If I have a bet that loses me 1 util on heads, and 2 utils on tails, I wont take it; it's a sure loss. Add a million to those values and we get a bet that I would take. So clearly u changes on addition of constants.

If you were really adding a constant to the utility function, you would also add a million to the utility of not taking the bet.

Let U be your original utility function and V be U + 1,000,000, differring by an additive constant.

Then

EU(refuse bet) = 0
EU(take bet) = .5 * (-1) + .5 * (-2) = -1.5

So, using U, you would refuse the bet.

And

EV(refuse bet) = 1,000,000
EV(take bet) = .5 * (999,999) + .5*(999.998) = 999,998.5

So, using V, you would also refuse to take the bet.

As expected, adding a constant to the utility function did not change the decision.