JACKSON, Miss. — Sometimes American politics is about ideas, powered by Jeffersons and Adamses and Reagans. Sometimes it is about strategy, with races determined by the chess-match machinations of Axelrods and Roves.

But every once in a while, the fate of governments is determined by a considerably less eminent character, one usually found lurking in back-alley craps games and on the Vegas strip: Lady Luck.

In Mississippi on Friday, luck smiled on a Democratic state representative, Blaine Eaton II, who had been forced, by state law, to draw straws for his seat after his race for re-election ended in a tie. On Friday afternoon, in a short, strange ceremony here presided over by Gov. Phil Bryant and Secretary of State Delbert Hosemann, Mr. Eaton and his Republican challenger, Mark Tullos, each removed a silver box from a bag. Mr. Eaton opened his box to reveal a long green straw.

And with that, a mathematically improbable tie for the House District 79 seat — each candidate had received exactly 4,589 votes — had been broken, though not by the voters.