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31 or more (Posted on 2017-10-21) Difficulty: 4 of 5
There several versions of "1 to 31" game, involving one die and two players (say you and your opponent), both gifted mathematicians.
My choice is the version defining as a final goal being the first to get a score
of 31 or more.

Here we go:
First: You throw the die and note the outcome.
Then: Your opponent makes a quarter turn* and add this outcome to the earlier sum.
Then: You make a quarter turn and add... and so on...
Until: Whoever gets first the score of 31, or more WINS...

Obviously - there are no draws.
*The quarter turn gets you one of the 4 neighboring faces - never the opposite one!

Design the optimal strategy, - for each of the players and evaluate their chances of victory, provided each makes the best possible moves and that the first number
is a perfectly random digit between 1 and 6.

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
Question Clarification needed | Comment 3 of 5 |

I read the problem to say that the die is randomly rolled only at the start of the game.  Charlie seems to have assumed that the die is rolled randomly once per turn.  Which is correct?

  Posted by Steve Herman on 2017-10-22 22:47:07
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