Question $6\_\_\_(4)$

Create a $\_\_\_$function$\_\_\_$ called $`$payout$`$ with three $\_\_\_$arguments$\_\_\_$: $`$player$\_$score$`,`$dealer$\_$score$`$ and $`$bet$`.$ Assign a default $\_\_\_$value$\_\_\_$ of $`1`$ to the $\_\_\_$argument$\_\_\_`$bet$`.$ The goal of the $\_\_\_$function$\_\_\_`$payout$`$ is to $\_\_\_$return$\_\_\_$ the amount that the player should receive $($positive number$)$ or pay$-$in $($negative number$)$ based on the values passed to the $`$player$\_$score$`,`$dealer$\_$score$`$ and $`$bet$`\_\_\_$arguments$\_\_\_.$ The final amount should be returned as a single $\_\_\_$numeric$\_\_\_$ value. For example, if the player wins without blackjack the function should return $1\backslash *$bet; implying that the player wins $1\backslash *$bet in this round.

Game Actions

We now have a way to define a deck of cards, draw a card, determine the score of a hand and determine the final payout. Next, we focus on implementing the actions in a game of blackjack.

In blackjack, the player performs his$/$her actions first. Once the player has performed their actions, it is the dealers turn to perform actions. After the dealer has performed his$/$her actions, the game is concluded and the payout is determined.

The action that a player should take is based on their cards and the first card dealt to the dealer where the first card dealt to the dealer is visible to the player.

## Player actions

Depending on the rules used in blackjack, a player can have multiple actions available. We will simplify the problem by only considering the actions hit and stand.

$1.$ When a player requests a $$hit$,$ one card is drawn from the deck and added to the hand of the player

$2.$ When a player chooses to $$stand$,$ the turn of the player ends.

$\_\_\_$Question $7\_\_\_(2)$

Define a $\_\_\_$function$\_\_\_$ called $`$hit$`.$ The $\_\_\_$function$\_\_\_`$hit$`$ has only one $\_\_\_$argument$\_\_\_,`$hand$`.$ When the $\_\_\_$function$\_\_\_`$hit$`$ is $\_\_\_$called$\_\_\_$ the $\_\_\_$function$\_\_\_$ should add a card to the vector passed to the $`$hand$`\_\_\_$argument$\_\_\_$ using the $\_\_\_$function$\_\_\_`$draw$\_$a$\_$card$`$ defined in $\_\_\_$question $3\_\_\_.$ The $\_\_\_$function$\_\_\_`$hit$`$ should $\_\_\_$return$\_\_\_$ the original vector passed to the $\_\_\_$argument$\_\_\_`$hand$`$ with a new card added to the last position of the vector.

Dealer actions

Once the player chooses to $`$stand$`$ or $`$bust$`$ as a result of $`$hitting$`,$ it is the dealers turn to play. According to the rules of blackjack, the dealer $\_\_$must$\_\_$ perform the action $`$hit$`$ when the hand value of the dealer is less than $17.$

$\_\_\_$For our game, the dealer performs the action $`$hit$`$ when the hand value of the dealer is less than $18.\_\_\_$

$\_\_\_$Question $8\_\_\_(4)$

Create a $\_\_\_$function$\_\_\_$ called $`$dealer$\_$strategy$`.$ The $\_\_\_$function$\_\_\_`$dealer$\_$strategy$`$ has only one $\_\_\_$argument$\_\_\_,`$hand$`.$ The $\_\_\_$function$\_\_\_`$dealer$\_$strategy$`$ should $\_\_\_$call$\_\_\_$ the $\_\_\_$function$\_\_\_`$hit$`$ defined in $\_\_\_$question $7\_\_\_$ until the dealer score is more than $18$ or the dealer $`$bust$`.$ Note based on the value passed to the $`$hand$`\_\_\_$argument$\_\_\_,$ the $\_\_\_$function$\_\_\_`$hit$`$ might be not be called, called once or called more than once.

Game agent

Now that we have implemented the game mechanics we can start by implementing an artificial agent $$ the player. To implement the artificial agent, we will make use of a lookup table to determine when the agent should perform the action $`$hit$`$ or when the agent should perform the action $`$stand$`.$

We can implement a lookup table in R using a $\_\_\_$data frame$\_\_\_.$ The $\_\_\_$data frame$\_\_\_$ will be used to determine if the player should perform the action $`$hit$`$ or $`$stand$`$ based on:

$1.\_$hand$\_$value$\_$: The sum of the cards in the player hand i$.$e$.$ column hand$\_$value

$2.\_$useable$\_$ace$\_$: Whether the hand of the player contains a useable ace, an ace than can count as $11$ without the player going $`$bust$`($column: usable$\_$ace$)$

$3.\_$dealer$\_$ace$\_$ to $\_$dealer$\_$ten$\_$: the face$-$up card of the dealer

Two lookup tables have been created, $`$df$\_$action$\_$lookup$`$ and $`$df$\_$action$\_$lookup$\_$alt$`.$

$`$df$\_$action$\_$lookup$`$ is the player's default strategy, while $`$df$\_$action$\_$lookup$\_$alt$`$ serves as the alternative strategy

$\_\_\_$Question $9\_\_\_(6)$

Create two functions that the player may use to implement their strategy.

Create a $\_\_\_$function$\_\_\_$ called $`$lookup$\_$action$`$ with two $\_\_\_$arguments$\_\_\_`$hand$`$ and $`$dealer$\_$card$`.$ The $\_\_\_$function$\_\_\_`$lookup$\_$action$`$ should $\_\_\_$return$\_\_\_$ whether the player should "Hit" or "Stand" using the $\_\_\_$data frame$\_\_\_`$df$\_$action$\_$lookup$`.$

Create another $\_\_\_$function$\_\_\_$ called $`$lookup$\_$action$\_$alt$`$ with the same arguments as $`$lookup$\_$action$`.$ The $\_\_\_$function$\_\_\_`$lookup$\_$action$\_$alt$`$ should $\_\_\_$return$\_\_\_$ whether the player should "Hit" or "Stand" using the $\_\_\_$data frame$\_\_\_`$df$\_$action$\_$lookup$\_$alt$`$