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Roll of the die (Posted on 2005-04-21) Difficulty: 4 of 5
The object of the dice game is to be the first player to reach a score of at least 100 points.
Each player’s turn consists of repeatedly rolling a die.
After each roll, the player has two choices: roll again, or stop.
- If the player rolls 1, nothing is scored in that turn and it becomes the opponent’s turn.
- If the player rolls a number other than 1, the number is added to the player’s turn total and the player’s turn continues.
- If the player stops, the turn total (the sum of the rolls during the turn), is added to the player’s score, and it becomes the opponent’s turn.

What's your strategy?

See The Solution Submitted by Hugo    
Rating: 4.1111 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(4): a wiser approach | Comment 14 of 23 |
(In reply to re(3): a wiser approach by Charlie)

Thanks, Charlie, for settling this.

a) I think my strategy is even stronger than this simulation shows.  The simulation could be changed to stop rolling and declare a win as soon as 100 points were achieved, instead of risking the win in hand in order in order to try to get the "full turn" of 20 points or 6 rolls (depending on the strategy).

b) I think that stopping on 20 or stopping on 21 are equally good strategies before you are ahead, but that stopping at 20 (being more conservative) is better once you are ahead.  I think this is the reason that stopping on 20 outperforms stopping on 21 in your simulations.  

c) You give two results for the stopping on 20 strategy, and two for the stopping on 21 strategy.  Is this because two of your results assume that the 20 or 21 strategy is the second player?  I assume that you did it both ways, and just wrote it up wrong.

Thanks again, Steve

  Posted by Steve Herman on 2005-04-25 14:39:01

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