Pig the dice game/Player
You are encouraged to solve this task according to the task description, using any language you may know.
The task is to create a dice simulator and scorer of Pig the dice game and add to it the ability to play the game to at least one strategy.
- State here the play strategies involved.
- Show play during a game here.
As a stretch goal:
- Simulate playing the game a number of times with two players of given strategies and report here summary statistics such as, but not restricted to, the influence of going first or which strategy seems stronger.
- Game Rules
The game of Pig is a multiplayer game played with a single six-sided die. The object of the game is to reach 100 points or more. Play is taken in turns. On each person's turn that person has the option of either
- Rolling the dice: where a roll of two to six is added to their score for that turn and the player's turn continues as the player is given the same choice again; or a roll of 1 loses the player's total points for that turn and their turn finishes with play passing to the next player.
- Holding: The player's score for that round is added to their total and becomes safe from the effects of throwing a one. The player's turn finishes with play passing to the next player.
- Reference
Contents |
[edit] Ada
Uses Ada 2012. Uses the package Pig from Pig the dice game.
We implement parameter-driven strategies. A strategy is defined by two parameters: When the given points in a round reach a Bound these points are collected, else we roll again. But if the other player is very close to winning (less than Final_Run points), we switch to an all-or nothing approach, collecting points until we have won -- or rolled a 1.
The implementation reads five parameters from the command line, in that order: (1) N the number of games to play, (2) the Bound for the first player, (3) the Final_Run for the first player, (4) the Bound for the second player and (5) the Final_Run for the second player. After reading these from the command line (or accepting reasonable defaults), it plays the game N times and counts how often either player wins.
with Pig; with Ada.Text_IO; with Ada.Command_Line;
procedure automatic_Pig is
use Pig;
type Robot is new Actor with record
Bound: Natural := 20;
Final_Run: Natural := 0;
end record;
function Roll_More(A: Robot; Self, Opponent: Player'Class) return Boolean;
function Roll_More(A: Robot; Self, Opponent: Player'Class) return Boolean is
((Self.All_Recent < A.Bound) or
else (Opponent.Score-100 > A.Final_Run));
function Arg(Position: Positive; Default: Natural) return Natural is
package ACL renames Ada.Command_Line;
begin
return Natural'Value(ACL.Argument(Position));
exception
when Constraint_Error => return Default;
end Arg;
T: Robot := (Bound => Arg(2, 35), Final_Run => Arg(3, 0));
F: Robot := (Bound => Arg(4, 20), Final_Run => Arg(5, 30));
T_Wins: Boolean;
Win_Count: array(Boolean) of Natural := (True=> 0, False => 0);
begin
for I in 1 .. Arg(1, 1000) loop
Play(T, F, T_Wins);
Win_Count(T_Wins) := Win_Count(T_Wins) + 1;
end loop;
Ada.Text_IO.Put_Line(Natural'Image(Win_Count(True)) &
Natural'Image(Win_Count(False)));
end Automatic_Pig;
- Output:
The output shows that the (Bound => 25, Final_Run => 25) strategy is just as good as (Bound => 25, Final_Run => 0): whoever is first wins by the same margin:
$ ./automatic_pig 1000000 25 25 25 0 527999 472001 $ ./automatic_pig 1000000 25 0 25 25 527935 472065
[edit] AutoHotkey
Strategies are defined at bottom of script.
Requires additional file from Pig the dice game/Player/AutoHotkey
#NoEnv
SetBatchLines, -1
#SingleInstance, Force
#Include Pig_the_dice_game_Optimal_Play.ahkl ; comment if you don't want to bother
Play:=10000 ; this is enough to give 2 digits of accuracy in win ratio
Wins0:=Wins1:=0
Player0(TurnSum, SumMe, SumOpp) {
Return practical(TurnSum, SumMe, SumOpp) ; set first player function name
}
Player1(TurnSum, SumMe, SumOpp) {
Return optimal(TurnSum, SumMe, SumOpp) ; set second player function name
}
Loop, % Play
{
;Random, FirstPlayer, 0, 1 ; to remove advantage of going first
CurrentPlayer := 0 ; set to FirstPlayer to compare same players with different N's
Sum0:=Sum1:=0
Loop
{
OtherPlayer:=!CurrentPlayer
If (Sum%CurrentPlayer%+TurnSum < 100
and Player%CurrentPlayer%(TurnSum, Sum%CurrentPlayer%, Sum%OtherPlayer%))
{
; Roll
Random, LastRoll, 1, 6
If (LastRoll != 1)
{
TurnSum += LastRoll
Continue
}
TurnSum := 0
}
; Hold
Sum%CurrentPlayer% += TurnSum
TurnSum := 0
If (Sum%CurrentPlayer% >= 100)
{
Wins%CurrentPlayer%++
Break
}
CurrentPlayer := !CurrentPlayer
}
}
Msgbox % "Player 0 won " Round(Wins0/Play*100,0) "%`nPlayer 1 won " Round(Wins1/Play*100,0) "%"
; Random; 1/N is ~ probablity of holding
Random(TurnSum, SumMe, SumOpp, N=9) {
Random, Roll, 0, N ; increase this last number to increase probability of rolling
Return Roll
}
; Always roll
Always(TurnSum, SumMe, SumOpp) {
Return 1
}
; Roll N times; N=6 beats all other RollNx players
RollNx(TurnSum, SumMe, SumOpp, N=6) {
Static Roll=0
Return Roll := TurnSum = 0 ? 1 : mod(Roll+1,N+1)
}
; Roll if TurnSum < N; N=19 beats all other RollToN players
RollToN(TurnSum, SumMe, SumOpp, N=19) {
Return Roll := TurnSum < N
}
; Roll if SumOpp > N or SumMe > N or TurnSum < 21 + (SumOpp - SumMe) / 8
Practical(TurnSum, SumMe, SumOpp, N=72) {
Return Roll := SumOpp > N or SumMe > N or TurnSum < 21+(SumOpp-SumMe)/8
}
; Optimal play per http://cs.gettysburg.edu/~tneller/nsf/pig/pig.pdf
Optimal(TurnSum, SumMe, SumOpp) {
Global Optimal
Roll := Optimal[SumMe,TurnSum,SumOpp+1]
Return Roll = "" ? 1 : Roll
}
- Output:
First Player win percent | Second Player: |
Always | Random N=9 |
RollNx N=6 |
RollToN N=19 |
Practical N=72 |
Optimal |
First Player: | |||||||
Always | 51% | 17% | 12% | 12% | 12% | 12% | |
Random N=9 |
84% | 52% | 30% | 29% | 27% | 26% | |
RollNx N=6 |
89% | 74% | 54% | 53% | 49% | 49% | |
RollToN N=19 |
89% | 76% | 54% | 54% | 49% | 49% | |
Practical N=72 |
88% | 77% | 58% | 58% | 53% | 53% | |
Optimal | 88% | 76% | 57% | 57% | 53% | 53% |
[edit] C++
The strategies implemented here are pretty simple:
Player 1 is a random player: he chooses a random number between 0 and 9 and if this number is smaller than 5 he'll roll otherwise he holds, unless his round score is zero, in this case he'll roll.
Player 2 always tries to score at least a quarter of the difference between he's current score and MAX_POINTS in a round.
Player 3 always tries to score at least 20 points in a round.
Player 4, just like player 3, always tries to score at least 20 points in a round. But as his round score increases, he gets a little "nervous", what increases the chances that he'll hold.
