[Benzooor]

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If I was in villains spot with 44 i'm definitely c/c rather than open shoving.

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wow that's terrible

all better hands shove, and all worse hands check behind

if you think there is value in 3betting the turn with 44, shoving >>>>>>>>>>> checking, and i think c/f > c/c, because he's never shoving worse hands

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And shoving the river with 44 only folds out hands you already beat.

Although you may be right about c/f being > c/c with 44 on the river.