"Handle" in this case means a nickname. For example, if you have ginger hair, your handle might be "Red." If you're six feet tall and weigh 350 lbs, you might acquire a handle such as "Moose." Checkers is a popular board game . "Kiting checks" is a slang term for writing and passing worthless checks. That is, writing a check as payment for something when you don't have the funds to back up the check.Jimmy: "Checkers" Hoagland. You get that handle because you play checkers? Maybe you kite checks.
"Running numbers" is a method of illegal gambling. Sort of an off-the-record, illegal lottery, where a person collects money from people and then pays off winnings based on some set of numbers, whether it be the local horse races or the final scores in some professional sports game. A "cab" is a taxi. The implication in this sentence is that the cab driver also ran an illegal gambling operation in order to earn extra money.Hoagland: Naw. Used to run numbers from a cab.
Pen = penitentiary, or prison. An "out of state pen" means a prison in a different state. For example, a person convicted in New York might serve his sentence in Pennsylvania, which would be "out of state" for him.Later Hoagland says: And I on'y talk to you. I don't testify. And protective custody in an outta-state pen.
DA's office = District Attorney's office. The District Attorney is the local public official who represents the government in the prosecution of alleged criminals. Sometimes accused criminals can "make a deal" with the DA's office in exchange for a lenient sentence. For example, an accomplice to a robbery might agree to tell the DA the names of everyone involved in the crime and also divulge other vital information if he is assured of a lesser prison sentence in exchange for this information.Later Jimmy says: I've never asked for a favor from D.A's office, have I?
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