Quarter

The quarter is an ancient coin, once used by the U.S. Government as part of its national currency, and much later acquired by Dr. Catherine Halsey as an antique. When testing a boy named John for his possible inclusion in the SPARTAN-II Program in 2517, she played a game with him to see if he could determine or affect on which side the quarter would land. When John succeeded, she judged that he was very capable or lucky, and would be a good inclusion in the program.

As a prize for winning the game, she gave the quarter to John. When John was forcibly inducted into the SPARTAN-II program, the UNSC confiscated the coin as John fought madly to get it back but was unsuccessful. In 2525, Mendez gave the quarter back to John as a going away present as their paths diverged. The ultimate fate of the quarter is unknown.

In 2552, while in the clutches of the Gravemind, Hasley's posthuman duplicate Cortana began to relive Halsey's memories. Cortana remembered how Halsey acquired John for the SPARTAN-II program using the quarter toss as the deciding factor, and because she felt guilty about it, declared his selection to be "the coin's fault".

Background
Equivalent to 25 cents, under the United Earth Government the currency was discontinued in favor of the UN Credit, and quarters have become valuable antiques, but have no value as currency anymore. One side of this variant of quarter bears an image of the U.S. General and President George Washington, while the other side bears an eagle, which was the national symbol of the U.S.

Trivia

 * Oddly, even though Halo: The Fall of Reach states that quarters and all forms of material currency was discontinued, various coins such as the quarter can be found in Halo 3: ODST.