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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(2): a wiser approach | Comment 11 of 23 |
(In reply to re: a wiser approach by Steve Herman)

I was thinking "strategy" for more than one match. 

I think that this is a very simple game, where just one parameter is to be decided by the player, and almost every thing is produced by fortune. On one hand, concrete situations during a game can be usually decided on basis of "common sense"; on the other winning or losing just one game doesn't mean too much (a baby could win a single match to a "experienced" player in this game). The difference between good and weak players emerges only on the long run. And, probably, the game has been thought to be played in series, more than one time.

I trust then that a math "strategy" about the right moment to stop the turn, would plavail, not in a game or in single situations, settled at least by common sense an fortune, but in a sufficient number of games, in the long run.

Anyway, I think your have post an interesting question. If I understand you properly, in a normal situation you prefer to stop once you have score 20 (or 21?). So we could create something like this:

Steve and Armando are playing the dice game where the object is to be the first player to reach a score of at least 100 points.
Each player’s turn consists ... (follows description of the game). Steve has decided that in his turns he'll try to keep rolling since he scores at least 20 (or 21) points, while Antonio has decide that he will rolls just 5 (or 6) times before the stop. Question is: who has a higher probability of winning the game?

I put this way because, more or less, both systems are similar (rolling five times means a medium value = 17,5; six times = 21), but they have some differences: I would be able to score 12 or 14, while you wouldn't; you will have some more turns with a 0 than me, but your scores would fruit more than mine... 

We could change the names and post it as a problem, to see what outcomes...

(PS: If Charlie sees, we have a sure solution).

  Posted by armando on 2005-04-24 21:38:45
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