Stamford Bridge Victory for Norway?

This battle is considered to mark the end of the Viking age.
What would happen? King Harald Hardrada intended to conquer England rather than just raid it. What would happen when William the Conqueror arrives a few weeks later? Would the Viking raids continue or would they start conquering other nations?
 
Harald Hardraada and William the Conqueror were both invading England because they believed they had cliams to the English throne. If Harald wins at Stamford Bridge, we can assume he had eliminated the English king as a rival to both himself and to William the Conqueror- meaning that Harald and William would still have to square off against each other. IOTL, the English army was exhausted at the Battle of Hastings because William had landed immediately after Stamford Bridge, meaning that the English had to force-march from north England to the south without any rest after the battle against the Vikings. If the Vikings had won, then they too would have to march south to meet the Normans... but there is enough speculation about the English being able to win at Hastings that the result of a battle between the Vikings and the Normans at the same place and time and in the same context could be relatively open ended, I think.
 
Yeah, that's what I was wondering about mainly. The Vikings had about 7,500 soldiers at the battle, so even if they lost only 2,000 men, that would still leave 5,500 soldiers against the 8,400 that William had. And the Vikings would have had to have marched south. I'm thinking for this to work, that the Norwegians would have to wait a while longer for reinforcements before taking on the invaders.
 
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