The old kahn had allowed the Golden Horde to conquer the west all the way to the ocean. And so they did. General Qadan led a vast army of Turkic, Russian and Mongolian horeback archers into Poland and in the spring of the year of our Lord, 1241, his troops encountered the Christians.

Led by the duke of Poland, a magnificent army awaited the Mongols. There were Hospitalers, Templars and Teutonic knights. The finest soldiers of the Christian world were assembled on the fields of Legnica. But that dreadful day, when the mightiest armies of the world met, the crusaders were lured into a trap. The Mongols tried their proven tactics. It had worked when they conquered Samarkand, they had applied it succesfully in the Middle East, and again they would show their tactical superiority. What good was it to be chivalrous if you were conquering the world? Upon the advance of the Polish, Qadan ordered his troops to retreat. The Christian warriors pursued them and were already cheering their victory. They had beaten the mighty Mongols, the Scourge of God... So they thought...

A shower of arrows came down upon the Christian knights and in spite of their helmets and their chain mail, they fell. That day the soil of Poland turned red and the Teutonic order was nearly wiped out. Their armor was crushed under the hooves of Mongolian horses and the general had an ear cut off every fallen Westener, so he could count their numbers...

In reality the story ends here, for the Great Kahn of the Mongol Empire died and the conquest of the west was cancelled. But what if, what if Ogotai had not died? If Batu Kahn had ordered Qadan even further westward?

The Mongol hordes would advance into the Holy Roman Empire and lay waste to Prague. The Northern European Plains would be ideal for their horses and they would easily overrun Germany, the Low Countries and France, leaving a trail of destruction behind. The western kings would either subdue or fall and only the Alps and Pyrenees would have halted their advance.

Perhaps Italy would have been forced into vassalry and the Spanish, wedged in between the Mongols and the Moors would have had a hard time. They would have allied with either one of the two, becoming hardly more than a protectorate.
The English would have been isolated and the Angevinian kingdom would have been destroyed. Their civilization would have developed in Britain alone...
Scandinavia too would have been cut off from Europe and its Christianization could easily have been reversed. In the north a new Viking state would have evolved, but it would have been unable to attack the Mongol dominated mainland. Their new conquests would probably lead them to the Americas instead.

Ogotai would of course have died eventually, and the West might have become an independent Kahnate. The new leaders would probably convert to Christianity, but unlike in the real world, the relations with the Islamic world wouldn't have been so troublesome, for it is logical to assume that if the Mongols had crushed Europe, they would soon have conquered the Middle East as well, leaving only North Africa and Andalucia to the caliphs...

What would the world look like today if Ogotai had lived a decade longer?