#include <windows.h>
#include <iostream>
#include <string>
//--------------------------------------------------------------------------------------------------
using namespace std;
//--------------------------------------------------------------------------------------------------
const int PLAYERS = 4, MAX_POINTS = 100;
//--------------------------------------------------------------------------------------------------
enum Moves { ROLL, HOLD };
//--------------------------------------------------------------------------------------------------
class player
{
public:
player() { current_score = round_score = 0; }
void addCurrScore() { current_score += round_score; }
int getCurrScore() { return current_score; }
int getRoundScore() { return round_score; }
void addRoundScore( int rs ) { round_score += rs; }
void zeroRoundScore() { round_score = 0; }
virtual int getMove() = 0;
virtual ~player() {}
protected:
int current_score, round_score;
};
//--------------------------------------------------------------------------------------------------
class RAND_Player : public player
{
virtual int getMove()
{
if( round_score + current_score >= MAX_POINTS ) return HOLD;
if( rand() % 10 < 5 ) return ROLL;
if( round_score > 0 ) return HOLD;
return ROLL;
}
};
//--------------------------------------------------------------------------------------------------
class Q2WIN_Player : public player
{
virtual int getMove()
{
if( round_score + current_score >= MAX_POINTS ) return HOLD;
int q = MAX_POINTS - current_score;
if( q < 6 ) return ROLL;
q /= 4;
if( round_score < q ) return ROLL;
return HOLD;
}
};
//--------------------------------------------------------------------------------------------------
class AL20_Player : public player
{
virtual int getMove()
{
if( round_score + current_score >= MAX_POINTS ) return HOLD;
if( round_score < 20 ) return ROLL;
return HOLD;
}
};
//--------------------------------------------------------------------------------------------------
class AL20T_Player : public player
{
virtual int getMove()
{
if( round_score + current_score >= MAX_POINTS ) return HOLD;
int d = ( 100 * round_score ) / 20;
if( round_score < 20 && d < rand() % 100 ) return ROLL;
return HOLD;
}
};
//--------------------------------------------------------------------------------------------------
class Auto_pigGame
{
public:
Auto_pigGame()
{
_players[0] = new RAND_Player();
_players[1] = new Q2WIN_Player();
_players[2] = new AL20_Player();
_players[3] = new AL20T_Player();
}
~Auto_pigGame()
{
delete _players[0];
delete _players[1];
delete _players[2];
delete _players[3];
}
void play()
{
int die, p = 0;
bool endGame = false;
while( !endGame )
{
switch( _players[p]->getMove() )
{
case ROLL:
die = rand() % 6 + 1;
if( die == 1 )
{
cout << "Player " << p + 1 << " rolled " << die << " - current score: " << _players[p]->getCurrScore() << endl << endl;
nextTurn( p );
continue;
}
_players[p]->addRoundScore( die );
cout << "Player " << p + 1 << " rolled " << die << " - round score: " << _players[p]->getRoundScore() << endl;
break;
case HOLD:
_players[p]->addCurrScore();
cout << "Player " << p + 1 << " holds - current score: " << _players[p]->getCurrScore() << endl << endl;
if( _players[p]->getCurrScore() >= MAX_POINTS )
endGame = true;
else nextTurn( p );
}
}
showScore();
}
private:
void nextTurn( int& p )
{
_players[p]->zeroRoundScore();
++p %= PLAYERS;
}
void showScore()
{
cout << endl;
cout << "Player I (RAND): " << _players[0]->getCurrScore() << endl;
cout << "Player II (Q2WIN): " << _players[1]->getCurrScore() << endl;
cout << "Player III (AL20): " << _players[2]->getCurrScore() << endl;
cout << "Player IV (AL20T): " << _players[3]->getCurrScore() << endl << endl << endl;
system( "pause" );
}
player* _players[PLAYERS];
};
//--------------------------------------------------------------------------------------------------
int main( int argc, char* argv[] )
{
srand( GetTickCount() );
Auto_pigGame pg;
pg.play();
return 0;
}
//--------------------------------------------------------------------------------------------------
- Output:
Player 1 rolled 1 - current score: 0 Player 2 rolled 5 - round score: 5 Player 2 rolled 1 - current score: 0 Player 3 rolled 3 - round score: 3 Player 3 rolled 5 - round score: 8 Player 3 rolled 4 - round score: 12 Player 3 rolled 5 - round score: 17 Player 3 rolled 6 - round score: 23 Player 3 holds - current score: 23 Player 4 rolled 5 - round score: 5 Player 4 rolled 1 - current score: 0 Player 1 rolled 5 - round score: 5 Player 1 holds - current score: 5 Player 2 rolled 6 - round score: 6 Player 2 rolled 2 - round score: 8 Player 2 rolled 3 - round score: 11 Player 2 rolled 2 - round score: 13 Player 2 rolled 3 - round score: 16 Player 2 rolled 6 - round score: 22 Player 2 rolled 6 - round score: 28 Player 2 holds - current score: 28 Player 3 rolled 3 - round score: 3 Player 3 rolled 2 - round score: 5 Player 3 rolled 3 - round score: 8 Player 3 rolled 1 - current score: 23 Player 4 rolled 5 - round score: 5 Player 4 rolled 2 - round score: 7 Player 4 rolled 5 - round score: 12 Player 4 rolled 5 - round score: 17 Player 4 holds - current score: 17 Player 1 rolled 2 - round score: 2 Player 1 holds - current score: 7 Player 2 rolled 6 - round score: 6 Player 2 rolled 3 - round score: 9 Player 2 rolled 2 - round score: 11 Player 2 rolled 6 - round score: 17 Player 2 rolled 1 - current score: 28 Player 3 rolled 4 - round score: 4 Player 3 rolled 3 - round score: 7 Player 3 rolled 1 - current score: 23 Player 4 rolled 3 - round score: 3 Player 4 rolled 6 - round score: 9 Player 4 rolled 4 - round score: 13 Player 4 holds - current score: 30 Player 1 rolled 5 - round score: 5 Player 1 holds - current score: 12 Player 2 rolled 2 - round score: 2 Player 2 rolled 6 - round score: 8 Player 2 rolled 2 - round score: 10 Player 2 rolled 1 - current score: 28 Player 3 rolled 4 - round score: 4 Player 3 rolled 4 - round score: 8 Player 3 rolled 4 - round score: 12 Player 3 rolled 2 - round score: 14 Player 3 rolled 4 - round score: 18 Player 3 rolled 2 - round score: 20 Player 3 holds - current score: 43 Player 4 rolled 2 - round score: 2 Player 4 rolled 2 - round score: 4 Player 4 rolled 1 - current score: 30 Player 1 rolled 1 - current score: 12 Player 2 rolled 2 - round score: 2 Player 2 rolled 2 - round score: 4 Player 2 rolled 3 - round score: 7 Player 2 rolled 2 - round score: 9 Player 2 rolled 1 - current score: 28 Player 3 rolled 6 - round score: 6 Player 3 rolled 4 - round score: 10 Player 3 rolled 3 - round score: 13 Player 3 rolled 5 - round score: 18 Player 3 rolled 5 - round score: 23 Player 3 holds - current score: 66 Player 4 rolled 3 - round score: 3 Player 4 rolled 1 - current score: 30 Player 1 rolled 5 - round score: 5 Player 1 holds - current score: 17 Player 2 rolled 5 - round score: 5 Player 2 rolled 6 - round score: 11 Player 2 rolled 5 - round score: 16 Player 2 rolled 3 - round score: 19 Player 2 holds - current score: 47 Player 3 rolled 1 - current score: 66 Player 4 rolled 2 - round score: 2 Player 4 rolled 5 - round score: 7 Player 4 holds - current score: 37 Player 1 rolled 2 - round score: 2 Player 1 rolled 6 - round score: 8 Player 1 holds - current score: 25 Player 2 rolled 4 - round score: 4 Player 2 rolled 6 - round score: 10 Player 2 rolled 4 - round score: 14 Player 2 holds - current score: 61 Player 3 rolled 4 - round score: 4 Player 3 rolled 6 - round score: 10 Player 3 rolled 2 - round score: 12 Player 3 rolled 5 - round score: 17 Player 3 rolled 6 - round score: 23 Player 3 holds - current score: 89 Player 4 rolled 2 - round score: 2 Player 4 holds - current score: 39 Player 1 rolled 6 - round score: 6 Player 1 holds - current score: 31 Player 2 rolled 1 - current score: 61 Player 3 rolled 5 - round score: 5 Player 3 rolled 1 - current score: 89 Player 4 rolled 2 - round score: 2 Player 4 rolled 2 - round score: 4 Player 4 rolled 3 - round score: 7 Player 4 holds - current score: 46 Player 1 rolled 1 - current score: 31 Player 2 rolled 3 - round score: 3 Player 2 rolled 3 - round score: 6 Player 2 rolled 4 - round score: 10 Player 2 holds - current score: 71 Player 3 rolled 6 - round score: 6 Player 3 rolled 6 - round score: 12 Player 3 holds - current score: 101 Player I (RAND): 31 Player II (Q2WIN): 71 Player III (AL20): 101 Player IV (AL20T): 46
[edit] Common Lisp
Just implemented two strategies. One is actually a variable strategy which holds until a specific value is reached and then turns the dice over. The default value is 25. The other is from "Practical Play of the Dice Game Pig" by ToddW. Neller and Clifton G.M. Presser. Their suggested strategy is "If either player’s score is 71 or higher, roll for the goal. Otherwise, hold at 21 + (j - i) / 8" where j is the other player's score and i is the strategizing player's score. The scoring is handled by generic functions on the player type.
(defclass player ()
((score :initform 0 :accessor score)
(name :initarg :name :accessor name)))
(defun make-player (name)
(make-instance 'player :name name))
(defmethod has-won ((player player))
(>= (score player) 100))
(defclass score-based (player)
((score-base :initarg :score-base :initform 25 :accessor score-base)))
(defun make-score-based (name &optional (base 25))
(make-instance 'score-based :score-base base :name name))
(defmethod roll-again ((player score-based) other turn-score)
(declare (ignorable other))
(< turn-score (score-base player)))
(defclass neller (player) ())
(defun make-neller (name) (make-instance 'neller :name name))
(defmethod roll-again ((player neller) other turn-score)
(let ((other-score (score other)) (my-score (score player)))
(or
(> other-score 71)
(> my-score 71)
(< turn-score (+ 21 (/ (- other-score my-score) 8))))))
(defun query-turn (player other roll added-score)
(format t "~A: Rolled a ~A - Turn: ~A Current Score: ~A Keep rolling (Y, N or Q)?"
