Server Administration :: Updating Table Through Concurrent Sessions

I have a table with counter value which will be incremented or decremented by several application servers.

SQL> select * from test;

COUNTER
----------
10

Application servers(multiple servers) will be running update against this row for increasing the counter value or decreasing the counter value.

update test set counter=counter+1;
update test set counter=counter-1;
update test set counter=counter+1;
update test set counter=counter+1;

So when update happens concurrently to this table will the counter value gets messed up?

I did a small test by opening multiple sessions for running update and the result I got for above update statement was 11,10,11,12.

But our developer is bit skeptical about this approach and he is using select for update and then updating the row.

Which approach will be better?