That, or you can fight smart and wait for the proper moment to attack. The AI tends to split its armies every now and then, take 'em apart piecemeal when they do. Have you checked what kind of units you're sending your cavalry heavy army against? Cavalry doesn't tend to fare that well against, say, pikemen, though I'm not sure if the game actually renders that. Also, western armies generally had more funding, training, and equipment, especially when it comes to infantry, which is why you're not winning 1:1 fights without some good generals or better tactics.
Also, you seem like you're getting pretty angry. Try to calm down, it helps make for better discussions.
I get annoyed when accused of nationalism; I'm not Polish or Russian or Cossack or well even eastern; and yes using actual facts and examples is furious.
Cavalry actually does very well against pikemen in eu3, and I don't think calling an ignoramous an ignoramous is annoyed I think it is informed. He goes against everyone and assigned a random arbitrary date to claim something that never happened happened all the while accusing me of being a nationalist.
Historically do you dispute that Swedish cavalry was trounced by Tatar cavalry during the 1650s? they are in eu3 terms not strictly eastern; but according to the idea that in the 1650s western cavalry had so outpaced eastern is well; I hope anyone suggesting it is a troll or joking. I agree western nations did develop infantry tactics in ways eastern nations didn't; but in term of funding lets not forget a western infantryman was more expensive. British infantry was entitled to red meat, cheese, bread, and later on even rice, a Russian soldier would just be given a few grots. Western Cavalry didn't outpace Eastern Cavalry; which is why eastern cavalry did well.
on gameplay mechanics your suggestion is to win when you outnumber them which is exactly what I do at the moment; at least until I modernize which is very easy because you are mostly to full centralization from your westernization.
Also would you please tell me what a western army is? Prussia was nothing in 1650, Austria struggled against the Ottomans and failed to defend their capital on their own, Saxony's army proved to be over estimated during the great northern war, the Swedes lost the struggle for dominance to Russia. Does what you say about western armies apply to Spain Venice, Bavaria, Denmark etc?
P.S. try not to be condescending; nobody insulted you and when insulted by somebody who has an ethnocentric view of history accusing me of nationalism because I didn't agree that in 1650 cavalrymen from Wessex genetically became better then the Polish Hussars I think I am well within rights to say they have no knowledge of history and not only that Joe claims you do win 1 vs 1 battles as eastern tech which according to your post isn't true.
Ignoramous just means somebody who is ignorant; and in the 1650s the Swedish cavalry who attacked Poland while the Polish Army fought the Russian one where defeated by Tatar Cavalry.
To be clear the term "western" when applied to tactics doesn't always make too much sense. Being western didn't give any advantage; adopting the latest technologies and the correct tactics did. French and British Soldiers had a tendency to outperform other armies; but does the same bonus make sense for Denmark or for Saxony or Thuringia?