(name player)
roll
added-score
(+ added-score (score player)))
(let ((ret (roll-again player other added-score)))
(if ret (format t "Y~%") (format t "N~%"))
ret))
(defun do-turns (player other)
(do ((new-score 0)
(take-turn t))
((not take-turn) (setf (score player) (+ (score player) new-score)))
(let ((roll (+ 1 (random 6))))
(cond
((>= (+ (score player) roll new-score) 100)
(format t "~A rolls a ~A and WINS!~%" (name player) roll)
(setf new-score (+ new-score roll))
(setf take-turn nil))
((eql 1 roll)
(format t "Ooh! Sorry - ~A rolled a 1 and busted!~%" (name player))
(setf new-score 0)
(setf take-turn nil))
(t
(setf new-score (+ new-score roll))
(setf take-turn (query-turn player other roll new-score)))))))
(defun play-pig-winner (p1 p2)
(do* ((otherplayer p2 curplayer)
(curplayer p1 (if (eql curplayer p1) p2 p1)))
((has-won otherplayer) otherplayer)
(do-turns curplayer otherplayer)))
(defun play-pig-player (player1 player2)
(catch 'quit (format t "Hooray! ~A won the game!"
Output:
Darrell: Rolled a 4 - Turn: 4 Current Score: 4 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 3 - Turn: 7 Current Score: 7 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 3 - Turn: 10 Current Score: 10 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Darrell rolled a 1 and busted!
Marvin: Rolled a 3 - Turn: 3 Current Score: 3 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 6 - Turn: 9 Current Score: 9 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 3 - Turn: 12 Current Score: 12 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 4 - Turn: 16 Current Score: 16 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Marvin rolled a 1 and busted!
Darrell: Rolled a 2 - Turn: 2 Current Score: 2 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 4 - Turn: 6 Current Score: 6 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Darrell rolled a 1 and busted!
Marvin: Rolled a 3 - Turn: 3 Current Score: 3 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 2 - Turn: 5 Current Score: 5 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Marvin rolled a 1 and busted!
Darrell: Rolled a 3 - Turn: 3 Current Score: 3 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 2 - Turn: 5 Current Score: 5 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Darrell rolled a 1 and busted!
Ooh! Sorry - Marvin rolled a 1 and busted!
Darrell: Rolled a 6 - Turn: 6 Current Score: 6 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 5 - Turn: 11 Current Score: 11 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 2 - Turn: 13 Current Score: 13 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Darrell rolled a 1 and busted!
Marvin: Rolled a 5 - Turn: 5 Current Score: 5 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 6 - Turn: 11 Current Score: 11 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 3 - Turn: 14 Current Score: 14 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 2 - Turn: 16 Current Score: 16 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 3 - Turn: 19 Current Score: 19 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 2 - Turn: 21 Current Score: 21 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 5 - Turn: 26 Current Score: 26 Keep rolling (Y, N or Q)?N
Darrell: Rolled a 3 - Turn: 3 Current Score: 3 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 2 - Turn: 5 Current Score: 5 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Darrell rolled a 1 and busted!
Ooh! Sorry - Marvin rolled a 1 and busted!
Ooh! Sorry - Darrell rolled a 1 and busted!
Ooh! Sorry - Marvin rolled a 1 and busted!
Darrell: Rolled a 6 - Turn: 6 Current Score: 6 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 2 - Turn: 8 Current Score: 8 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 3 - Turn: 11 Current Score: 11 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 6 - Turn: 17 Current Score: 17 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 3 - Turn: 20 Current Score: 20 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 3 - Turn: 23 Current Score: 23 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 5 - Turn: 28 Current Score: 28 Keep rolling (Y, N or Q)?N
Marvin: Rolled a 6 - Turn: 6 Current Score: 32 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 5 - Turn: 11 Current Score: 37 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Marvin rolled a 1 and busted!
Darrell: Rolled a 6 - Turn: 6 Current Score: 34 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 5 - Turn: 11 Current Score: 39 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 6 - Turn: 17 Current Score: 45 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 4 - Turn: 21 Current Score: 49 Keep rolling (Y, N or Q)?N
Marvin: Rolled a 5 - Turn: 5 Current Score: 31 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 3 - Turn: 8 Current Score: 34 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 5 - Turn: 13 Current Score: 39 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 5 - Turn: 18 Current Score: 44 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 5 - Turn: 23 Current Score: 49 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 5 - Turn: 28 Current Score: 54 Keep rolling (Y, N or Q)?N
Darrell: Rolled a 6 - Turn: 6 Current Score: 55 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 5 - Turn: 11 Current Score: 60 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 6 - Turn: 17 Current Score: 66 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Darrell rolled a 1 and busted!
Ooh! Sorry - Marvin rolled a 1 and busted!
Darrell: Rolled a 6 - Turn: 6 Current Score: 55 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 5 - Turn: 11 Current Score: 60 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 4 - Turn: 15 Current Score: 64 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 5 - Turn: 20 Current Score: 69 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Darrell rolled a 1 and busted!
Marvin: Rolled a 2 - Turn: 2 Current Score: 56 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 5 - Turn: 7 Current Score: 61 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 4 - Turn: 11 Current Score: 65 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 5 - Turn: 16 Current Score: 70 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 2 - Turn: 18 Current Score: 72 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Marvin rolled a 1 and busted!
Ooh! Sorry - Darrell rolled a 1 and busted!
Marvin: Rolled a 6 - Turn: 6 Current Score: 60 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Marvin rolled a 1 and busted!
Darrell: Rolled a 4 - Turn: 4 Current Score: 53 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 6 - Turn: 10 Current Score: 59 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 6 - Turn: 16 Current Score: 65 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 2 - Turn: 18 Current Score: 67 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 4 - Turn: 22 Current Score: 71 Keep rolling (Y, N or Q)?N
Marvin: Rolled a 5 - Turn: 5 Current Score: 59 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 5 - Turn: 10 Current Score: 64 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 5 - Turn: 15 Current Score: 69 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 6 - Turn: 21 Current Score: 75 Keep rolling (Y, N or Q)?Y
Marvin: Rolled a 4 - Turn: 25 Current Score: 79 Keep rolling (Y, N or Q)?N
Darrell: Rolled a 2 - Turn: 2 Current Score: 73 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 4 - Turn: 6 Current Score: 77 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 2 - Turn: 8 Current Score: 79 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 3 - Turn: 11 Current Score: 82 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 4 - Turn: 15 Current Score: 86 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Darrell rolled a 1 and busted!
Marvin: Rolled a 4 - Turn: 4 Current Score: 83 Keep rolling (Y, N or Q)?Y
Ooh! Sorry - Marvin rolled a 1 and busted!
Darrell: Rolled a 5 - Turn: 5 Current Score: 76 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 3 - Turn: 8 Current Score: 79 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 5 - Turn: 13 Current Score: 84 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 3 - Turn: 16 Current Score: 87 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 6 - Turn: 22 Current Score: 93 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 2 - Turn: 24 Current Score: 95 Keep rolling (Y, N or Q)?Y
Darrell: Rolled a 2 - Turn: 26 Current Score: 97 Keep rolling (Y, N or Q)?Y
Darrell rolls a 3 and WINS!
Hooray! Darrell won the game!
NIL
[edit] D
import std.stdio, std.random;
enum nPlayers = 4, maxPoints = 100;
enum Moves { roll, hold }
abstract class Player {
public:
final void addCurrScore() pure nothrow {
current_score += round_score;
}
final int getCurrScore() const pure nothrow {
return current_score;
}
final int getRoundScore() const pure nothrow {
return round_score;
}
final void addRoundScore(in int rs) pure nothrow {
round_score += rs;
}
final void zeroRoundScore() pure nothrow {
round_score = 0;
}
Moves getMove();
protected int current_score, round_score;
}
final class PlayerRand: Player {
override Moves getMove() {
if (round_score + current_score >= maxPoints)
return Moves.hold;
if (uniform(0, 2) == 0)
return Moves.roll;
if (round_score > 0)
return Moves.hold;
return Moves.roll;
}
}
final class PlayerQ2Win: Player {
override Moves getMove() {
if (round_score + current_score >= maxPoints)
return Moves.hold;
int q = maxPoints - current_score;
if (q < 6)
return Moves.roll;
q /= 4;
if (round_score < q)
return Moves.roll;
return Moves.hold;
}
}
final class PlayerAL20: Player {
override Moves getMove() {
if (round_score + current_score >= maxPoints)
return Moves.hold;
if (round_score < 20)
return Moves.roll;
return Moves.hold;
}
}
final class PlayerAL20T: Player {
override Moves getMove() {
if (round_score + current_score >= maxPoints)
return Moves.hold;
immutable d = (100 * round_score) / 20;
if (round_score < 20 && d < uniform(0, 100))
return Moves.roll;
return Moves.hold;
}
}
void main() {
auto players = [new PlayerRand, new PlayerQ2Win,
new PlayerAL20, new PlayerAL20T];
void nextTurn(ref uint p) nothrow {
players[p].zeroRoundScore;
p = (p + 1) % nPlayers;
}
uint p = 0;
bool endGame = false;
while (!endGame) {
final switch (players[p].getMove) {
case Moves.roll:
immutable die = uniform(1, 7);
if (die == 1) {
writeln("Player ", p + 1, " rolled ", die,
" - current score: ",
players[p].getCurrScore, "\n");
nextTurn(p);
continue;
}
players[p].addRoundScore(die);
writeln("Player ", p + 1, " rolled ", die,
" - round score: ",
players[p].getRoundScore);
break;
case Moves.hold:
players[p].addCurrScore;
writeln("Player ", p + 1,
" holds - current score: ",
players[p].getCurrScore, "\n");
if (players[p].getCurrScore >= maxPoints)
endGame = true;
else
nextTurn(p);
}
}
writeln;
writeln("Player I (Rand): ", players[0].getCurrScore);
writeln("Player II (Q2Win): ", players[1].getCurrScore);
writeln("Player III (AL20): ", players[2].getCurrScore);
writeln("Player IV (AL20T): ", players[3].getCurrScore, "\n\n");
}
The output is similar to the C++ entry.
