
card1 + card2 + card3 + card4 + card5 + 5
)
)
)
)
)
)
BlackJack <- setNode(BlackJack, playerFinalPoints, "determ", define=fromFormula(),
nodeFormula = playerFinalPoints ~
ifelse(hit1 == 0,
initialPoints,
ifelse(hit2 == 0,
pointsAfterCard3,
ifelse(hit3 == 0, pointsAfterCard4, pointsAfterCard5)
)
)
)
BlackJack <- setDecisionNodes(BlackJack, hit1, hit2, hit3)
BlackJack <- setUtilityNodes(BlackJack, payoff)
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