I know that with a cut sticky blood cells called platelets are used to prevent an extended amount of blood loss from the wound.
How do blood thinners prevent this?
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There are 2 types of blood thinners anticoagulants and antiplatelets. Simply:
Anticoagulants work by interrupting the process involved in the formation of blood clots. They're sometimes called "blood-thinning" medicines, although they don't actually make the blood thinner
Vitamin K is essential for those reactions. Warfarin (Coumadin) works by decreasing the activity of vitamin K; lengthening the time it takes for a clot to form.
Antiplatelet drugs, such as aspirin, prevent blood cells called platelets from clumping together to form a clot.
Anticoagulant and antiplatelet drugs work by stopping platelets from adhering to one another and clotting proteins from binding together.
Many medications can cause low platelet count by causing immunologic reaction against platelets, called drug-induced thrombocytopenia.
So basically on this stuff it takes you longer to clot and therefore increased the time you bleed.
As far as I know, the only blood thinner that is known for its potential to reduce platelet count is Heparine. See e.g. Wikipedia, HIT - heparin induced thrombocytopenia, www.en.wikipedia.org/wiki/Heparin-induced_thrombocytopenia
"If someone receiving heparin develops new or worsening thrombosis, or if the platelet count falls, HIT can be confirmed with specific blood tests."
Some other link on "HIT": https://www.ahajournals.org/doi/full/10.1161/circulationaha.106.632653
For a popular blood thinner that seems to be based on heparin see https://en.wikipedia.org/wiki/Enoxaparin_sodium
For several other substances of the same category see e.g. https://www.ahajournals.org/doi/full/10.1161/circulationaha.106.632653
The question says: "creation" of platelets. There is not known any "blood thinner" that prevents the creation of platelets. Typically, Vitamin K which is blocked by certain blood thinners, is needed for the creation of factors of the coagulation cascade. Thus, blood thinners interfering with vitamine K do not prevent the "creation" of platelets/thrombocytes (which medication blocking cell division does, cp. cancer medication), but the creation of coagulation factors.
Creation of platelets is different from "creation of blood clots" and its prevention. The question is not coherent in respect of its explanatory text. The answer to the question reformulated in the explanatory note "...platelets are used to prevent ... blood loss from the wound, so how do Blood Thinners prevent this?":
They inhibit the aggregation of platelets by interfering with the thrombocyte's signaling hormone thromboxane.
See https://en.wikipedia.org/wiki/Thromboxane#Inhibitors "The widely used drug aspirin acts by inhibiting the ability of the COX enzyme to synthesize the precursors of thromboxane within platelets." https://en.wikipedia.org/wiki/Thromboxane#Inhibitors
There are blood thinners that do not directly act on platelets but on the coagulation cascade.The question does not seem to refer to these. What's more, they do not lead to low platelet count and do not interfere with cell devision i.e. creation of platelets. However, for some dispute on Thrombocytopenia in the context of novel blood thinners see e.g. https://pubmed.ncbi.nlm.nih.gov/3219062