[edit] Erlang
Four players take turns starting. Their strategy is how long to wait before holding. They aim for 5, 10, 15 and 20 rolls. Player20 managed better than I thought it would.
-module( pig_dice_player ).
-export( [task/0] ).
task() ->
Goal = pig_dice:goal(),
Players_holds = [{"Player"++ erlang:integer_to_list(X), X} || X <- [5, 10, 15, 20]],
Fun = fun ({Player, Total}, Dict) when Total >= Goal -> dict:update_counter( Player, 1, Dict );
(_Player_total, Dict) -> Dict
end,
Dict = lists:foldl( Fun, dict:new(), task_play(Players_holds, Goal, []) ),
display( dict:to_list(Dict) ).
display( Results ) ->
[{Name, Total} | Rest] = lists:reverse( lists:keysort(2, Results) ),
io:fwrite( "Winner is ~p with total of ~p wins~n", [Name, Total] ),
io:fwrite( "Then follows: " ),
[io:fwrite("~p with ~p~n", [N, T]) || {N, T} <- Rest].
is_goal_reached( Score, Player, Goal, Player, Game ) ->
Score + proplists:get_value(Player, pig_dice:players_totals(Game)) >= Goal;
is_goal_reached( _Score, _Other_player, _Goal, _Player, _Game ) -> false.
loop( Hold, Hold, Goal, Player, Game ) ->
pig_dice:hold( Player, Game ),
loop( 1, Hold, Goal, Player, Game );
loop( N, Hold, Goal, Player, Game ) ->
loop_await_my_turn( pig_dice:player_name(Game), Player, Game ),
pig_dice:roll( Player, Game ),
Is_goal_reached = is_goal_reached( pig_dice:score(Game), pig_dice:player_name(Game), Goal, Player, Game ),
loop_done( Is_goal_reached, N, Hold, Goal, Player, Game ).
loop_await_my_turn( Player, Player, _Game ) -> ok;
loop_await_my_turn( _Other, Player, Game ) -> loop_await_my_turn( pig_dice:player_name(Game), Player, Game ).
loop_done( true, _N, _Hold, _Goal, Player, Game ) -> pig_dice:hold( Player, Game );
loop_done( false, N, Hold, Goal, Player, Game ) -> loop( N + 1, Hold, Goal, Player, Game ).
rotate( [H | T] ) -> T ++ [H].
task_play( Players_holds, _Goal, Acc ) when erlang:length(Players_holds) =:= erlang:length(Acc) -> lists:flatten( Acc );
task_play( Players_holds, Goal, Acc ) ->
Results = [task_play_n(Players_holds, Goal) || _X <- lists:seq(1, 100)],
task_play( rotate(Players_holds), Goal, [Results | Acc] ).
task_play_n( Players_holds, Goal ) ->
Game = pig_dice:game( [X || {X, _Y} <- Players_holds] ),
Pids = [erlang:spawn(fun() -> loop(1, Y, Goal, X, Game) end) || {X, Y} <- Players_holds],
receive
{pig, Result, Game} ->
[erlang:exit(X, kill) || X <- [Game | Pids]],
Result
end.
- Output:
115> pig_dice_player:task(). Winner is "Player10" with total of 121 wins Then follows: "Player15" with 120 "Player20" with 85 "Player5" with 74
[edit] Go
package pig
import (
"fmt"
"math/rand"
"time"
)
type (
PlayerID int
MessageID int
StrategyID int
PigGameData struct {
player PlayerID
turnCount int
turnRollCount int
turnScore int
lastRoll int
scores [2]int
verbose bool
}
)
const (
// Status messages
gameOver = iota
piggedOut
rolls
pointSpending
holds
turn
gameOverSummary
// Players
player1 = PlayerID(0)
player2 = PlayerID(1)
noPlayer = PlayerID(-1)
// Max score
maxScore = 100
// Strategies
scoreChaseStrat = iota
rollCountStrat
)
// Returns "s" if n != 1
func pluralS(n int) string {
if n != 1 {
return "s"
}
return ""
}
// Creates an intializes a new PigGameData structure, returns a *PigGameData
func New() *PigGameData {
return &PigGameData{0, 0, 0, 0, 0, [2]int{0, 0}, false}
}
// Create a status message for a given message ID
func (pg *PigGameData) statusMessage(id MessageID) string {
var msg string
switch id {
case gameOver:
msg = fmt.Sprintf("Game is over after %d turns", pg.turnCount)
case piggedOut:
msg = fmt.Sprintf(" Pigged out after %d roll%s", pg.turnRollCount, pluralS(pg.turnRollCount))
case rolls:
msg = fmt.Sprintf(" Rolls %d", pg.lastRoll)
case pointSpending:
msg = fmt.Sprintf(" %d point%s pending", pg.turnScore, pluralS(pg.turnScore))
case holds:
msg = fmt.Sprintf(" Holds after %d turns, adding %d points for a total of %d", pg.turnRollCount, pg.turnScore, pg.PlayerScore(noPlayer))
case turn:
msg = fmt.Sprintf("Player %d's turn:", pg.player+1)
case gameOverSummary:
msg = fmt.Sprintf("Game over after %d turns\n player 1 %d\n player 2 %d\n", pg.turnCount, pg.PlayerScore(player1), pg.PlayerScore(player2))
}
return msg
}
// Print a status message, if pg.Verbose is true
func (pg *PigGameData) PrintStatus(id MessageID) {
if pg.verbose {
fmt.Println(pg.statusMessage(id))
}
}
// Play a given strategy
func (pg *PigGameData) Play(id StrategyID) (keepPlaying bool) {
if pg.GameOver() {
pg.PrintStatus(gameOver)
return false
}
if pg.turnCount == 0 {
pg.player = player2
pg.NextPlayer()
}
pg.lastRoll = rand.Intn(6) + 1
pg.PrintStatus(rolls)
pg.turnRollCount++
if pg.lastRoll == 1 {
pg.PrintStatus(piggedOut)
pg.NextPlayer()
} else {
pg.turnScore += pg.lastRoll
pg.PrintStatus(pointSpending)
success := false
switch id {
case scoreChaseStrat:
success = pg.scoreChaseStrategy()
case rollCountStrat:
success = pg.rollCountStrategy()
}
if success {
pg.Hold()
pg.NextPlayer()
}
}
return true
}
// Get the score for a given player
func (pg *PigGameData) PlayerScore(id PlayerID) int {
if id == noPlayer {
return pg.scores[pg.player]
}
return pg.scores[id]
}
// Check if the game is over
func (pg *PigGameData) GameOver() bool {
return pg.scores[player1] >= maxScore || pg.scores[player2] >= maxScore
}
// Returns the Player ID if there is a winner, or -1
func (pg *PigGameData) Winner() PlayerID {
for index, score := range pg.scores {
if score >= maxScore {
return PlayerID(index)
}
}
return noPlayer
}
// Get the ID of the other player
func (pg *PigGameData) otherPlayer() PlayerID {
// 0 becomes 1, 1 becomes 0
return 1 - pg.player
}
func (pg *PigGameData) Hold() {
pg.scores[pg.player] += pg.turnScore
pg.PrintStatus(holds)
pg.turnRollCount, pg.turnScore = 0, 0
}
func (pg *PigGameData) NextPlayer() {
pg.turnCount++
pg.turnRollCount, pg.turnScore = 0, 0
pg.player = pg.otherPlayer()
pg.PrintStatus(turn)
}
func (pg *PigGameData) rollCountStrategy() bool {
return pg.turnRollCount >= 3
}
func (pg *PigGameData) scoreChaseStrategy() bool {
myScore := pg.PlayerScore(pg.player)
otherScore := pg.PlayerScore(pg.otherPlayer())
myPendingScore := pg.turnScore + myScore
return myPendingScore >= maxScore || myPendingScore > otherScore || pg.turnRollCount >= 5
}
// Run the simulation
func main() {
// Seed the random number generator
rand.Seed(time.Now().UnixNano())
// Start a new game
pg := New()
pg.verbose = true
strategies := [2]StrategyID{scoreChaseStrat, rollCountStrat}
// Play until game over
for !pg.GameOver() {
pg.Play(strategies[pg.player])
}
pg.PrintStatus(gameOverSummary)
}
Sample run, player one just tries to keep ahead, while player two always tries to take three rolls, no more.
