"Just my two cents" or "My two cents worth" is used to loosely mean "stating one's opinion". But the main point of "my two cents worth," is that it is a faux-modest, self-deprecating tactic used to disarm your audience before you announce your opinion. (Especially important in the event that your opinion turns out to be idiotic).

Origin: The phrase "Put my two cents in" originates from an older phrase "put my two bits in" which has its origin in the game of Poker. When playing poker, one starts with making a small bet before the cards are dealt. This is called an "ante".

As ante gains entry in the game, this phrase gains one an entry into the conversation.

Now, what is "two bits"? - Well, two bits means one quarter. Today we have coins that are minted in specific denominations - cent, nickel, dime, quarter, dollar etc. - but in the starting, coins were made of gold and silver with the value of a coin equal to the value of the Gold or Silver contained in it. To make change, a coin would be scored and split into pieces.

A coin could thus be split into halfs, quarters, and eighths. One eighth of a coin was called a "piece of eight" and also called a "bit". So two pieces, or 'two bits' would make one quarter.

This is also the origin of word 'Bit' for the binary unit in computers (a bit is a "piece of eight" of a byte).

Also, "Smashed to bits" literally means to break something into eighths.


Source: http://www.word-detective.com/back-k.html

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