If Ogadei Khan Hadn't Died

I gather that the effectiveness of these against Hungarian castles was somewhat limited, however. Which will have the crops taken into them before the siege begins.

A Mongol invasion of Europe is like the Nazis attacking the Maginiot line in a Blitzkrieg head on... only the Maginot line is so deep that it stretches through all of France.

The Mongols may be able to defeat European armies in the field to start off with (generalising enormously), but the problem comes later in the campaign when they're running out of plains to feed their masses of horses on (an estimate somewhere-I can't remember exactly where, unfortunately-had about 20,000 horses from the Great Hungarian Plain, or was it 20,000 fully armed Mongol warriors? I can't remember, but anyway, not exactly the Great Hordes of Asia), they're getting attacked by angry peasants and the garrisons of all those castles they missed out on, they may be having to fight in the dense forests of some parts of Europe, or in the Alps (NOT good cavalry country), and all for an area which wasn't at this time particularly worth the effort in terms of potential plunder.
 
Top