Kelly with a Cash-Reserve Floor

You may stake on an even-money coin with win probability $p=0.8$, but a liquidity rule requires you to keep at least half your total wealth in untouched cash at all times, so the staked fraction satisfies $f\le 0.5$. Set up the constrained maximization of expected log-growth, use the KKT conditions to determine the optimal stake, and state whether the reserve constraint binds.