Average Pig Turns

Pig is a folk jeopardy dice game with simple rules: Two players race to reach 100 points. Each turn, a player repeatedly rolls a die until either a 1 ("pig") is rolled or the player holds and scores the sum of the rolls (i.e. the turn total). At any time during a player's turn, the player is faced with two decisions:

• roll - If the player rolls a
  • 1: the player scores nothing and it becomes the opponent's turn.
  • 2 - 6: the number is added to the player's turn total and the player's turn continues.
• hold - The turn total is added to the player's score and it becomes the opponent's turn.

Problem: What is the expected number of turns per solitaire game with a hold-at-20-or-goal play policy?  Simulate a given number of solitaire Pig games where a player rolls until a 1 ("pig") is rolled, or the turn total is greater than or equal to 20, or the score plus the turn total is greater than or equal to 100.  Report the average number of turns per game.

Input Format:  Enter a single positive integer indicating the number of games simulated.  (Larger numbers will tend to yield better estimations.)

Output Format:

• Initially, prompt the user with "Games? ".
• After the simulations, print "Average turns: " followed by the average turns taken per simulated game.

Sample Transcript:

Highlight the transcript in the space immediately below to check your result (your approximation will vary in latter decimal places):

Games? 1000000
Average turns: 12.634906

Common Error:  When creating nested loops, perform loop initialization directly before the relevant loop.  Note:

<loop 1 initialization>
<loop 1>
        <loop 2 initialization>
        <loop 2>

is not the same as

<loop 1 initialization>
<loop 2 initialization>
<loop 1>   
        <loop 2>

In the latter case, <loop 2> is not properly initialized each time.

Todd Neller