It's called rat poison and I was threatened with it as "drain cleaner". I am a bit mystified why a doctor would want to put a patient on to it when it is such a strong anti-coagulant when clotting or blockage of an artery in the heart to cause a heart attack hasn't been identified as a risk factor.
I was on Cartia aspirin for a long time, but haven't take it for several years.
I do know that when I was admitted to hospital with my heart attack and was transfused with the next level of medication down from Warfarin, a big bruise on my leg sustained while sailing three days previously increased substantially in size and became annoyingly painful because of the additional bleeding. I would caution greatly about getting overconfident when taking Warfarin. I became a real bleeder when just taking aspirin.
Certainly, you should cover the ground again with your doctor and inquire as to why he would want you taking Warfarin, and for him to identify the likely risks (for example have you had a predisposition to stomach ulcers?).
As far a strokes are concerned, taking Warfarin or aspirin would not be a good thing.