Dice Simulation
by Stan Munson
Adjust the slider for the number of rolls you want to simulate.
Note that you can also use the left and right arrow keys to change this value.
Then click the Roll count button.
The DICE chart shows each die separately. One die is tabulated in the columns; the other die is tabulated in the rows. This lets you see, for example, how many times you rolled a 5/4 combination compared to a 4/5 combination.
The DICE chart tabulates all die rolls. The total here is always twice your request since the simulation is for pairs of dice. The ROLL chart tabluates the sum of each dice roll.
The percentages for the DICE chart rows and columns and the percentages for the DIE rows should be very close when a large number of rolls is requested. The percentages for the ROLL chart are a starting points for investigating the game of craps.
Note that you can turn off the dice roll animation for large numbers.
Dice_Simulation.lgo
TO WORKSHEET :SNAME :ROWS :COLS :ROW.TITLES :COL.TITLES :SIZE :SXY
(LOCAL "BNAME "BX "BY "BWIDTH "BHEIGHT "ROW "COL)
MAKE "BWIDTH FIRST :SIZE
MAKE "BHEIGHT LAST :SIZE
MAKE "BX (FIRST :SXY) + (:BWIDTH / 2)
MAKE "BY (LAST :SXY) - (:BHEIGHT / 2)
MAKE "ROW 0
WHILE [.LE :ROW :ROWS] [
MAKE "COL 0
WHILE [.LE :COL :COLS] [
MAKE "BNAME (WORD :SNAME ".R :ROW "C :COL)
DECLARE "EDITBOX :BNAME
PPROP :BNAME "POSITION LIST :BX :BY
PPROP :BNAME "SIZE :SIZE
MAKE "COL :COL + 1
MAKE "BX :BX + (:BWIDTH - 1)
]
MAKE "BX (FIRST :SXY) + (:BWIDTH / 2)
MAKE "ROW :ROW + 1
MAKE "BY :BY - (:BHEIGHT - 1)
]
; Fill in column headings with bold font
MAKE "ROW 0
MAKE "COL 1
WHILE [.LE :COL :COLS] [
MAKE "BNAME (WORD :SNAME ".R :ROW "C :COL)
PPROP :BNAME "TEXT ITEM :COL :COL.TITLES
PPROP :BNAME "FONT SENTENCE BUTLAST GPROP :BNAME "FONT 1
MAKE "COL :COL + 1
]
; Fill in row headings with bold font
MAKE "ROW 1
MAKE "COL 0
WHILE [.LE :ROW :ROWS] [
MAKE "BNAME (WORD :SNAME ".R :ROW "C :COL)
PPROP :BNAME "TEXT ITEM :ROW :ROW.TITLES
PPROP :BNAME "FONT SENTENCE BUTLAST GPROP :BNAME "FONT 1
MAKE "ROW :ROW + 1
]
; Set row 0 column 0 font to bold
MAKE "BNAME (WORD :SNAME ".R0C0)
PPROP :BNAME "FONT SENTENCE BUTLAST GPROP :BNAME "FONT 1
PPROP :BNAME "TEXT :SNAME
; Set the properties of the SNAME
PPROPS :SNAME (SENTENCE "MAXROW :ROWS "MAXCOL :COLS)
END
TO GET.CELL :GRIDNAME :ROW :COL
OUTPUT GPROP (WORD :GRIDNAME ".R :ROW "C :COL) "TEXT
END
TO SET.CELL :GRIDNAME :ROW :COL :VALUE
PPROP (WORD :GRIDNAME ".R :ROW "C :COL) "TEXT :VALUE
END
TO INC.CELL :GRIDNAME :ROW :COL [:INC 1] 3
LOCAL "TEMP
MAKE "TEMP GET.CELL :GRIDNAME :ROW :COL
IF EMPTY? :TEMP MAKE "TEMP 0
IF NOT NUMBER? :TEMP [
(THROW "INC.CELL (LIST "|Cell| (WORD :GRIDNAME ".R :ROW "C :COL) "|is not numeric.|))
]
MAKE "TEMP :TEMP + :INC
