Henry Ernest Dudeney/Modern Puzzles/204 - Turning the Die

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Modern Puzzles by Henry Ernest Dudeney: $204$

Turning the Die
This is played with a single die.
The first player calls any number he chooses, from $1$ to $6$, and the second player throws the die at hazard.
Then they take it in turns to roll over the die in any direction they choose, but never giving it more than a quarter turn.
The score increases as they proceed, and the player wins who manages to score $25$ or forces his opponent to score beyond $25$.
I will give an example game.
Player $A$ calls $6$, and $B$ happens to throw $3$, making the score $9$.
Now $A$ decides to turn up $1$, scoring $10$;
$B$ turns up $3$, scoring $13$;
$A$ turns up $6$, scoring $19$;
$B$ turns up $3$, scoring $22$;
$A$ turns up $1$, scoring $23$;
and $B$ turns up $2$, scoring $25$ and winning.
What call should $A$ make in order to have the best chance at winning?
Remember that the numbers on opposite sides of a correct die always sum to $7$, that is, $1 - 6$, $2 - 5$, $3 - 4$.


Click here for solution

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