Just to add a bit to Mrerick's answer:
Euchre is what is known as a "trick card game." It's simple structure belies a complexity that involves psychological bluffing as well as sometimes intricate mathematics.
For Steinbeck to have chosen the ranch hands to play this game is symbolic of the intelligence of his characters, who though poor and uneducated are themselves more complex than their "simple structure" might appear.
The suggestion is made as a distraction from thinking about Carlson about to shoot Candy's dog.
This is just something about George playing cards.
Notice, whenever George and Lennie are in the bunkhouse, George is always playing solitaire. Solitaire, is of course a game for one person. This may symbolize (if Steinbeck put Solitare in for a reason) that although George and Lennie are companions, they may not truly be friends. Instead, George still feels lonely and needs someone.
playing card just like randoming life