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“My two cents” and its longer version “put my two cents in” is an American idiomatic expression, taken from the original British idiom expression: to put in “my two pennies worth” or “my tuppence worth.” It used to preface the tentative stating of one’s opinion. By deprecating the opinion to follow — suggesting its value is only two cents, a very small amount — the user of the phrase hopes to lessen the impact of a possibly contentious statement, showing politeness and humility. However, it is also sometimes used with irony when expressing a strongly felt opinion. The phrase is also used out of habit to preface uncontentious opinions.
For example: “If I may put my two cents in, that hat doesn’t do you any favors.” (More polite way of saying, for example: That hat is ugly.) An example of the shortened version: “My two cents is that you should sell that stock now.”
There is some speculation as to the origin of the idiom. Some believe that the phrase originates in betting card games, such as poker. In these games, one must make a small bet, or ante, before beginning play. Thus, the phrase makes an analogy between entering the game and entering a conversation. However, there is no documentary evidence of this being the origin of the idiom and as such, is merely speculation. Other likely origins are that “my two pennies worth” is derived from the much older 16th Century British expression, “a penny for your thoughts”. There is also some belief that the idiom may have its origins in the early cost of postage in Britain, the “twopenny post”, where two pennies was the normal charge of sending a letter containing one’s words and thoughts or feelings to someone.
“Two cents” and its variations may also be used in place of the noun “opinion” or the verb phrase “state [subject’s] opinion”, e.g., “You had to put your two cents in, didn’t you?” or “But that’s just my two cents.”
The phrase “If you don’t put your two cents in, how can you get change?” encourages an expression of opinion. It makes a pun on the word “change”. One meaning of change is an alteration — presumably to bring someone or something in agreement with an expressed opinion. Another meaning of change is the cash equivalent of an overpayment. Thus the reference to two cents is in accord with another idiom that values opinions at one cent (A Penny for Your Thoughts).
This expression is also often used at the end of a statement, e.g., “Just my two cents.” In this usage, there are many variations that serve the same purpose, such as “Just my $0.02 worth” or “Just my 1/50th of a dollar.”
A related expression is “Would you buy it for a quarter?”, coined by C. M. Kornbluth in The Marching Morons, indicating that the thing in question isn’t even worth 25¢.