FPIC Archive 6: P-P-P-Pokerface

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https://github.com/iloveponies/p-p-p-pokerface

Here are the instructions if you need them. Be sure to fork the repository behind the link above.

Data representation

A traditional playing card has a rank and a suit. The rank is a number from 2 to 10, J, Q, K or A and the suit is Clubs, Diamonds, Hearts or Spades.

We want a simple way to represent poker hands and cards. A card is simply going to be a string of the form "5C" where the first character represents the rank and the second character represents the suit. To keep the representation at 2 characters, we’ll use the following coding for values between 10 and 14:

RankCharacter10T11J12Q13K14A

So, for example, the Queen of Hearts is "QH" and the Ace of Spades is "AS".

Rank and suit

We’ll want a couple of helper functions to read the rank and suit of a card.

A useful thing to note is that Strings are sequencable, so you can use sequence destructuring on them:

(let [[fst snd] "5H"] [fst snd]) ;=> [\5 \H]

If you are only interested in some destructured values, it is idiomatic to use the name _ for ignored values:

(let [[_ snd] "AH"] snd) ;=> \H

And finally, remember that you can use (str value) to turn anything into its string representation, including characters.

(str \C) ;=> "C"

You should now be able to write the (suit card) function that returns the suit of a card.

Exercise 1

Write the function (suit card) which takes a singe card and returns the suit of the card as a one character string.

(suit "2H") ;=> "H" (suit "2D") ;=> "D" (suit "2C") ;=> "C" (suit "3S") ;=> "S"

To get the rank, you’ll need to convert a character into an integer. To see if a character is a digit, like \5 or \2, you can use (Character/isDigit char):

(Character/isDigit \5) ;=> true (Character/isDigit \A) ;=> false

If a character is a digit, you can use (Integer/valueOf string) to convert it to an integer. You will first have to convert the character into a string.

(Integer/valueOf "12") ;=> 12 (Integer/valueOf (str \5)) ;=> 5

Finally, to turn the characters T, J, Q, K and A into integers, using a map to store the values is very useful:

(get {\A 100, \B 20} \B) ;=> 20 ({\A 100, \B 20} \B) ;=> 20 (def replacements {\A 100, \B 20}) (replacements \B) ;=> 20

You can now write the (rank card) function.

Exercise 2

Write the function (rank card) which takes a single card and returns the rank as a number between 2 and 14.

(rank "2H") ;=> 2 (rank "4S") ;=> 4 (rank "TS") ;=> 10 (rank "JS") ;=> 11 (rank "QS") ;=> 12 (rank "KS") ;=> 13 (rank "AS") ;=> 14

Some additional functions

Here’s a couple of functions that should prove useful.

(frequencies sequence) is used to see how many times an element appears in a sequence. It returns a map where elements are mapped to their appearance counts:

(frequencies [4 7 7 4 7]) ;=> {4 2, 7 3}

In this case, we had three sevens and two fours.

If you are only interested in the keys or values of a map, you can get them with (keys a-map) and (vals a-map):

(vals (frequencies [4 7 7 4 7])) ;=> (2 3) ; ^-- now that looks a lot like a full house

(max num1 num2 num3 ...) returns its largest parameter and (min num1 num2 num3 ...) returns its smallest paremeter.

(max 1 5 4 2) ;=> 5 (min 1 5 4 2) ;=> 1

But what should you do if you have a sequence of numbers, like the vector [1 -4 2 3 5], and you want its smallest or largest value? There is a very useful special form called apply for this: (apply function parameter-sequence) calls function with the parameters from parameter-sequence.

(apply str ["Over " 9000 "!"]) ;=> (str "Over " 9000 "!") ;=> "Over 9000!"

(apply max [5 3 2]) ;=> (max 5 3 2) ;=> 5

That’s quite a lot to remember, but these should provide useful when detecting different hands. If you get stuck, the functions introduced above might help.

Hands

If you don’t remember a hand, the Poker hands article at Wikipedia has them listed and explained.

Our representation for a poker hand is simply a vector of cards:

(def high-seven ["2H" "3S" "4C" "5C" "7D"])

Here’s a bunch of hands to use for testing:

(def high-seven ["2H" "3S" "4C" "5C" "7D"]) (def pair-hand ["2H" "2S" "4C" "5C" "7D"]) (def two-pairs-hand ["2H" "2S" "4C" "4D" "7D"]) (def three-of-a-kind-hand ["2H" "2S" "2C" "4D" "7D"]) (def four-of-a-kind-hand ["2H" "2S" "2C" "2D" "7D"]) (def straight-hand ["2H" "3S" "6C" "5D" "4D"]) (def low-ace-straight-hand ["2H" "3S" "4C" "5D" "AD"]) (def high-ace-straight-hand ["TH" "AS" "QC" "KD" "JD"]) (def flush-hand ["2H" "4H" "5H" "9H" "7H"]) (def full-house-hand ["2H" "5D" "2D" "2C" "5S"]) (def straight-flush-hand ["2H" "3H" "6H" "5H" "4H"]) (def low-ace-straight-flush-hand ["2D" "3D" "4D" "5D" "AD"]) (def high-ace-straight-flush-hand ["TS" "AS" "QS" "KS" "JS"])

Exercise 3

Write the function (pair? hand) that returns true if there is a pair in hand and false if there is no pair in hand.

(pair? pair-hand) ;=> true (pair? high-seven) ;=> false

Exercise 4

Write the function (three-of-a-kind? hand) that returns true if the hand contains a three of a kind.

(three-of-a-kind? two-pairs-hand) ;=> false (three-of-a-kind? three-of-a-kind-hand) ;=> true

Exercise 5

Write the function (four-of-a-kind? hand) that returns true if the hand contains a four of a kind.

