Modify 3 Dice outcomes to a Single Die Throw

Σ	Face Values	#
3	(1,1,1)*	1
4	(1,1,2)+	3
5	(1,1,3)+ (1,2,2)+	6
6	(1,1,4)+ (1,2,3)- (2,2,2)*	10
7	(1,1,5)+ (1,2,4)- (1,3,3)+ (2,2,3)+	15
8	(1,1,6)+ (1,2,5)- (1,3,4)- (2,2,4)+ (2,3,3)+	21
9	(1,2,6)- (1,3,5)- (1,4,4)+ (2,2,5)+ (2,3,4)- (3,3,3)*	25
10	(1,3,6)- (1,4,5)- (2,2,6)+ (2,3,5)- (2,4,4)+ (3,3,4)+	27
11	(1,4,6)- (1,5,5)+ (2,3,6)- (2,4,5)- (3,3,5)+ (3,4,4)+	27
12	(1,5,6)- (2,4,6)- (2,5,5)+ (3,4,5)- (3,3,6)+ (4,4,4)*	25
13	(1,6,6)+ (2,5,6)- (3,4,6)- (3,5,5)+ (4,4,5)+	21
14	(2,6,6)+ (3,5,6)- (4,4,6)+ (4,5,5)+	15
15	(3,6,6)+ (4,5,6)- (5,5,5)*	10
16	(4,6,6)+ (5,5,6)+	6
17	(5,6,6)+	3
18	(6,6,6)*	1
	TOTAL OUTCOMES	216
Keys	* == unique (#1),  + == 3! / 2! (#3) , - == 3!  (#6)

import java.util.* ;

int [] sumOfThree = new int[19] ;

void setup() {

    // 3 dice summation simulation

    

    for (int d1 = 1 ; d1 < 7 ; d1++) {

      for(int d2 = 1 ; d2 < 7 ; d2++) {

        for (int d3 = 1 ; d3 < 7 ; d3++) {

              int sum = (d1 + d2 + d3) ; 

              sumOfThree[sum]++ ;

        }

      }

    }

    

    for(int i = 3 ; i < 19 ; i++) {

      println("Sum ",i,"# outcomes",sumOfThree[i]) ;  

    }

    

    // Group sum outcomes together and check if the are equally distrubuted

    // Note all these groups should be the same - 6 groups of 36  (216 outcomes - throwing 3 dice)

    

    println("Group 1", sumOfThree[3]  + sumOfThree[6] + sumOfThree[9]) ;

    println("Group 2",sumOfThree[18]  + sumOfThree[15] + sumOfThree[12]) ;

    println("Group 3",sumOfThree[4]  + sumOfThree[5] + sumOfThree[10]) ;

    println("Group 4",sumOfThree[17]  + sumOfThree[16] + sumOfThree[11]) ;

    

    println("Group 5",sumOfThree[7]  + sumOfThree[8]) ;

    println("Group 6",sumOfThree[13]  + sumOfThree[14]) ;

    

    // Generate a HashMap which maps sum of 3 dice to a single die throw outcome.

    // We have noted that the 3 dice 'summation' outcomes can be split into 

    // the groups (3,6,9), (4,5,10), (7,8), (13,14) (11,16,17), (12,15,18)

    // with each of these SIX groups adding up to 36.

    

    Map<Integer,Integer> singleThrow = new HashMap() ;

    

    // Throw 1

    singleThrow.put(3,1) ; singleThrow.put(6,1) ; singleThrow.put(9,1) ;

    

    // Throw 2

    singleThrow.put(18,2) ; singleThrow.put(15,2) ; singleThrow.put(12,2) ;

    

    // Throw 3

    singleThrow.put(4,3) ; singleThrow.put(5,3) ; singleThrow.put(10,3) ;

    // Throw 4

    singleThrow.put(17,4) ; singleThrow.put(16,4) ; singleThrow.put(11,4) ;

    // Throw 5

    singleThrow.put(7,5) ; singleThrow.put(8,5) ; 

   // Throw 6

    singleThrow.put(14,6) ; singleThrow.put(13,6) ; 

    // We now have a new map which maps the sum of 3 dice to a single die outcome.

    // go through all 216 outcomes and make sure that our 'roll' comes out evenly distributed.

    int [] roll = new int[7] ;

    for (int d1 = 1 ; d1 < 7 ; d1++) {

      for(int d2 = 1 ; d2 < 7 ; d2++) {

        for (int d3 = 1 ; d3 < 7 ; d3++) {

              int sum = (d1 + d2 + d3) ; 

              int die = singleThrow.get(sum) ;

              roll[die - 1]++ ;

        }

      }

    }

    

    for(int i = 0 ; i < 6 ; i++) {

      println("Die Face ",(i + 1),"Outcomes of of 216 = ",roll[i], "Pass:", roll[i] == 36) ;  

    }

    exit() ;

    

}