{"status": "success", "data": {"description_md": "**Full credit goes to the staff team at Canada Math for authoring these problems.**\n\nA game starts with $$1$ in the bank and starts at stage $1$. At stage $n$, the player rolls a die. If a $1$ or $2$ is rolled, the game ends and they win nothing. If a $3$, $4$, or $5$ is rolled, the game ends and they win all the money currently in the bank. If $6$ is rolled, they advance to stage $n+1$, and the amount of money in the bank doubles. If $E$ is the game's expected value, find $1000E$.", "description_html": "<p><strong>Full credit goes to the staff team at Canada Math for authoring these problems.</strong></p>&#10;<p>A game starts with $<span class=\"katex--inline\">1</span> in the bank and starts at stage <span class=\"katex--inline\">1</span>. At stage <span class=\"katex--inline\">n</span>, the player rolls a die. If a <span class=\"katex--inline\">1</span> or <span class=\"katex--inline\">2</span> is rolled, the game ends and they win nothing. If a <span class=\"katex--inline\">3</span>, <span class=\"katex--inline\">4</span>, or <span class=\"katex--inline\">5</span> is rolled, the game ends and they win all the money currently in the bank. If <span class=\"katex--inline\">6</span> is rolled, they advance to stage <span class=\"katex--inline\">n+1</span>, and the amount of money in the bank doubles. If <span class=\"katex--inline\">E</span> is the game&#8217;s expected value, find <span class=\"katex--inline\">1000E</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Canada Math Contest #2 - Problem 5", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}