Player 1's turn: Rolls 4 4 points pending Holds after 1 turns, adding 4 points for a total of 4 Player 2's turn: Rolls 4 4 points pending Rolls 1 Pigged out after 2 rolls Player 1's turn: Rolls 6 6 points pending Holds after 1 turns, adding 6 points for a total of 10 Player 2's turn: Rolls 6 6 points pending Rolls 3 9 points pending Rolls 4 13 points pending Holds after 3 turns, adding 13 points for a total of 13 Player 1's turn: Rolls 4 4 points pending Holds after 1 turns, adding 4 points for a total of 14 Player 2's turn: Rolls 4 4 points pending Rolls 6 10 points pending Rolls 1 Pigged out after 3 rolls Player 1's turn: Rolls 4 4 points pending Holds after 1 turns, adding 4 points for a total of 18 Player 2's turn: Rolls 3 3 points pending Rolls 4 7 points pending Rolls 2 9 points pending Holds after 3 turns, adding 9 points for a total of 22 Player 1's turn: Rolls 2 2 points pending Rolls 1 Pigged out after 2 rolls Player 2's turn: Rolls 1 Pigged out after 1 roll Player 1's turn: Rolls 4 4 points pending Rolls 1 Pigged out after 2 rolls Player 2's turn: Rolls 5 5 points pending Rolls 1 Pigged out after 2 rolls Player 1's turn: Rolls 5 5 points pending Holds after 1 turns, adding 5 points for a total of 23 Player 2's turn: Rolls 5 5 points pending Rolls 4 9 points pending Rolls 4 13 points pending Holds after 3 turns, adding 13 points for a total of 35 Player 1's turn: Rolls 1 Pigged out after 1 roll Player 2's turn: Rolls 3 3 points pending Rolls 3 6 points pending Rolls 2 8 points pending Holds after 3 turns, adding 8 points for a total of 43 Player 1's turn: Rolls 1 Pigged out after 1 roll Player 2's turn: Rolls 6 6 points pending Rolls 4 10 points pending Rolls 1 Pigged out after 3 rolls Player 1's turn: Rolls 4 4 points pending Rolls 1 Pigged out after 2 rolls Player 2's turn: Rolls 2 2 points pending Rolls 4 6 points pending Rolls 2 8 points pending Holds after 3 turns, adding 8 points for a total of 51 Player 1's turn: Rolls 1 Pigged out after 1 roll Player 2's turn: Rolls 4 4 points pending Rolls 2 6 points pending Rolls 3 9 points pending Holds after 3 turns, adding 9 points for a total of 60 Player 1's turn: Rolls 2 2 points pending Rolls 6 8 points pending Rolls 3 11 points pending Rolls 6 17 points pending Rolls 4 21 points pending Holds after 5 turns, adding 21 points for a total of 44 Player 2's turn: Rolls 4 4 points pending Rolls 2 6 points pending Rolls 3 9 points pending Holds after 3 turns, adding 9 points for a total of 69 Player 1's turn: Rolls 6 6 points pending Rolls 5 11 points pending Rolls 6 17 points pending Rolls 5 22 points pending Rolls 4 26 points pending Holds after 5 turns, adding 26 points for a total of 70 Player 2's turn: Rolls 5 5 points pending Rolls 4 9 points pending Rolls 2 11 points pending Holds after 3 turns, adding 11 points for a total of 80 Player 1's turn: Rolls 6 6 points pending Rolls 6 12 points pending Holds after 2 turns, adding 12 points for a total of 82 Player 2's turn: Rolls 2 2 points pending Rolls 3 5 points pending Rolls 3 8 points pending Holds after 3 turns, adding 8 points for a total of 88 Player 1's turn: Rolls 5 5 points pending Rolls 2 7 points pending Holds after 2 turns, adding 7 points for a total of 89 Player 2's turn: Rolls 3 3 points pending Rolls 2 5 points pending Rolls 5 10 points pending Holds after 3 turns, adding 10 points for a total of 98 Player 1's turn: Rolls 6 6 points pending Rolls 3 9 points pending Rolls 6 15 points pending Holds after 3 turns, adding 15 points for a total of 104 Player 2's turn: Game over after 32 turns player 1 104 player 2 98
[edit] J
This is a partial implementation of the current task.
This is a routine to estimate the value of rolling, given the current total of rolls which the player is building (left argument) and the current total of rolls which are a permanent part of the player's score (right argument).
If the expected value is positive, it's probably in the best interest of the player to take the roll. That said, a more sophisticated strategy might play cautiously when a player is sufficiently ahead of the other player(s).
pigval=:4 :0
(+/%#)(-x),}.(1+i.6)<.100-y+x
)
Examples:
10 pigval 90
_1.66667
If we have 10 points from our current rolls and have 90 permanent points, rolling again is a bad idea.
0 5 10 15 20 pigval"0/60 65 70 75 80 85 90 95 100
3.33333 3.33333 3.33333 3.33333 3.33333 3.33333 3.33333 3.16667 0
2.5 2.5 2.5 2.5 2.5 2.5 2.33333 _0.833333 _5
1.66667 1.66667 1.66667 1.66667 1.66667 1.5 _1.66667 _5.83333 _10
0.833333 0.833333 0.833333 0.833333 0.666667 _2.5 _6.66667 _10.8333 _15
0 0 0 _0.166667 _3.33333 _7.5 _11.6667 _15.8333 _20
If we have 70 permanent points (or less) we should probably re-roll when our uncommitted rolls total to less than 20.
(1+i.19) ([,:1+i:~) +/ 0 < pigval"0/~ 1+i.100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
98 97 96 95 93 92 91 90 89 87 86 85 84 82 81 80 78 77 75
This is a table of decision points. First row represents sum of our current uncommitted rolls. Second row represents the maximum permanent score where you should roll again with that number of uncommitted points, if we are using this estimation mechanism to choose our actions. Note that the first four columns here should have some obvious validity -- for example, if we have 96 permanent points and we have rolled 4 uncommitted points, we have won the game and we gain nothing from rerolling... Note also that this decision mechanism says we should never reroll if we have at least 20 uncommitted points.
[edit] Perl 6
This implements a pig player class where you can customize the strategy it uses. Pass a strategy code reference in that will evaluate to a Boolean value. The player will roll the die then decide whether to roll again or lock in its winnings based on its strategy. It will continue to roll until it gets a 1 (bust) or the strategy code reference evaluates to True (finished turn).
Set up as many players as you want, then run it. It will play 100 games (by default) then report the score for each game then the win totals for each player. If you want to play a different number of games, pass the number at the command line as a parameter.
Here we have 5 players:
player 0 uses the default strategy, always roll if it can. player 1 will roll up to 5 times then lock in whatever it earned. player 2 will try to get at least 20 points per turn. player 3 randomly picks whether to roll again or not biased so that there is a 90% chance that it will. player 4 randomly chooses to roll again but gets more consrvative as its score get closer to the goal.
my $games = @*ARGS ?? (shift @*ARGS) !! 100;
constant DIE = 1 .. 6;
constant GOAL = 100;
class player {
has $.score is rw = 0;
has $.ante is rw;
has $.rolls is rw;
has &.strategy is rw = sub { False }; # default, always roll again
method turn {
my $done_turn = False;
$.rolls = 0;
$.ante = 0;
repeat {
given DIE.roll {
$.rolls++;
when 1 {
$.ante = 0;
$done_turn = True;
}
when 2..* {
$.ante += $_;
}
}
$done_turn = True if $.score + $.ante >= GOAL or (&.strategy)();
} until $done_turn;
$.score += $.ante;
}
}
my @players;
# default, go-for-broke, always roll again
@players[0] = player.new;
# try to roll 5 times but no more per turn
@players[1] = player.new( strategy => sub { @players[1].rolls >= 5 } );
# try to accumulate at least 20 points per turn
@players[2] = player.new( strategy => sub { @players[2].ante > 20 } );
# random but 90% chance of rolling again
@players[3] = player.new( strategy => sub { 1.rand < .1 } );
# random but more conservative as approaches goal
@players[4] = player.new( strategy => sub { 1.rand < ( GOAL - @players[4].score ) * .6 / GOAL } );
my @wins = 0 xx @players;
for ^ $games {
my $player = -1;
repeat {
$player++;
@players[$player % @players].turn;
} until @players[$player % @players].score >= GOAL;
@wins[$player % @players]++;
say join "\t", @players>>.score;
@players[$_].score = 0 for ^@players; # reset scores for next game
}
say "\nSCORES: for $games games";
say join "\t", @wins;
Sample output for 10000 games
0 103 46 5 40 0 100 69 0 48 0 105 22 7 44 0 75 69 19 102 105 21 23 5 17 0 101 85 12 29 0 70 66 103 23 0 0 104 69 20 0 100 44 0 20 0 102 63 75 30 0 56 101 12 40 0 103 71 2 38 0 103 91 21 32 0 18 102 47 28 ... ... ... 104 0 69 14 47 0 68 101 13 22 0 99 89 102 31 SCORES: for 10000 games 947 3534 3396 1714 409
[edit] Python
There are now three player strategies:
- A random player RandPlay that rolls randomly.
- The RollTo20 player that rolls if that rounds score is less than 20.
- The Desparat player that plays like RollTo20 until any player gets within 20 of winning whereupon it desperately keeps rolling.
Details of the RollTo20 and Desparat strategy came from a paper referenced from here.
