die is rolled three times. After the first
and the second roll a player has an option to take gain equal to result of the
rolling and end the game or discard the result and continue the game to the
next rolling. At the last rolling the player's gain is the result of the last
rolling. What is the optimal stopping strategy and what is the fair price for
participation in the game?
We introduce the
function
Clearly,
Also,
where the
is the mathematical expectation applied to the variable
.
We
have
Therefore, after the second rolling the player should reject 3,
.
Similarly,
where
Therefore, after the first rolling the player should reject 4,
.
The fair price for participation in the game is
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