Bob's best response to a revealed coin bias

Alice and Bob each choose the heads probability of their own coin and then each flip once. If both coins show heads, Alice pays Bob $6; if both show tails, Alice pays Bob $4; if they differ, Bob pays Alice $5. Alice must announce her heads probability $p_1$ before Bob chooses his, $p_2$. If $p_1=\tfrac34$, Bob has positive expected profit exactly when $p_2\in(a,1)$ for a reduced fraction $a$. What is $a$?

$a=\tfrac{11}{24}$. Weighting Bob's payoffs $+6$, $+4$, $-5$ by the outcome probabilities and collecting terms, his expected profit is $(20p_1-9)p_2+4-9p_1$, linear in $p_2$. At $p_1=\tfrac34$ this becomes $6p_2-\tfrac{11}{4}$, which is positive exactly when $p_2>\tfrac{11}{24}$.