Player instances are passed full (single) game statistics and so can be more complex in their behaviour.
Notice how Pythons Counter class from the standard library is used to collate the winning statistics near the end of the program without much additional code.
#!/usr/bin/python3
'''
See: http://en.wikipedia.org/wiki/Pig_(dice)
This program scores, throws the dice, and plays for an N player game of Pig.
'''
from random import randint
from collections import namedtuple
import random
from pprint import pprint as pp
from collections import Counter
playercount = 2
maxscore = 100
maxgames = 100000
Game = namedtuple('Game', 'players, maxscore, rounds')
Round = namedtuple('Round', 'who, start, scores, safe')
class Player():
def __init__(self, player_index):
self.player_index = player_index
def __repr__(self):
return '%s(%i)' % (self.__class__.__name__, self.player_index)
def __call__(self, safescore, scores, game):
'Returns boolean True to roll again'
pass
class RandPlay(Player):
def __call__(self, safe, scores, game):
'Returns random boolean choice of whether to roll again'
return bool(random.randint(0, 1))
class RollTo20(Player):
def __call__(self, safe, scores, game):
'Roll again if this rounds score < 20'
return (((sum(scores) + safe[self.player_index]) < maxscore) # Haven't won yet
and(sum(scores) < 20)) # Not at 20 this round
class Desparat(Player):
def __call__(self, safe, scores, game):
'Roll again if this rounds score < 20 or someone is within 20 of winning'
return (((sum(scores) + safe[self.player_index]) < maxscore) # Haven't won yet
and( (sum(scores) < 20) # Not at 20 this round
or max(safe) >= (maxscore - 20))) # Someone's close
def game__str__(self):
'Pretty printer for Game class'
return ("Game(players=%r, maxscore=%i,\n rounds=[\n %s\n ])"
% (self.players, self.maxscore,
',\n '.join(repr(round) for round in self.rounds)))
Game.__str__ = game__str__
def winningorder(players, safescores):
'Return (players in winning order, their scores)'
return tuple(zip(*sorted(zip(players, safescores),
key=lambda x: x[1], reverse=True)))
def playpig(game):
'''
Plays the game of pig returning the players in winning order
and their scores whilst updating argument game with the details of play.
'''
players, maxscore, rounds = game
playercount = len(players)
safescore = [0] * playercount # Safe scores for each player
player = 0 # Who plays this round
scores=[] # Individual scores this round
while max(safescore) < maxscore:
startscore = safescore[player]
rolling = players[player](safescore, scores, game)
if rolling:
rolled = randint(1, 6)
scores.append(rolled)
if rolled == 1:
# Bust!
round = Round(who=players[player],
start=startscore,
scores=scores,
safe=safescore[player])
rounds.append(round)
scores, player = [], (player + 1) % playercount
else:
# Stick
safescore[player] += sum(scores)
round = Round(who=players[player],
start=startscore,
scores=scores,
safe=safescore[player])
rounds.append(round)
if safescore[player] >= maxscore:
break
scores, player = [], (player + 1) % playercount
# return players in winning order and all scores
return winningorder(players, safescore)
if __name__ == '__main__':
game = Game(players=tuple(RandPlay(i) for i in range(playercount)),
maxscore=20,
rounds=[])
print('ONE GAME')
print('Winning order: %r; Respective scores: %r\n' % playpig(game))
print(game)
game = Game(players=tuple(RandPlay(i) for i in range(playercount)),
maxscore=maxscore,
rounds=[])
algos = (RollTo20, RandPlay, Desparat)
print('\n\nMULTIPLE STATISTICS using %r\n for %i GAMES'
% (', '.join(p.__name__ for p in algos), maxgames,))
winners = Counter(repr(playpig(game._replace(players=tuple(random.choice(algos)(i)
for i in range(playercount)),
rounds=[]))[0])
for i in range(maxgames))
print(' Players(position) winning on left; occurrences on right:\n %s'
% ',\n '.join(str(w) for w in winners.most_common()))
- Output:
First is shown the game data for a single game with reduced maxscore then statistics on multiple games.
Desparat beats RollTo20 beats RandPlay on average. It doesn't matter if they play first or not when playing against another strategies. When both players use the same strategies there may be an advantage in going first.
ONE GAME Winner: RandPlay(0); Scores: [24, 12] Game(players=(RandPlay(0), RandPlay(1)), maxscore=20, rounds=[ Round(who=RandPlay(0), start=0, scores=[], safe=0), Round(who=RandPlay(1), start=0, scores=[6, 2], safe=8), Round(who=RandPlay(0), start=0, scores=[], safe=0), Round(who=RandPlay(1), start=8, scores=[], safe=8), Round(who=RandPlay(0), start=0, scores=[], safe=0), Round(who=RandPlay(1), start=8, scores=[4], safe=12), Round(who=RandPlay(0), start=0, scores=[4, 5, 6, 4, 5], safe=24) ]) MULTIPLE STATISTICS using 'RollTo20, RandPlay, Desparat' for 100000 GAMES Players(position) winning on left; occurrences on right: ('(Desparat(1), RandPlay(0))', 11152), ('(RollTo20(1), RandPlay(0))', 11114), ('(Desparat(0), RandPlay(1))', 11072), ('(RollTo20(0), RandPlay(1))', 11007), ('(Desparat(0), RollTo20(1))', 6405), ('(RollTo20(0), RollTo20(1))', 6013), ('(Desparat(0), Desparat(1))', 5820), ('(Desparat(1), RollTo20(0))', 5772), ('(RandPlay(0), RandPlay(1))', 5667), ('(RandPlay(1), RandPlay(0))', 5481), ('(RollTo20(0), Desparat(1))', 5385), ('(Desparat(1), Desparat(0))', 5235), ('(RollTo20(1), RollTo20(0))', 5090), ('(RollTo20(1), Desparat(0))', 4625), ('(RandPlay(0), Desparat(1))', 59), ('(RandPlay(1), RollTo20(0))', 37), ('(RandPlay(1), Desparat(0))', 35), ('(RandPlay(0), RollTo20(1))', 31)
Note: ('(RollTo20(1), RandPlay(0))', 25063) means that the algorithm RollTo20 playing as the second player, (1) wins against algorithm RandPlay of the first player, (0) and wins 25063 times. (Zero based indexing so the first player is player(0)).
[edit] Racket
Same as Pig_the_dice_game#Racket, with three strategy makers, and
simulation code for trying out strategies.
#lang racket
(define (pig-the-dice #:print? [print? #t] . players)
(define prn (if print? (λ xs (apply printf xs) (flush-output)) void))
(define names (for/list ([p players] [n (in-naturals 1)]) n))
(define points (for/list ([p players]) (box 0)))
(with-handlers ([(negate exn?) identity])
(for ([nm (in-cycle names)] [tp (in-cycle points)] [pl (in-cycle players)])
(prn (string-join (for/list ([n names] [p points])
(format "Player ~a, ~a points" n (unbox p)))
"; " #:before-first "Status: " #:after-last ".\n"))
(let turn ([p 0] [n 0])
(prn "Player ~a, round #~a, [R]oll or [P]ass? " nm (+ 1 n))
(define roll? (pl (unbox tp) p n))
(unless (eq? pl human) (prn "~a\n" (if roll? 'R 'P)))
(if (not roll?) (set-box! tp (+ (unbox tp) p))
(let ([r (+ 1 (random 6))])
(prn " Dice roll: ~s => " r)
(if (= r 1) (prn "turn lost\n")
(let ([p (+ p r)]) (prn "~a points\n" p) (turn p (+ 1 n)))))))
(prn "--------------------\n")
(when (<= 100 (unbox tp)) (prn "Player ~a wins!\n" nm) (raise nm)))))
(define (human total-points turn-points round#)
(case (string->symbol (car (regexp-match #px"[A-Za-z]?" (read-line))))
[(R r) #t] [(P p) #f] [else (human total-points turn-points round#)]))
;; Always do N rolls
(define ((n-rounds n) total-points turn-points round#) (< round# n))
;; Roll until a given number of points
(define ((n-points n) total-points turn-points round#) (< turn-points n))
;; Random decision
(define ((n-random n) total-points turn-points round#) (zero? (random n)))
(define (n-runs n . players)
(define v (make-vector (length players) 0))
(for ([i n])
(define p (sub1 (apply pig-the-dice #:print? #f players)))
(vector-set! v p (add1 (vector-ref v p))))
(for ([wins v] [i (in-naturals 1)])
(printf "Player ~a: ~a%\n" i (round (/ wins n 1/100)))))
;; Things to try
;; (n-runs 1000 (n-random 2) (n-random 3) (n-random 4))
;; (n-runs 1000 (n-rounds 5) (n-points 24))
;; (n-runs 1000 (n-rounds 5) (n-random 2))
[edit] REXX
The strategy for a computer player is to roll again if the total score (including the current inning) has not won, and to roll again if the inning score is less than a quarter of the score needed to win.
The (somewhat aggressive) "quarter" strategy was chosen to give the advantage to a human (it was presumed that this dice game would be played with a CBLF).
