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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.)
re: computer aided solution | Comment 2 of 5 |
(In reply to computer aided solution by Charlie)

It might be said that, if possible, leave your opponent with 3+7k where k is an integer. But if that's not possible, then refer to the sheet for the next best choice.
  Posted by Charlie on 2017-10-21 17:16:49

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