Shelley Duncan, NYY AL, has started his career with a bang.  Thru his first three career games with an at-bat, he had 3 homers and 7 RBI.

Only one other player in the last 50 years has had three homers in his first three career games with an AB:  Billy Conigliaro in April 1969:

Apr 15, 1969: defensive sub, one AB, no homers
Apr 16, 1969: 2-for-4, 2 homers
Apr 17, 1969: 3-for-5, 1 homer

Billy is the brother of the more famous Tony Conigliaro.

And Duncan's the first guy to have 7 RBI in his first three games since the eminent George Bjorkman, HOU NL, had 7 RBI in 1983:

Jul 10, 1983: 1RBI
Jul 12, 1983: 1RBI
Jul 13, 1983: 5RBI

Shelley went 1-for-5 with no homers or RBI on Monday, but he did start his career with three straight games with an RBI.  The top RBI streaks to start a career since 1957 are:

G	PLAYER	DATES	RBI
5	Bobby Knoop	4/13-4/21/1964	5
5	Mike Lansing	4/07-4/11/1993	8
4	Ron Cash	9/04-9/10/1973	4
4	Jesse Barfield	9/03-9/06/1981	6

Those are all great, but they're nowhere close to the all-time record for consec. games with an RBI to start a career:
11-John Anderson, Brooklyn, Sep 8 - Sep 22, 1894.

A Century of Cobb
Ty Cobb's Batting Line from 100 years ago:
July 24, 1907: at Boston; 1-for-4 with an outfield assist; opposing starter: Tannehill