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The extra red blood cells make your blood thicker than normal. As a result, blood clots can form more easily. These clots can block blood flow through your arteries and veins, which can cause a heart attack or stroke. Thicker blood also doesn't flow as quickly to your body as normal blood.
However, if you on a blood thinning medication like Coumadin (Warfarin) or Plavix (Clopidogrel), talk to your doctor about dangers of consuming too much blood thinning foods coupled with prescriptions that could lead to excessive bleeding.