We draw a blank on Monday and Tueday, but from then on there are a series of good match-ups and talented pitchers scheduled to be on the mound.
The games include CC Sabathia taking on his former team, the Cleveland Indians, Cole Hamels facing the Marlins, R.A. Dickey taking on the Giants and Max Scherzer facing the Rays.
All times are in BST.
Monday 3 June
No early games
Tuesday 4 June
No early games
Wednesday 5 June
17.10. Pittsburgh at Atlanta (Rodriguez – Teheran) *MLB.com Free Game of the Day
18.05. Cleveland at NY Yankees (Kluber – Sabathia) *ESPN America
18.05. Miami at Philadelphia (Turner – Hamels)
19.10. Oakland at Milwaukee (Colon – Gallardo)
20.40. Chicago White Sox at Seattle (Axelrod – Iwakuma)
20.45. Toronto at San Francisco (Dickey – Zito) *ESPN America
Thursday 6 June
18.08. Tampa Bay at Detroit (Hernandez – Scherzer) *BBC 5LSX, MLB.com Free Game of the Day
19.10. Baltimore at Houston (Gonzalez – Norris) *ESPN America
Friday 7 June
19.20. Pittsburgh at Chicago Cubs (Liriano – Wood) *ESPN America
All of these games are available to watch live via the MLB.TV subscription at MLB.com. The early games being shown on ESPN America are highlighted above, while the full ESPN/ESPN America schedule can be found on their website. BBC 5 Live Sports Extra can be found on digital radio, digital TV and on the BBC.co.uk website (coverage on the website is only available to UK residents). The complete schedule for this week’s MLB games can be found on MLB.com