blackjack

Testing your understanding of higher order functions by creating strategys for Blackjack (also called Pontoon or 21)

We are going to build an increasingly complex model of playing Blackjack alongside strategys to play the game

Starting out

A simple model for the deck

We begin with a very simple model of both cards and the deck, we assume that they take a value from 1-10 and anything is equally likely, we can get a new card by calling deal

(defn deal []
  (inc (rand-int 10)))

Modelling hands

See the simple-hand namespace: If a hand is a vector of numbers, we can make a new hand by defining

(defn new-hand [] [(deal)])

and have the following helper functions to deal with them

(defn up-card [hand]
  (first hand))

(defn add-card [hand card]
  (conj hand card))

(defn total [hand]
  (reduce + hand))

Strategies

We will model a strategy as a procedure of the current hand and the dealers 'up card' (which a decent strategy will take into account) that returns true or false if it decides to 'hit'.

Take a look at the play-game procedure: it takes 2 strategies, for the player and dealer then uses play-hand to play the players hand and then (if the player didnt bust), plays the dealers hand. It returns 1 if the player wins and 0 if she loses.

The play-hand procedure takes a strategy, a hand (list of cards) and the visible card of the opponent, it always returns a hand and will stop if either

• the strategy decides to stop

or

• the player goes bust

otherwise it takes a card and recurs

For you to complete

'Stop at 17'

Write a strategy called stop-at-17 It should hit for as long as the hand is worth (strictly) less than 17

Test strategies

Write a procedure that takes a player-strategy a house-strategy and a number n of games to play and returns how many the player won that lets you know what fraction of the games was won by the player

(when I did it (test-strategy stop-at-17 stop-at-17 100000) was about 0.41)

'Stop at n'

Write a procedure called stop-at-n that takes a number and returns a strategy that will stop when it gets higher than that number (so stop-at-17 should be 'the same' as (stop-at-n 17))

'Watched'

Write a procedure called watched that takes a strategy and returns a strategy that behaves the same way only also prints (as a side-effect) the arguments it was called with (hand and up-card) and the decision to hit or not

Taking into account the dealers hand

Take a look at Basic Strategy in the Wikipedia Article

You can see that if we take into account the dealers hand that you should stop at 13 if their card is 6 or less, write a strategy that does this (maybe you can use other strategies you have created)

Majority

Write a procedure that takes a list of strategies and hits if a majority say they should hit. (think about what to do if the size of the list is even and there is a tie)

Just one more

Write a procedure that takes a strategy and returns a strategy that always stops one card later than the original

License

Copyright © 2015 Tom Hall