Calling [self methodName] from inside a block?

Yes, you can do this.

Note, however, that the block will retain self. If you end up storing this block in an ivar, you could easily create a retain cycle, which means neither would ever get deallocated.

To get around this, you can do:

- (void) someMethodWithAParameter:(id)aParameter {

  __block MySelfType *blocksafeSelf = self;
  void (^tempFunction)(void) = ^ {
      [blocksafeSelf changeWindow:game];
  };

  [self doSomethingWithBlock:tempFunction];

}

The __block keyword means (among other things) that the referenced object will not be retained.