/*REXX program plays pig the dice game (any # of CBLFs and/or silicons).*/
signal on syntax; signal on novalue /*handle REXX program errors. */
sw=linesize()-1 /*get the width of the terminal. */
parse arg hp cp win die _ . '(' names ")" /*obtain optional arguments.*/
/*names with blanks should use _ */
if _\=='' then call err 'too many arguments were specified: ' _
@nhp = 'number of human players' ; hp =scrutinize( hp,@nhp , 0, 0, 0)
@ncp = 'number of computer players'; cp =scrutinize( cp,@ncp , 0, 0, 2)
@sn2w = 'score needed to win' ; win=scrutinize(win,@sn2w, 1,1e6,60)
@nsid = 'number of sides in die' ; die=scrutinize(die,@nsid, 2,999, 6)
if hp==0 & cp==0 then cp=2 /*if both counts are zero, 2 HALs*/
if hp==1 & cp==0 then cp=1 /*if one human, then use 1 HAL.*/
name.= /*nullify all names (to a blank).*/
L=0 /*maximum length of a player name*/
do i=1 for hp+cp /*get the player's names, maybe. */
if i>hp then @='HAL_'i"_the_computer" /*use this for default.*/
else @='player_'i /* " " " " */
name.i = translate( word( strip( word(names,i)) @, 1),,'_')
L=max(L, length(name.i)) /*use L for nice name formatting.*/
end /*i*/ /*underscores are changed─►blanks*/
hpn=hp; if hpn==0 then hpn='no' /*use normal English for display.*/
cpn=cp; if cpn==0 then cpn="no" /* " " " " " */
say 'Pig (the dice game) is being played with:' /*introduction to pig.*/
if cpn\==0 then say right(cpn,9) 'computer player's(cp)
if hpn\==0 then say right(hpn,9) 'human player's(hp)
say 'and the' @sn2w "is: " win ' (or greater).'
!.=; dieNames='ace deuce trey square nickle boxcar' /*die face names.*/
/*note: snake eyes is for 2 aces.*/
!w=0; do i=1 for die; !.i=' ['word(dieNames,i)"]"
!w=max(!w, length(!.i)) /*!w ──► maximum length die name.*/
end /*i*/
s.=0 /*set all player's scores to zero*/
!w=!w+length(die)+3 /*pad the die number and die name*/
@=copies('─',9) /*an eyecatcher (for prompting). */
@jra='just rolled a '; @ati='and the inning' /*nice literals to have.*/
/*──────────────────────────────────────────────────let's play some pig.*/
do game=1; in.=0 /*set each inning's score to zero*/
say; say copies('█',sw) /*display a fence for da eyeballs*/
do k=1 for hp+cp /*display the scores (as a recap)*/
say 'The score for ' left(name.k,L) " is " right(s.k,length(win))'.'
end /*k*/
say copies('█',sw) /*display a fence for da eyeballs*/
do j=1 for hp+cp /*let each player roll their dice*/
say; say copies('─',sw); /*display a fence for da eyeballs*/
it=name.j
say it', your total score (so far) in this pig game is: ' s.j"."
do until stopped /*keep prompting/rolling 'til not*/
r=random(1,die) /*get a random die face (number).*/
!=left(space(r !.r','), !w) /*for color, use a die-face name.*/
in.j=in.j+r /*add die-face number to inning. */
if r==1 then do; say it @jra ! || @ati "is a bust."; leave; end
say it @jra ! || @ati "total is: " in.j
stopped=what2do(j) /*determine|ask to stop rolling.*/
if j>hp & stopped then say ' and' name.j "elected to stop rolling."
end /*until stopped*/
if r\==1 then s.j=s.j+in.j /*if not a bust, then add inning.*/
if s.j>=win then leave game /*we have a winner, so game ends.*/
end /*j*/ /*that's the end of the players. */
end /*game*/
say; say; say; say; say center(''name.j "won! ",sw,'═'); say; say; exit
exit /*stick a fork in it, we're done.*/
/*──────────────────────────────────S subroutine────────────────────────*/
s: if arg(1)==1 then return arg(3); return word(arg(2) 's',1) /*plural?*/
/*──────────────────────────────────SCRUTINIZE subroutine───────────────*/
scrutinize: parse arg ?,what,min,max /*? is the number, or maybe not. */
if ?=='' | ?==',' then return arg(5)
if \datatype(?,'N') then call err what "isn't numeric: " ?; ?=?/1
if \datatype(?,'W') then call err what "isn't an integer: " ?
if ?==0 & min>0 then call err what "can't be zero."
if ?<min then call err what "can't be less than" min': ' ?
if ?==0 & max>0 then call err what "can't be zero."
if ?>max & max\==0 then call err what "can't be greater than" max': ' ?
return ?
/*──────────────────────────────────what2do subroutine──────────────────*/
what2do: parse arg who /*"who" is a human or a computer.*/
if j>hp & s.j+in.j>=win then return 1 /*an easy choice for HAL.*/
if j>hp & in.j>=win%4 then return 1 /*a simple stategy for HAL.*/
if j>hp then return 0 /*HAL says, keep truckin'! */
say @ name.who', what do you want to do? (a QUIT will stop the game),'
say @ 'press ENTER to roll again, or anything else to STOP rolling.'
pull action; action=space(action) /*remove any superfluous blanks. */
if \abbrev('QUIT',action,1) then return action\==''
say; say; say; say center(' quitting. ',sw,'─'); say; say; say; exit
/*───────────────────────────────error handling subroutines and others.─*/
err: say; say; say center(' error! ',max(40,linesize()%2),"*"); say
do j=1 for arg(); say arg(j); say; end; say; exit 13
novalue: syntax: call err 'REXX program' condition('C') "error",
,condition('D'),'REXX source statement (line' sigl"):",
,sourceline(sigl)
The $T REXX program makes use of LINESIZE BIF which returns the terminals width (linesize).
Some REXXes doen't have a LINESIZE BIF, so one is included here ──► LINESIZE.REX.
To play this game with two computer players (simulate), use the following arguments:
0 2
Optionally, you may use (for instance):
0 2 ( HAL R2D2
to specify names for the (two) computer players.
output:
Pig (the dice game) is being played with: 2 computer players no human players and the score needed to win is: 60 (or greater). ███████████████████████████████████████████████████████████████████████████████ The score for HAL 1 the computer is 0. The score for HAL 2 the computer is 0. ███████████████████████████████████████████████████████████████████████████████ ─────────────────────────────────────────────────────────────────────────────── HAL 1 the computer, your total score (so far) in this pig game is: 0. HAL 1 the computer just rolled a 2 [deuce], and the inning total is: 2 HAL 1 the computer just rolled a 5 [nickle], and the inning total is: 7 HAL 1 the computer just rolled a 2 [deuce], and the inning total is: 9 HAL 1 the computer just rolled a 1 [ace], and the inning is a bust. ─────────────────────────────────────────────────────────────────────────────── HAL 2 the computer, your total score (so far) in this pig game is: 0. HAL 2 the computer just rolled a 6 [boxcar], and the inning total is: 6 HAL 2 the computer just rolled a 4 [square], and the inning total is: 10 HAL 2 the computer just rolled a 4 [square], and the inning total is: 14 HAL 2 the computer just rolled a 5 [nickle], and the inning total is: 19 and HAL 2 the computer elected to stop rolling. ███████████████████████████████████████████████████████████████████████████████ The score for HAL 1 the computer is 0. The score for HAL 2 the computer is 19. ███████████████████████████████████████████████████████████████████████████████ ─────────────────────────────────────────────────────────────────────────────── HAL 1 the computer, your total score (so far) in this pig game is: 0. HAL 1 the computer just rolled a 1 [ace], and the inning is a bust. ─────────────────────────────────────────────────────────────────────────────── HAL 2 the computer, your total score (so far) in this pig game is: 19. HAL 2 the computer just rolled a 1 [ace], and the inning is a bust. ███████████████████████████████████████████████████████████████████████████████ The score for HAL 1 the computer is 0. The score for HAL 2 the computer is 19. ███████████████████████████████████████████████████████████████████████████████ ─────────────────────────────────────────────────────────────────────────────── HAL 1 the computer, your total score (so far) in this pig game is: 0. HAL 1 the computer just rolled a 6 [boxcar], and the inning total is: 6 HAL 1 the computer just rolled a 6 [boxcar], and the inning total is: 12 HAL 1 the computer just rolled a 6 [boxcar], and the inning total is: 18 and HAL 1 the computer elected to stop rolling. ─────────────────────────────────────────────────────────────────────────────── HAL 2 the computer, your total score (so far) in this pig game is: 19. HAL 2 the computer just rolled a 6 [boxcar], and the inning total is: 6 HAL 2 the computer just rolled a 3 [trey], and the inning total is: 9 HAL 2 the computer just rolled a 6 [boxcar], and the inning total is: 15 and HAL 2 the computer elected to stop rolling. ███████████████████████████████████████████████████████████████████████████████ The score for HAL 1 the computer is 18. The score for HAL 2 the computer is 34. ███████████████████████████████████████████████████████████████████████████████ ─────────────────────────────────────────────────────────────────────────────── HAL 1 the computer, your total score (so far) in