Payoff Table: Outcome of the Casino Game: Decision Alternative: Pair | Suited | Other Full Bet: $750 | $400 | -$100 Partial Bet: $350 | $200 | -$50 No Bet: $0 | $0 | $0 Probabilities of States: P(Pair) | P(Suited) | P(Other) Problem: You have been provided a payoff table associated with a new, fictional casino game. You have three choices in this game: you can do a ‘Full Bet’, you can do a ‘Partial Bet,’ or you can do a ‘No Bet.’ In other words, the set of decision alternatives is {Full Bet, Partial Bet, No Bet}. In this game, the dealer will flip over one card from a deck of cards and then roll a 6-sided die. There are 52 cards in a deck. There are 13 different values of cards (which are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King), each of which appear once in each of the four suits of cards (Clubs, Diamonds, Hearts, Spades). There are two distinct ways, with distinct payoffs, to win: 1. the ‘Pair’ win: the flipped over card ‘matches’ the outcome of the die (assuming Ace = 1). In other words, the following outcomes win for Pair: (Card = Any Ace, Roll = 1), (Card = Any 2, Roll = 2), (Card = Any 3, Roll = 3), (Card = Any 4, Roll = 4), (Card = Any 5, Roll = 5), (Card = Any 6, Roll = 6); 2. the ‘Suited’ win: the flipped over card is a 7, 8, 9, 10, Jack, Queen, King and then the die outcome is the same ‘suit’ as the flipped over come where we map a roll of 1 to Clubs, a roll of 2 to Diamonds, a roll of 3 to Hearts, and a roll of 4 to Spades. In other words, the following outcomes win for Suited: (Card = Any Club that is either a 7, 8, 9, 10, Jack, Queen, or King, Roll = 1), (Card = Any Diamond that is either a 7, 8, 9, 10, Jack, Queen, or King, Roll = 2), (Card = Any Heart that is either a 7, 8, 9, 10, Jack, Queen, or King, Roll = 3), and (Card = Any Spade that is either a 7, 8, 9, 10, Jack, Queen, or King, Roll = 4). The potential outcomes of the game, therefore, are {Pair, Suited, Other}. The payoff table, without probabilities in it, is provided to you. You will be asked to solve the following parts of this problem: (a) Determine the probability of the Pair win, i.e., P(Pair), the probability of the Suited win, i.e., P(Suited), and the probability of the other outcome (i.e., the outcome of the game is not a Pair win or a Suited win), i.e., P(Other). Please show and explain any calculations you used to determine these probabilities. Just list any logical probabilities for (a) and move onto (b) through (e). (b) Determine the selected decision according to the maximin payoff criteria. (c) Determine the selected decision according to the maximum likelihood criteria. (d) Determine the selected decision according to Bayes Decision Rule. (e) Determine the expected value of perfect information for this decision-making environment.
Please answer the whole practice problem with all parts done correctly and quickly
Payoff Table:
Outcome of the Casino Game:
Decision Alternative: Pair | Suited | Other
Full Bet: $750 | $400 | -$100
Partial Bet: $350 | $200 | -$50
No Bet: $0 | $0 | $0
Probabilities of States: P(Pair) | P(Suited) | P(Other)
Problem: You have been provided a payoff table associated with a new, fictional casino game. You have
three choices in this game: you can do a ‘Full Bet’, you can do a ‘Partial Bet,’ or you can do a ‘No Bet.’ In
other words, the set of decision alternatives is {Full Bet, Partial Bet, No Bet}.
In this game, the dealer will flip over one card from a deck of cards and then roll a 6-sided die. There
are 52 cards in a deck. There are 13 different values of cards (which are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10,
Jack, Queen, King), each of which appear once in each of the four suits of cards (Clubs, Diamonds, Hearts,
Spades). There are two distinct ways, with distinct payoffs, to win:
1. the ‘Pair’ win: the flipped over card ‘matches’ the outcome of the die (assuming Ace = 1). In other
words, the following outcomes win for Pair: (Card = Any Ace, Roll = 1), (Card = Any 2, Roll = 2),
(Card = Any 3, Roll = 3), (Card = Any 4, Roll = 4), (Card = Any 5, Roll = 5), (Card = Any 6, Roll
= 6);
2. the ‘Suited’ win: the flipped over card is a 7, 8, 9, 10, Jack, Queen, King and then the die outcome is
the same ‘suit’ as the flipped over come where we map a roll of 1 to Clubs, a roll of 2 to Diamonds, a
roll of 3 to Hearts, and a roll of 4 to Spades. In other words, the following outcomes win for Suited:
(Card = Any Club that is either a 7, 8, 9, 10, Jack, Queen, or King, Roll = 1), (Card = Any Diamond
that is either a 7, 8, 9, 10, Jack, Queen, or King, Roll = 2), (Card = Any Heart that is either a 7, 8, 9,
10, Jack, Queen, or King, Roll = 3), and (Card = Any Spade that is either a 7, 8, 9, 10, Jack, Queen,
or King, Roll = 4).
The potential outcomes of the game, therefore, are {Pair, Suited, Other}. The payoff table, without probabilities in it, is provided to you. You will be asked to solve the following parts of this problem:
(a) Determine the
i.e., P(Suited), and the probability of the other outcome (i.e., the outcome of the game is not a Pair win
or a Suited win), i.e., P(Other). Please show and explain any calculations you used to determine these
probabilities.
Just list any logical probabilities for (a) and move onto (b) through (e).
(b) Determine the selected decision according to the maximin payoff criteria.
(c) Determine the selected decision according to the maximum likelihood criteria.
(d) Determine the selected decision according to Bayes Decision Rule.
(e) Determine the
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