formula question If logic

[RobertCo]

Hi guys I have a question for some reason my brain is not capable of figuring out..
I have 5 cells
A B C D E
Joewins, JoeLooses, Mikewins, Mikelooses, Winner
0 0 0 0 blank
1 0 0 1 Joe
0 1 1 0 Mike
0 1 0 1 tie or leave blank


If any of the first 4 coumns contains a value > 0 then Winner needs to be populated
What I have come up with so far only handles 2 colums the winner columns

IF(AND(A1=0),"",IF(AND(C1=0),"",IF(A1>C1,"Joe","Mike")))

What I was doing was a bunch of "IF AND" conditions
I am not sure how to do "IF OR" conditions and am looking for an example of how to handle that.
Any help would be appreciated.
Thanks

[DonkeyOte]

=IF(SUM(A1:D1),IF(B1+D1=2,"Tie",IF(A1,"Joe","Mike")),"")