[Butch7999]

Hi Derek -- correct on Groh, and yes, the card backs are all identical.
Funny thing with card designs in this era -- there seem to be at least a few unexpected crossovers.
The Major League Base Ball Game by Parker Brothers, which has a confoundingly confusing history
involving a variety of back and face designs for its cards, multiple name changes, and copyright issues
with basically identical games made by other companies, includes on its rules sheet, for no apparent reason,
photos of the Cobb and Ruth cards from the E120 American Caramel and/or V61 Neilson Chocolate sets.

By the way, we took a few minutes to run through our files, and besides the Mails game (just us,
but we don't consider the cut-out player-figures from the Major League Ball game "cards"),
1920s games with cards also include...

'Babe' Ruth's Baseball Game (Milton Bradley, 1929-36)
"Babe Ruth" Witch-E Base-Ball Game (Baltimore Novelty Co Inc, c1920)
Hall's National League Card Game ~ Baseball (Hall's Baseball Card Co, 1925)
Hatfield's Parlor Base-Ball Game (The Hatfield Co, 1914-21) /
Hatfield's Parlor Base Ball (Federal Specialty Co, 1926)
Knickerbocker Base Ball (Reinig Game Co, 1923)
Lloyd's Scientific Baseball (Lloyd's Scientific Game Co, 1927)
The Major League Base Ball Game (Parker Brothers, c1922)
National Card Baseball Game (National Card Baseball Co, c1923?)
New Card Baseball Game (National Card Baseball Co, c1922-23?)
Olsen's Base Ball played with Cards (Olsen Games Co, 1922)
PlayBall (Warren Manufacturing Co, 1922)
Psychic Baseball (M C Meyer, 1920s) /
Psychic Base Ball (Psychic Base Ball Corp, 1927)
Universal Baseball Playing Cards (Lewis A Bedard, 1929)
Waner's Baseball Game (Waner's Baseball Inc, 1928-1930s)
World's Champion Base Ball Card Game (The Champion Amusement Co, 1919-1920s)

At least eight of those are what we'd call "scarce" to "rare." If anybody sees any of 'em, we call dibs.
None of those feature player photos, although most (not all) have at least some baseball-themed
illustration.

There's also The National-American Base Ball Game (the "Lajoie game") by Parker Brothers,
which debuted prior to or during WWI but may have stayed in production and on the market
into the 1920s. And one or two Japanese games may possibly qualify for the list as well.
As always, if we're wrong on the dates for any of those, we welcome corrections.