SET.CELL :GRIDNAME :ROW :COL :TEMP
END
TO SUM.ROW :GRIDNAME :ROW
(LOCAL "TOTAL "COL "MAXCOL)
MAKE "MAXCOL GPROP :GRIDNAME "MAXCOL
MAKE "TOTAL 0
MAKE "COL 1
WHILE [.LE :COL :MAXCOL] [
MAKE "TEMP GET.CELL :GRIDNAME :ROW :COL
IF NUMBER? :TEMP [MAKE "TOTAL :TOTAL + :TEMP]
MAKE "COL :COL + 1
]
OUTPUT :TOTAL
END
TO SUM.COL :GRIDNAME :COL
(LOCAL "TOTAL "ROW "MAXROW)
MAKE "MAXROW GPROP :GRIDNAME "MAXROW
MAKE "TOTAL 0
MAKE "ROW 1
WHILE [.LE :ROW :MAXROW] [
MAKE "TEMP GET.CELL :GRIDNAME :ROW :COL
IF NUMBER? :TEMP [MAKE "TOTAL :TOTAL + :TEMP]
MAKE "ROW :ROW + 1
]
OUTPUT :TOTAL
END
TO SUM.CELLS :GRIDNAME :UPPER.ROW :LEFT.COL :LOWER.ROW :RIGHT.COL
(LOCAL "ROW "COL "ROW.BEGIN "ROW.END "COL.BEGIN "COL.END "TOTAL)
MAKE "ROW.BEGIN :UPPER.ROW
MAKE "COL.BEGIN :LEFT.COL
MAKE "ROW.END :LOWER.ROW
MAKE "COL.END :RIGHT.COL
MAKE "TOTAL 0
MAKE "ROW :ROW.BEGIN
WHILE [.LE :ROW :ROW.END] [
MAKE "COL :COL.BEGIN
WHILE [.LE :COL :COL.END] [
MAKE "TEMP GET.CELL :GRIDNAME :ROW :COL
IF NUMBER? :TEMP [MAKE "TOTAL :TOTAL + :TEMP]
MAKE "COL :COL + 1
]
MAKE "ROW :ROW + 1
]
OUTPUT :TOTAL
END
TO INIT.GRID :GRIDNAME :VALUE
(LOCAL "ROW "COL "MAXROW "MAXCOL)
MAKE "MAXROW GPROP :GRIDNAME "MAXROW
MAKE "MAXCOL GPROP :GRIDNAME "MAXCOL
MAKE "ROW 1
WHILE [.LE :ROW :MAXROW] [
MAKE "COL 1
WHILE [.LE :COL :MAXCOL] [
SET.CELL :GRIDNAME :ROW :COL :VALUE
MAKE "COL :COL + 1
]
MAKE "ROW :ROW + 1
]
END
TO SIMULATE :THROWS
FOREACH [DICE ROLL DIE] [INIT.GRID "? 0]
FOR "ROLLS 1 :THROWS [TABULATE]
END
TO TABULATE
(LOCAL "ROLL "DIE1 "DIE2)
MAKE "ROLL ROLL.DICE
MAKE "DIE1 FIRST :ROLL
MAKE "DIE2 LAST :ROLL
; Change the image of the dice to simulate the actual roll
IF GPROP "ANIMATION.CHECK "STATE [
ASK "DIE.1 [LOADSHAPE (WORD "~HOME/TOOLBOX/DICE/DICE PICK THING WORD "D :DIE1 ".PNG)]
ASK "DIE.2 [LOADSHAPE (WORD "~HOME/TOOLBOX/DICE/DICE PICK THING WORD "D :DIE2 ".PNG)]
]
INC.CELL "DICE :DIE1 :DIE2
INC.CELL "DICE :DIE1 7
INC.CELL "DICE 7 :DIE2
INC.CELL "DICE 7 7
INC.CELL "ROLL 1 (:DIE1 + :DIE2 - 1)
INC.CELL "ROLL 1 12
INC.CELL "DIE :DIE1 1
INC.CELL "DIE 7 1
INC.CELL "DIE :DIE2 1
INC.CELL "DIE 7 1
FOR "I 1 6 [
SET.CELL "DICE :I 8 PRODUCT 100 QUOTIENT (GET.CELL "DICE :I 7) :ROLLS
SET.CELL "DICE 8 :I PRODUCT 100 QUOTIENT (GET.CELL "DICE 7 :I) :ROLLS
SET.CELL "DIE :I 2 PRODUCT 100 QUOTIENT (GET.CELL "DIE :I 1) (2 * :ROLLS)
]
FOR "I 2 12 [
SET.CELL "ROLL 2 (:I - 1) PRODUCT 100 QUOTIENT (GET.CELL "ROLL 1 (:I - 1)) :ROLLS
]
END
TO ROLL.DICE
OUTPUT LIST RANDOM 6 RANDOM 6
END
TO ABOUT
(LOCAL "LF "PP "SAMPLE.TEXT "P1 "P2 "P3 "P4 "P5 "P6 "P7 "P8 "P9 "P10)
MAKE "LF CHAR 10
MAKE "PP WORD :LF :LF
MAKE "P1 "|Adjust the slider for the number of rolls you want to simulate and click |
MAKE "P2 "|the roll count button. |
MAKE "P3 "|The DICE chart shows each die separately. One die is tabulated in the columns; |
