Retired cop here - listen to this dude. My job was to sit down in a room, read a person their rights, make sure they understand it, have them initial 4 places, sign, and date that they understand it, make it clear to them in no uncertain terms that everything they say will be against their benefit, and they have nothing to gain by talking to me.

Then they'd talk to me. Many cases started with a great suspect who had motive, opportunity, corroborating evidence, but there was still reasonable doubt. Then the suspect would tell me all sorts of stuff that I didn't know, which really helped out.

Further, the cops don't assume your arrest, or statements, are invalid due to a lack of Miranda warning. Statements made by the suspect who hasnt been advised of their rights are only inadmissible if the suspect is in some sort of custody, and under some form of interrogation.

If you are sitting on your couch in your home talking to a single cop who hasn't arrested you or anything, you aren't in custody, so the cop can ask you questions all day, and its fair game.

If you get arrested and the cop asks "Are you feeling okay", and you go on and on about the crime you committed, you are making spontaneous statements that aren't the subject of an interrogation, so these are likely admissible as well.

There are gray areas. If you are in the back of the cop car, and 2 cops up front are having a conversation about the case, hoping to guilt you into giving up information, those statements may be inadmissible unless you were advised of the miranda warning.

There was a homicide case where the cops had a suspect, but couldn't prove it. It was the victim's boyfriend. Detectives spoke to him, and asked if they could take him to breakfast on Saturday. The guy cautiously obliged, because free breakfast. He drove his own car, met them there, and they had a nice breakfast. Talked about sports, TV, life, etc. No mention of the case. The cops asked if they wanted to meet them for breakfast again next week. He did. They did this for over a month.

One morning, between bites of pancakes, the Detective asks, "So why'd you kill Jane". The suspect, not missing a beat, replies, "Man, she just pissed me off".

In hindsight, if you didn't commit a crime, follow the advice of the parent post. If you did commit the crime, always talk to the cops; you're smarter than them, you can convince them you're innocent.