I think that is like the classic gambler's fallacy 
The profit should reach EV because the numbers get bigger, not because it's more likely to be "extra EV". The 1% HE is the same for both sites.
In comparison: gamblers say that when you have a coinflip, and after 1000 bets it's 40% tail, it's more likely to be "head" because it will get close to 50%. However, it will get close to 50% because the sample will become bigger, not because there is a bigger chance for any side to win - that's still 50%.
The profit should reach EV because the numbers get bigger, not because it's more likely to be "extra EV". The 1% HE is the same for both sites.
In comparison: gamblers say that when you have a coinflip, and after 1000 bets it's 40% tail, it's more likely to be "head" because it will get close to 50%. However, it will get close to 50% because the sample will become bigger, not because there is a bigger chance for any side to win - that's still 50%.
Exactly. Wikipedia has a good gif demonstration of this. I edited my previous answer a little bit. but same thinking.
