There is a runner on third with two out. Batter hits a slow roller to first base. First baseman charges and picks up the ball. Runner from third crosses home. First baseman tags the runner running from home to first, does the run count ?
The run does not count. According to MLB rules:
4.09 HOW A TEAM SCORES.
(a) One run shall be scored each time a runner legally advances to and touches first, second, third and home base before three men are put out to end the inning. EXCEPTION: A run is not scored if the runner advances to home base during a play in which the third out is made (1) by the batter-runner before he touches first base; (2) by any runner being forced out; or (3) by a preceding runner who is declared out because he failed to touch one of the bases.
Since the batter-runner does not make it to first base safely, the run does not count. Similar to a force out.
In English. All base runners that need beat a force play need to reach their base for the run to score.
The last time that the Cubs won a world series came down to this rule.
Fred Merkle did not run from 1st to 2nd and what looked like the winning run scored but because he ran to the dugout instead the ball was retrieved and he was called out.
Its forever known as Merkle's boner.
That game was won by the Cubs who won the League by a game and went on to win the World Series