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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(5): a wiser approach | Comment 15 of 23 |
(In reply to re(4): a wiser approach by Steve Herman)

The two results for each of stopping on 20 and stopping on 21 are for the second player playing exactly 5 or exactly 6 rolls.

In addition to stopping when 100 is achieved, the real strategy would also continue rolling to much higher values than 20  if the opponent had 99. If the opponent had 98 or other such high score, then the 20 should probably be extended, but to a lesser extent, also taking into consideration how far behind or ahead one is.

  Posted by Charlie on 2005-04-25 15:20:41
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