straight face
straight face {n.}
A face that is not laughing or smiling.
Mary told all the funny stories she knew to try to make Joan laugh, but Joan kept a straight face.
It is hard to tell when Jim is teasing you. He can tell a fib with a straight face.
When Bob fell into the water, he looked funny and I could hardly keep a straight face.
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Source: A Dictionary of American Idioms