Discussion

Explanation:

The initial board is:

Since both of you play intelligently, your objective is to get the maximum possible gain while your friend's objective is to give you the minimum possible gain. 

Case I: You select (retain right). 
Since your friend also plays intelligently, he will select (retain lower) so that your gain does not cross Rs. 6. If he selects (retain upper), your gain can possibly go up to Rs. 9
Now, you will select (retain left) to get a maximum possible gain of Rs. 6.
Finally, in order to minimise your gain, your friend will select (retain upper). 
This will limit your gain to Rs. 4.
Thus, with intelligent moves, your maximum gain in this case is Rs. 4.

Case II​​​​: You select (retain left). 
Now, if your friend selects (retain upper), the profit you can earn (both playing intelligently) is Rs. 4 when you again select (retain right).
On the other hand, if your friend selects (retain lower), the profit you can earn (both playing intelligently) is Rs. 2 when you again select (retain right).
Since your friend also plays intelligently, he will select (retain lower) so that your profit is only Rs. 2.

Since you want to maximize your gain, your first intelligent move will be (retain right) i.e., case I.

As per Case I, your gain will be Rs. 4. 

Hence, option (a).

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