Gwen Carr tells TMZ ... she has her doubts about the system working in Floyd's favor, because she went through this nightmare when her son was choked to death during his 2014 NYC arrest.
Gwen says the cops involved in George's killing absolutely deserve to be held accountable, but she's warning Floyd's family not to bank on it, because she sees it as a roll of the dice in these cases.
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Eric's mother tells us she's pleased Derek Chauvin -- the fired cop who pressed his knee into Floyd's neck for 8 minutes and 46 seconds -- has been charged with murder. However, she also believes Minneapolis police were playing politics when they fired and arrested Chauvin.
Gwen says more needs to be done to stop the widespread riots, and while she's not promoting or condoning the violence, she tells us she understands folks' frustrations all too well. She's been there.
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As you know ... the footage of Eric's death infamously captured his final words, "I can't breathe."
His mom says she thought it was a slam dunk the involved officers would be charged with murder because her son was killed on camera -- but only one cop was ever arrested, and all charges were eventually dropped.
Eric's daughter, Emerald Garner, tells TMZ ... police would think twice about killing unarmed black people if there were laws specifically for cops involved in incidents like Garner's and Floyd's.
Eric's mother added some friendly advice for the Floyd family -- she's encouraging them to not sit on the sidelines and let law enforcement handle the case.
Gwen says, in her experience, George's loved ones must speak out to anyone who will lend an ear -- especially lawmakers -- and adds they should not be discouraged by the uphill battle they're already facing.