{"status": "success", "data": {"description_md": "**POTD December 1, 2023**\n**Author:** munch\n\nMunch rigs a coin to land heads with probability $p$.  Then, Munch flips the coin until two consecutive heads are flipped. If the total number of flips is odd, Munch wins $p$ dollars; otherwise, Munch wins nothing. Let $q$ be the value of $p$ that Munch should pick to maximize his expected win. If $q = a-\\sqrt{b}$, where $a, b \\in \\mathbb{Z}$ and $\\sqrt{b}$ cannot be simplified, find $a^b$.", "description_html": "<p><strong>POTD December 1, 2023</strong><br/>&#10;<strong>Author:</strong> munch</p>&#10;<p>Munch rigs a coin to land heads with probability <span class=\"katex--inline\">p</span>.  Then, Munch flips the coin until two consecutive heads are flipped. If the total number of flips is odd, Munch wins <span class=\"katex--inline\">p</span> dollars; otherwise, Munch wins nothing. Let <span class=\"katex--inline\">q</span> be the value of <span class=\"katex--inline\">p</span> that Munch should pick to maximize his expected win. If <span class=\"katex--inline\">q = a-\\sqrt{b}</span>, where <span class=\"katex--inline\">a, b \\in \\mathbb{Z}</span> and <span class=\"katex--inline\">\\sqrt{b}</span> cannot be simplified, find <span class=\"katex--inline\">a^b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #12", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}