Stroke order is not decoration — it determines how the character looks handwritten and how dictionaries index it.
The radical is the part a paper dictionary files a kanji under, and it usually hints at meaning. 鬥 is filed under 鬥 (fight) — radical number 191 of the 214 in the Kangxi system.
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鬥 means Broken Gate Radical (no. 191).
鬥 is written with 10 strokes. The animated diagram on this page shows the correct order.
The radical of 鬥 is 鬥 (fight), radical number 191 of the 214 Kangxi radicals. The radical is the component a dictionary files the character under, and it usually points at the character's meaning.
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