(four-of-a-kind? two-pairs-hand) ;=> false (four-of-a-kind? four-of-a-kind-hand) ;=> true

Exercise 6

Write the function (flush? hand) that returns true if the hand is a flush.

(flush? pair-hand) ;=> false (flush? flush-hand) ;=> true)

(sort a-seq) returns a sequence with the elements of a-seq in a sorted order.

(sort [5 -1 3 17 -10]) ;=> (-10 -1 3 5 17) (sort [6 4 5 7 3]) ;=> (3 4 5 6 7) ; ^ ; | ;kind of looks like a straight---

(range lower-bound upper-bound) takes two integers and returns a sequence with all integers from lower-bound to upper-bound, but does not include upper-bound.

(range 1 5) ;=> (1 2 3 4) (range 5) ;=> (0 1 2 3 4)

You can test for equality between sequences with =.

(= [3 4 5 6 7] (range 3 (+ 3 5))) ;=> (= [3 4 5 6 7] ; (3 4 5 6 7)) ;=> (and (= 3 3) (= 4 4) (= 5 5) (= 6 6) (= 7 7)) ;=> true (= [1 2 3] (seq [1 2])) ;=> false

Two sequences are equal if their elements are equal and in the same order.

Exercise 7

Write the function (full-house? hand) that returns true if hand is a full house, and otherwise false.

(full-house? three-of-a-kind-hand) ;=> false (full-house? full-house-hand) ;=> true

Exercise 8

Write the function (two-pairs? hand) that return true if hand has two pairs, and otherwise false.

Note that a four of a kind is also two pairs.

(two-pairs? two-pairs-hand) ;=> true (two-pairs? pair-hand) ;=> false (two-pairs? four-of-a-kind-hand) ;=> true

In a straight, an ace is accepted as either 1 or 14, so both of the following hands have a straight:

["2H" "3S" "4C" "5D" "AD"] ["TH" "AS" "QC" "KD" "JD"]

A useful function here is (replace replace-map a-seq). It takes a map of replacements and a sequence and replaces the keys of replace-map in a-seq with their associated values.

(replace {1 "a", 2 "b"} [1 2 3 4]) ;=> ["a" "b" 3 4]

Finally we can implement straight?.

Exercise 9

Write the function (straight? hand) that returns true if hand is a straight, and otherwise false.

Note that an ace is accepted both as a rank 1 and rank 14 card in straights.

(straight? two-pairs-hand) ;=> false (straight? straight-hand) ;=> true (straight? low-ace-straight-hand) ;=> true (straight? ["2H" "2D" "3H" "4H" "5H"]) ;=> false (straight? high-ace-straight-hand) ;=> true

And finally, there’s straight flush. This shouldn’t be very difficult after having already defined flush and straight.

Exercise 10

Write the function (straight-flush? hand) which returns true if the hand is a straight flush, that is both a straight and a flush, and otherwise false.

(straight-flush? straight-hand) ;=> false (straight-flush? flush-hand) ;=> false (straight-flush? straight-flush-hand) ;=> true (straight-flush? low-ace-straight-flush-hand) ;=> true (straight-flush? high-ace-straight-flush-hand) ;=> true

Now that we have functions that check for each hand type, it would be nice to be able to assign a value to each hand. We’re going to use the following values:

HandValueHigh card (nothing)0Pair1Two pairs2Three of a kind3Straight4Flush5Full house6Four of a kind7Straight flush8

Exercise 11

Write the function (value hand), which returns the value of a hand according to the table above.

(value high-seven) ;=> 0 (value pair-hand) ;=> 1 (value two-pairs-hand) ;=> 2 (value three-of-a-kind-hand) ;=> 3 (value straight-hand) ;=> 4 (value flush-hand) ;=> 5 (value full-house-hand) ;=> 6 (value four-of-a-kind-hand) ;=> 7 (value straight-flush-hand) ;=> 8

It might be helpful to add a checker (high-card? hand):

(defn high-card? [hand] true) ; All hands have a high card.

You can create a sequence of [matcher value] pairs like so:

(let [checkers #{[high-card? 0] [pair? 1] [two-pairs? 2] [three-of-a-kind? 3] [straight? 4] [flush? 5] [full-house? 6] [four-of-a-kind? 7] [straight-flush? 8]}] ...)

You can now use filter, map and apply max to get the highest value that a hand has. The function second can be useful. Remember to use let to give the intermediate results readable names.

(second [:i :am :a :sequence]) ;=> :am (second [two-pairs? 2]) ;=> 2

Data representation

Our representation for poker hands is rather simple, but it allows us to use existing sequence and other functions to work with them. However, the current API is bound to the representation. This has the unfortunate consequence that we can not change the internal representation of cards or hands without changing the external API. There can be good reasons to change the internal representation, including efficiency.

No worries, this is fixable. Let’s create two functions for creating a card and creating a hand from the representation we already use:

(defn hand [a-hand] a-hand) (defn card [a-card] a-card)

Which you would use like this:

(card "2H") (hand ["AH" "AC" "AD" "AS" "4H"])

While these functions in their current form don’t do anything, it allows us to change the internal representation if we want to. You would use the existing functions like this:

(rank (card "2H")) ;=> 2 (value (hand ["2H" "3H" "4H" "5H" "6H"])) ;=> 4

Now the functions card, hand, rank and suit form the abstraction for a playing card. They are the only functions that need to know about the internal representatin of the card. This means that we would now be able to change the internal representation to something like this, if we wanted to:

(card "2H") ;=> {:rank 2, :suit :hearts}

What’s Next

Now that you have mastered evaluating poker hands, it’s time to understand recursion.

Predicates →