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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.)
Hints/Tips Nearly there | Comment 16 of 23 |

You guys have developped a nice and correct theory for the start of the game and have indeed found out that the strategy should change as a function of yours and the opponents score.  Nice work.
The total solution is probably  not something for this web site, more for a highly specialised math web site.  But there is one thing I should like to see:
A general idea of when/how you will change your strategy and start taking risks.

One remark: several comments mentionned that you should  take very large risks if the opponent is at 99.  Then my question is: Why would the opponent stop at 99?

  Posted by Hugo on 2005-04-25 16:58:55
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