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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.)
Some Thoughts re(4): a wiser approach............. Att: Charlie Comment 23 of 23 |
(In reply to re(3): a wiser approach by Charlie)

Although it is an old problem, I have discovered it only this morning, tried to solve it firstly guided by my intuition, then by some elementary probability considerations and finally read all the comments published back in 2005.

I believe that the simulation should be a decisive tool in selecting the optimal strategy and your program checked quite reasonable assumptions.
However nothing in the program addresses the clear advantage of being the 1st player (imagine that the goal was 15 points instead of 100! - being 1st outweighs any strategy!! ).
I believe that two extra tests should be run:

a.Both players use the same strategy (for 2-3 predefined strategies),  
2.One player uses a pre-selected strategy , the second becomes more conservative if leading  and more aggressive if lagging ,- plus switching roles.

I am sure that will make the results more conclusive, at least more convincing- have no idea to what extent.

If you have the time and inclination,- please post both the results and your conclusions and we will see whether they have changed significantly or not.
Thank you for your attention.

  Posted by Ady TZIDON on 2013-12-26 02:50:17
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