Optimal strategy for this d6 game In my attempts to learn the foundations, I was given the following game in a mock interview:

Two players each roll a d6, and are not able to see each other's
  rolls. The player with the higher value wins \$1. After the players
  roll their dice, each player may either pay \$0.25 to increase their
  individual roll by 2 or keep their roll. What is the optimal strategy
  and payout? Consider the cases for which i) nothing happens when both
  players roll the same number, and ii) the players keep rerolling (for free) until
  different numbers appear.

What is the best strategy here? Is it important for both players to have the same strategy for Nash/symmetric equilibrium (not sure what the terminology I should be using is)? What should my considerations be in calculating the expected value? Please help prod me to attempt deriving the strategy, thanks!
 A: Let the probability distribution of the other person's roll be $P(i)$.   
Hint: If you roll a $n$, what will make you indifferent to pay $0.25$ to increase your roll?

 You are indifferent if $P(n) + P(n+1) = 0.25$.    

Is there a probability distribution when you are always indifferent?   

 The probability distribution is $P(i) = \frac{1}{8}$. (Each outcome is equally likely)  

If yes, can that be achieved via the rules?   

 It can be achieved. Specifically, what is the strategy?

If yes, is that a symmetric Nash equilibrium?   

 Yes, see comment. 

If yes, what is the payout?   

 The payout under case 1 is $\frac{5}{16}$, under case 2 is $\frac{1}{2}$. Why?   

Is this the max possible payout? Why, or why not?
Case 1: (I had an error so now I'm not certain)
Case 2a: My interpretation for Case 2 was that they don't have to pay the \$0.25 and get to reroll. If so, the total payout in each turn is 1, and since the strategy is symmetric, hence the max payout is $\frac{1}{2}$.
Case 2b: An equally valid interpretation is that they will have to pay the \$0.25 regardless. Under this interpretation, it's not immediately clear to me what the strategy should be.   
