First, we need to determine what the optimal strategy is to maximise the payoff of playing the game. The optimal strategy is to reroll if your first die roll has a lower value than the expected payoff of the final die roll. Since, the final die roll has an expected payoff of £3.5, then we should reroll if our first roll has a value in $\{1, 2, 3\}$. So, if our first roll has a value in $\{4,5,6\}$, then we should stick and take the payoff. The expected payoff if we stick is therefore the average of $\{4,5,6\}$ which is $5$, and the expected payoff of rerolling is the expected payoff of a single die roll, $3.5$. It is straightforward to see that sticking or rerolling occur with equal probability. $$ E[\text{Payoff}] = \frac{1}{2} (5) + \frac{1}{2} (3.5) = 4.25 $$