Earlier in the day, acting as his own attorney, 66-year-old Alcala had pointed out to the jury that if they recommended the death sentence, his case would end up being appealed for another 15 to 20 years.
As part of his closing argument, Alcala also played a song for the jury from the Arlo Guthrie album "Alice's Restaurant."
Alcala is convicted of torturing and murdering four women in Los Angeles County and a 12-year-old Huntington Beach girl in the 1970s.
Alcala has been twice before convicted and sentenced to death for kidnapping and murdering Samsoe. The death sentence was twice overturned on appeal.
Jurors had to decide whether Alcala should be sentenced to death or whether he should spend the rest of his life in jail without the possibility of parole.
Earlier on during Alcala's penalty phase of the trial, which began last week, a defense psychiatrist testified that Alcala can't remember some of his own actions due to a borderline personality disorder.
The prosecution pointed out that Alcala only mentioned to the doctor the crimes he's already served time for, and the doctor was paid $20,000 to be a witness for the convicted serial killer.
AP contributed to this report.
