Going back to the original question - Aspirins anti-thrombotic mode of action is not to "thin the blood". Rather, it reduces the risk of clot formation by reducing the ability of platelets to aggutinate and form the "mesh" of a clot. Aspirin manages this by inhibiting the production within the body of prostaglandins and more importantly, thromboxane, the agent most associated with the "stickiness" of platelets.It achieves this by inactivating cyclo-oxygenase, or rather one form of cyclo-oxygenase, COX1. other Non Steroidal Anti-Inflammatory Drugs (NSAIDS) act on the same mechanism, which is why it is important to be aware of other drugs being taken.
As far as the most appropriate dose to achieve this anti- thrombotic effect is concerned - many trials have been performed over the years, the largest and best controlled one being the ASPECT trial, which established the value of taking aspirin prophylactically in high risk patients. Other trials have looked at the dose requirements, and have found that this anti-thrombotic effect can be achieved with doses as low as 40mg daily. Higher doses will inhibit the COX pathway to a greater extent,although you are up against the law of diminishing returns, and additionally it has been hypothesised that aspirin works on other pathways to achieve plalelet inhibition, since there is some clinical observations to suggest that higher doses work better in certain classes of patients.
In summary, best clinical practice for anti-thrombotic activity of aspirin, maximising the COX inhibition and reducing the risk of bleeding disorders, is for a daily dose to be around 75-150mg daily.
300mg daily is not that much more, relatively speaking, so will certainly offer the anti- thrombotic effect just as well as a lower dose.
If it was me, and bear in mind that I am a pedant when it comes to stuff like this, I would want to ascertain from your medical professional why they want y