;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Author: Steve Lombardi
;	http://www.stephenlombardi.com/
; Date: August 13th, 2008
; Description: 
;	Generates the probability of winning
; 	a game of blackjack
;
; MIT license
; I make no garuntees that this software
; doesn't become self aware and take over
; the world.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

; The hand is stored as the value of the cards added together 
; (with aces counting as 11), as well as the number of aces
; in the hand. It is important to keep track of the number of
; aces so that you can count the appropriate aces as having a
; value of one if the hand goes over 21.

; Special note: don't use this function to determine if a hand goes
; over 21; if it's not possible to reduce a hand to under 21, the 
; function simply returns 21. Use bust? to test if a hand is over.
(defun max-hand-value (value aces)
	"converts the appropriate aces to have a value of one if the hand would otherwise bust"
	(- value (* 10
		(min
			(max (truncate (/ (- value 12) 10)) 0)
			aces
		)
	))
)

(defun bust? (value aces)
	"returns true if the value is over 21 (accounting for aces)"
	(if (> (- value (* aces 10)) 21)
		t
		nil
	)
)

(defun outcome (dealervalue dealeraces playervalue playeraces)
	"returns the winner of the blackjack game - 1.0 if the player wins, 0.0 if the dealer wins, 0.5 for a push"
	(let (
			(pval (max-hand-value playervalue playeraces))
			(dval (max-hand-value dealervalue dealeraces))
		)
		(if (= pval dval)
			0.5
			(if (> pval dval)
				1.0
				0.0
			)
		)
	)
)

(defun dealer-turn (dealervalue dealeraces playervalue playeraces)
	"checks to see if dealer has less than 17 or 'soft-17' (A,6), if so hit, otherwise stay"
	(cond
		((and (= dealeraces 0) (<= dealervalue 16))
			(dealer-hit dealervalue dealeraces playervalue playeraces)
		)
		((and (> dealeraces 0) (<= (max-hand-value dealervalue dealeraces) 17))
			(dealer-hit dealervalue dealeraces playervalue playeraces)
		)
		(t
			(dealer-stand dealervalue dealeraces playervalue playeraces)
		)
	)
)

(defun dealer-hit (dealervalue dealeraces playervalue playeraces)
	"takes the average of the possiblities of winning for each card that the dealer could get"
	(/ (loop for cardval in '(2 3 4 5 6 7 8 9 10 10 10 11) as isace in '(0 0 0 0 0 0 0 0 0 0 0 1) sum
		(dealer-turn (+ dealervalue cardval) (+ dealeraces isace) playervalue playeraces)
	) 13)
)

(defun dealer-stand (dealervalue dealeraces playervalue playeraces)
	"returns the probability of the player winning if the dealer accepts no more cards"
	(if (bust? dealervalue dealeraces)
		1.0
		(outcome dealervalue dealeraces playervalue playeraces)
	)
)

(defun player-turn (dealervalue dealeraces playervalue playeraces)
	"returns the probability of the player winning with the current hand"
	(cond
		((bust? playervalue playeraces)
			0.0
		)
		(t
			(max
				(player-hit dealervalue dealeraces playervalue playeraces)
				(player-stand dealervalue dealeraces playervalue playeraces)
			)
		)
	)	
)

(defun player-hit (dealervalue dealeraces playervalue playeraces)
	"returns the probability if the player accepts an additional card to their hand"
	(/ (loop for cardval in '(2 3 4 5 6 7 8 9 10 10 10 11) as isace in '(0 0 0 0 0 0 0 0 0 0 0 1) sum
		(player-turn dealervalue dealeraces (+ playervalue cardval) (+ playeraces isace))
	) 13)
)

(defun player-stand (dealervalue dealeraces playervalue playeraces)
	"returns the probability of the player winning if the player does not accept additional cards"
	(dealer-turn dealervalue dealeraces playervalue playeraces)
)

(defun probability-table ()
	"produces a table which gives the optimal move for any given initial player hand value and dealer card"
	(format t " ~0,8@T 2 3 4 5 6 7 8 9 J A~%")
	(loop for player in '(17 16 15 14 13 12 20 19 18 17 16) as playeraces in '(0 0 0 0 0 0 1 1 1 1 1) do
		(format t "~a~0,8@T" player)
		(loop for dealer in '(2 3 4 5 6 7 8 9 10 11) as dealeraces in '(0 0 0 0 0 0 0 0 0 1) do
			(if (> (player-hit dealer dealeraces player playeraces) (player-stand dealer dealeraces player playeraces))
				(format t "H ")
				(format t "S ")
			)
		)
		(format t "~%")
	)
)

(defun probability-table2 ()
	"produces a table which gives the probability of winning for a hit or stand for any given initial player hand value and dealer card"
	(format t "player~0,8@Tdealer~%")
	(loop for player in '(17 16 15 14 13 12 20 19 18 17 16) as playeraces in '(0 0 0 0 0 0 1 1 1 1 1) do
		(loop for dealer in '(2 3 4 5 6 7 8 9 10 11) as dealeraces in '(0 0 0 0 0 0 0 0 0 1) do
			(format t "~a~0,8@T" player)
			(format t "~a~0,8@T" dealer)
			(format t "H: ~0,5f S: ~0,5f" (player-hit dealer dealeraces player playeraces) (player-stand dealer dealeraces player playeraces))
			(format t "~%")
		)
	)
)

; Example of use:
;	>(player-hit 10 0 16 0)
;	0.19261277031149104
;	>(player-stand 10 0 16 0)
;	0.18343373756546313
;	>(probability-table)
;	        2 3 4 5 6 7 8 9 J A
;	17      S S S S S S S S S H
;	16      S S S S S H H H H H
;	15      S S S S S H H H H H
;	14      S S S S S H H H H H
;	13      H S S S S H H H H H
;	12      H H H S S H H H H H
;	20      S S S S S S S S S S
;	19      S S S S S S S S S S
;	18      S S S S ...
;	>(probability-table2)
;	player dealer
;	17      2       H: .17970 S: .30711
;	17      3       H: .18349 S: .32520
;	17      4       H: .18737 S: .34428
;	17      5       H: .19161 S: .36357
;	17      6       H: .19302 S: .38865
;	17      7       H: .21852 S: .36688
;	17      8       H: .21233 S: .27054
;	17      9       H: .19594 S: .25250
;	17      10      H: .17458 S: .23441
;	17      11      H: .13365 S: .12780
;	...