Brainteaser - Heads-or-Tails Oracle

A coin with an unknown head-probability \(p\) will be flipped 100 times. Before each flip you may announce "heads" or "tails"; a correct call earns \(\$1\), a wrong one earns nothing. You may update your strategy after seeing previous outcomes. What is your expected total payoff (as a function of \(p\)) if you play optimally?