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?
(In reply to
re(3): a wiser approach by Charlie)
Thanks, Charlie, for settling this.
a) I think my strategy is even stronger than this simulation
shows. The simulation could be changed to stop rolling and
declare a win as soon as 100 points were achieved, instead of risking
the win in hand in order in order to try to get the "full turn" of 20
points or 6 rolls (depending on the strategy).
b) I think that stopping on 20 or stopping on 21 are equally good
strategies before you are ahead, but that stopping at 20 (being more
conservative) is better once you are ahead. I think this is the
reason that stopping on 20 outperforms stopping on 21 in your
simulations.
c) You give two results for the stopping on 20 strategy, and two for
the stopping on 21 strategy. Is this because two of your results
assume that the 20 or 21 strategy is the second player? I assume
that you did it both ways, and just wrote it up wrong.
Thanks again, Steve
re(4): a wiser approach