this pig game is: 18. HAL 1 the computer just rolled a 5 [nickle], and the inning total is: 5 HAL 1 the computer just rolled a 1 [ace], and the inning is a bust. ─────────────────────────────────────────────────────────────────────────────── HAL 2 the computer, your total score (so far) in this pig game is: 34. HAL 2 the computer just rolled a 4 [square], and the inning total is: 4 HAL 2 the computer just rolled a 4 [square], and the inning total is: 8 HAL 2 the computer just rolled a 3 [trey], and the inning total is: 11 HAL 2 the computer just rolled a 5 [nickle], and the inning total is: 16 and HAL 2 the computer elected to stop rolling. ███████████████████████████████████████████████████████████████████████████████ The score for HAL 1 the computer is 18. The score for HAL 2 the computer is 50. ███████████████████████████████████████████████████████████████████████████████ ─────────────────────────────────────────────────────────────────────────────── HAL 1 the computer, your total score (so far) in this pig game is: 18. HAL 1 the computer just rolled a 4 [square], and the inning total is: 4 HAL 1 the computer just rolled a 1 [ace], and the inning is a bust. ─────────────────────────────────────────────────────────────────────────────── HAL 2 the computer, your total score (so far) in this pig game is: 50. HAL 2 the computer just rolled a 1 [ace], and the inning is a bust. ███████████████████████████████████████████████████████████████████████████████ The score for HAL 1 the computer is 18. The score for HAL 2 the computer is 50. ███████████████████████████████████████████████████████████████████████████████ ─────────────────────────────────────────────────────────────────────────────── HAL 1 the computer, your total score (so far) in this pig game is: 18. HAL 1 the computer just rolled a 6 [boxcar], and the inning total is: 6 HAL 1 the computer just rolled a 6 [boxcar], and the inning total is: 12 HAL 1 the computer just rolled a 4 [square], and the inning total is: 16 and HAL 1 the computer elected to stop rolling. ─────────────────────────────────────────────────────────────────────────────── HAL 2 the computer, your total score (so far) in this pig game is: 50. HAL 2 the computer just rolled a 6 [boxcar], and the inning total is: 6 HAL 2 the computer just rolled a 3 [trey], and the inning total is: 9 HAL 2 the computer just rolled a 5 [nickle], and the inning total is: 14 and HAL 2 the computer elected to stop rolling. ═══════════════════════════HAL 2 the computer won! ════════════════════════════
[edit] Tcl
or alternatively with Tcl 8.5 and |
First the structure of the game (from the parent page):
package require TclOO
oo::class create Player {
variable me
constructor {name} {
set me $name
}
method name {} {
return $me
}
method wantToRoll {safeScore roundScore} {}
method rolled {who what} {
if {$who ne [self]} {
#puts "[$who name] rolled a $what"
}
}
method turnend {who score} {
if {$who ne [self]} {
#puts "End of turn for [$who name] on $score"
}
}
method winner {who score} {
if {$who ne [self]} {
#puts "[$who name] is a winner, on $score"
}
}
}
oo::class create HumanPlayer {
variable me
superclass Player
method wantToRoll {safeScore roundScore} {
while 1 {
puts -nonewline "$me (on $safeScore+$roundScore) do you want to roll? (Y/n)"
flush stdout
if {[gets stdin line] < 0} {
# EOF detected
puts ""
exit
}
if {$line eq "" || $line eq "y" || $line eq "Y"} {
return 1
}
if {$line eq "n" || $line eq "N"} {
return 0
}
}
}
method stuck {score} {
puts "$me sticks with score $score"
}
method busted {score} {
puts "Busted! ($me still on score $score)"
}
method won {score} {
puts "$me has won! (Score: $score)"
}
}
proc rollDie {} {
expr {1+int(rand() * 6)}
}
proc rotateList {var} {
upvar 1 $var l
set l [list {*}[lrange $l 1 end] [lindex $l 0]]
}
proc broadcast {players message score} {
set p0 [lindex $players 0]
foreach p $players {
$p $message $p0 $score
}
}
proc pig {args} {
set players $args
set scores [lrepeat [llength $args] 0]
while 1 {
set player [lindex $players 0]
set safe [lindex $scores 0]
set s 0
while 1 {
if {$safe + $s >= 100} {
incr safe $s
$player won $safe
broadcast $players winner $safe
return $player
}
if {![$player wantToRoll $safe $s]} {
lset scores 0 [incr safe $s]
$player stuck $safe
break
}
set roll [rollDie]
broadcast $players rolled $roll
if {$roll == 1} {
$player busted $safe
break
}
incr s $roll
}
broadcast $players turnend $safe
rotateList players
rotateList scores
}
}
Then the classes that create the various implemented strategies:
oo::class create RoboPlayer {
superclass Player
variable me
constructor {name} {
# Add a symbol to the name to mark a robot...
next "$name\u00ae"
}
method wantToRoll {safeScore roundScore} {
puts -nonewline "$me has ($safeScore,$roundScore)... "
set decision [my Decide $safeScore $roundScore]
puts [lindex {stick roll} $decision]
return $decision
}
method stuck {score} {
puts "$me sticks with score $score"
}
method busted {score} {
puts "Busted! ($me still on score $score)"
}
method won {score} {
puts "$me has won! (Score: $score)"
}
}
# Just takes a random decision as to what to play
oo::class create RandomPlayer {
superclass RoboPlayer
constructor {} {next "Random"}
method Decide {a b} {expr {rand() < 0.5}}
}
# Rolls until it scores at least 20 from a round or goes bust
oo::class create To20Player {
superclass RoboPlayer
constructor {} {next "To20"}
method Decide {safeScore roundScore} {expr {$roundScore < 20}}
}
# Like To20, but will roll desperately once another player reaches 80
oo::class create Desperate {
superclass RoboPlayer
variable me scores
constructor {} {
next "Desperate"
set scores {}
}
method Decide {safeScore roundScore} {
dict for {who val} $scores {
if {$who ne [self] && $val >= 80} {
return 1
}
}
return [expr {$roundScore < 20}]
}
# Keep an eye on other players
method turnend {who score} {
next $who $score
dict set scores $who $score
}
}
Demonstration, pitting the three of them against each other:
pig [RandomPlayer new] [To20Player new] [Desperate new]
- Output:
Random® has (0,0)... roll Busted! (Random® still on score 0) To20® has (0,0)... roll To20® has (0,4)... roll Busted! (To20® still on score 0) Desperate® has (0,0)... roll Desperate® has (0,6)... roll Desperate® has (0,10)... roll Desperate® has (0,13)... roll Desperate® has (0,17)... roll Desperate® has (0,21)... stick Desperate® sticks with score 21 Random® has (0,0)... roll Busted! (Random® still on score 0) To20® has (0,0)... roll To20® has (0,2)... roll To20® has (0,7)... roll To20® has (0,11)... roll To20® has (0,16)... roll To20® has (0,19)... roll To20® has (0,25)... stick To20® sticks with score 25 Desperate® has (21,0)... roll Desperate® has (21,6)... roll Desperate® has (21,12)... roll Busted! (Desperate® still on score 21) Random® has (0,0)... stick Random® sticks with score 0 To20® has (25,0)... roll Busted! (To20® still on score 25) Desperate® has (21,0)... roll Desperate® has (21,4)... roll Desperate® has (21,7)... roll Desperate® has (21,9)... roll Busted! (Desperate® still on score 21) Random® has (0,0)... stick Random® sticks with score 0 To20® has (25,0)... roll To20® has (25,5)... roll Busted! (To20® still on score 25) Desperate® has (21,0)... roll Desperate® has (21,2)... roll Desperate® has (21,7)... roll Desperate® has (21,11)... roll Desperate® has (21,14)... roll Desperate® has (21,19)... roll Desperate® has (21,24)... stick Desperate® sticks with score 45 Random® has (0,0)... stick Random® sticks with score 0 To20® has (25,0)... roll To20® has (25,5)... roll To20® has (25,8)... roll To20® has (25,14)... roll To20® has (25,18)... roll To20® has (25,20)... stick To20® sticks with score 45 Desperate® has (45,0)... roll Desperate® has (45,6)... roll Desperate® has (45,11)... roll Desperate® has (45,14)... roll Desperate® has (45,18)... roll Desperate® has (45,21)... stick Desperate® sticks with score 66 Random® has (0,0)... roll Random® has (0,2)... stick Random® sticks with score 2 To20® has (45,0)... roll To20® has (45,6)... roll To20® has (45,12)... roll To20® has (45,18)... roll To20® has (45,24)... stick To20® sticks with score 69 Desperate® has (66,0)... roll Desperate® has (66,6)... roll Busted! (Desperate® still on score 66) Random® has (2,0)... roll Busted! (Random® still on score 2) To20® has (69,0)... roll To20® has (69,4)... roll To20® has (69,8)... roll To20® has (69,14)... roll To20® has (69,20)... stick To20® sticks with score 89 Desperate® has (66,0)... roll Desperate® has (66,6)... roll Desperate® has (66,10)... roll Desperate® has (66,12)... roll Desperate® has (66,18)... roll Desperate® has (66,23)... roll Desperate® has (66,27)... roll Desperate® has (66,29)... roll Desperate® has (66,31)... roll Desperate® has won! (Score: 101)