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| Roll of the die (Posted on 2005-04-21) |
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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?
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Submitted by Hugo
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Rating: 4.1111 (9 votes)
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Solution:
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(Hide)
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Each roll is viewed as a bet that a 1 will not be rolled: the odds are 1 to 5.
A successful throw produces one of the numbers 2, 3, 4, 5, and
6. On average, you will gain four points. If you put 20 points at stake
this brings the odds to 4 to 20, that is 1 to 5, and makes a fair game.
Whenever your accumulated points are less than 20, you should continue
throwing, because the odds are in your favor.
However...
There are many circumstances in which one should deviate from this “hold at 20” policy.
For example: Your opponent has a score of 99 and will likely win in the next turn. You have a score of 78 and a turn total of 20.
The above solution is from Knizia [1999, 129] and is good enough in my opinion.
A more thorough analysis "Optimal Play of the Dice Game Pig" can be downloaded here |
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