MAKE "P4 "|the other die is tabulated in the rows. This lets you see, for example, how many |
MAKE "P5 "|times you rolled a 5/4 combination compared to a 4/5 combination. |
MAKE "P6 "|The DIE chart tabulates all die rolls. The total here is always twice your request since |
MAKE "P7 "|the simulation is for pairs of dice. The ROLL chart tabulates the sum of each dice roll. |
MAKE "P8 "|The percentages for DICE chart rows and columns and the percentages for the DIE rows |
MAKE "P9 "|should be very close when a large number of rolls is requested. |
MAKE "P10 "|The percentages for the ROLL chart are a starting point for investigating the game of craps.|
MAKE "SAMPLE.TEXT (WORD :P1 :P2 :PP :P3 :P4 :P5 :PP :P6 :P7 :PP :P8 :P9 :P10)
IGNORE ALERT :SAMPLE.TEXT
END
TO MAIN
PRINT `Move the slider for the number of times to roll the dice.`
PRINT `Then click the button to roll that many times.`
PRINT `Turn off animation for large numbers.`
CLEARSCREEN DRAW
PPROP "LOGO.ENV "LAYOUT "SMALL
SPLITSCREEN
; "ROLL.ROWHEADING "ROLL.COLHEADING
MAKE "DICE.ROWHEADING [1 2 3 4 5 6 |Total| | % |]
MAKE "DICE.COLHEADING [1 2 3 4 5 6 |Total| | % |]
MAKE "ROLL.ROWHEADING [|Total| | % |]
MAKE "ROLL.COLHEADING [2 3 4 5 6 7 8 9 10 11 12 |Rolls|]
MAKE "DIE.ROWHEADING [1 2 3 4 5 6 |Total|]
MAKE "DIE.COLHEADING [|Total| | % |]
WORKSHEET "DICE 8 8 :DICE.ROWHEADING :DICE.COLHEADING [50 20] [-300 130]
WORKSHEET "ROLL 2 12 :ROLL.ROWHEADING :ROLL.COLHEADING [40 20] [-300 -50]
WORKSHEET "DIE 7 2 :DIE.ROWHEADING :DIE.COLHEADING [50 20] [200 130]
INIT.GRID "DICE 0
INIT.GRID "ROLL 0
INIT.GRID "DIE 0
; Set up button and slider
DECLARE "SLIDER "ROLL.SLIDER
PPROPS "ROLL.SLIDER [POSITION [-140 -140] MINIMUM 1 MAXIMUM 5000 VALUE 77 TOOLTIP |Set the number of rolls|]
PPROP "ROLL.SLIDER "RUN [PPROP "ROLL.BUTTON "TEXT (WORD "|Roll count: | GPROP "ROLL.SLIDER "VALUE)]
DECLARE "BUTTON "ROLL.BUTTON
PPROPS "ROLL.BUTTON [POSITION [-30 -140] TEXT "|Roll count: 77| RUN [SIMULATE GPROP "ROLL.SLIDER "VALUE] TOOLTIP |Click to begin|]
DECLARE "CHECKBOX "ANIMATION.CHECK
PPROPS "ANIMATION.CHECK [POSITION [250 -140] STATE TRUE TEXT "|Check to animate dice| TOOLTIP |Check to see the dice images change|]
; The dice images all show 3 numbers but the value of the die is the first digit.
MAKE "D1 [123 135 142 154]
MAKE "D2 [214 231 246 263]
MAKE "D3 [312 326 351 365]
MAKE "D4 [415 421 456 462]
MAKE "D5 [513 536 541 564]
MAKE "D6 [624 632 645 653]
DECLARE "BITMAP "DIE.1
DECLARE "BITMAP "DIE.2
TELL "DIE.1 SETXY [250 -70]
TELL "DIE.2 SETXY [320 -70]
SIMULATE 77 ; just to get things started
END
MAIN
| Procedure | MAIN |
| Description | An analysis of rolls of pairs of dice. |
| Level | Advanced |
| Tags | Math, Random |