Both of our large macaws have demonstrated a great liking for a fun macaw "game" that I call "Beaky-Beak".  I've seen macaws play this with each other in aviaries and zoos.  The birds whip their heads about wildly and make a kind of heavy-breathing sound - something halfway between a hiss and "hah-hah".  Sometimes they flair their tails (as they would if they were really agitated), but the wild whipping of their necks tells you it's just play, not serious.  They frequently will make a loud "wooo!" sound as well.  And they spar at each other, swinging their beaks at each other, striking, grabbing, letting go, and then doing it again.  When playing with a human, they will strike at whatever is closest - if it's a hand, they'll grab a finger with the top beak, release it, grab it again, release it again, grab one more time and make a quick, but quite hard, grind with the lower beak, then release.  My interpretation is that scoring a "grind" is worth points somehow.  It seems to be the object of the game.  

"Beaky-Beak" is lots of fun - for the macaw.  For everyone else, it's a bit too rough.

When I'm invited (by a macaw) to play "Beaky-Beak", I am careful not to get too close.  I don't mind the jabs with the top beak, but it's the lower beak grinding that hurts - and can do damage to my hand (not that her upper beak is exactly "safe" - I'm sure she could tear quite a slash in my face if it got close).  Neither Jesse nor Laka has ever tried to come after me to play like this (unlike "wrassling", where they run up to me and flip over to play), but if I approach them they clearly take it as the signal that I'm willing to participate.  And there's no point in trying to get them to play gently.  "Beaky-Beak" is what it is.  Apparently if you play, you play to win.

When invited to play, I may try to get the bird interested in some other fun and high-energy activity.  Playing "peek-a-boo" sometimes works (although I have to admit that sometimes it just cranks them up tighter).  Mostly, however, I just ensure they are safely locked in their cages and leave the area until they settle down.  If Laka is out of her cage, I will hold my left hand above her head and just out of reach and snap my fingers, then reach quickly with my other hand to pick her up.  The "one/two" motion distracts her and she'll step on my hand peaceably enough and allows me to put her back in her cage (but I am careful to hold her well away from my face and body).

Ned, our Green Cheek Conure has had first-hand experience with "Beaky-Beak".  Ned is, frankly, something of an idiot.  He's a very aggressive little bird and for some reason we don't understand, he's taken an active dislike to Laka.  When he's out of his cage he will (if we don't stop him) fly to Laka's cage and follow her around, snapping at her and challenging her to a duel.  To Ned this is deadly serious business.  His body language (wings cocked, tail flared) clearly shows he means to do serious harm.  But when Laka's sees him, she thinks he's trying to play "Beaky-Beak".

On morning Ned flew to Laka's cage while my husband was changing his food and water dishes.  Laka was on one side of her cage, and was ignoring Ned (who was clinging to the other side, fanning his tail and trying to stick his head through the bars).  My husband thought the sight of this was hilarious, and because his camera was nearby, he snapped some photos.  While he was taking pictures, Laka looked up, saw Ned, and with great speed, climbed over to Ned's side of the cage.  The last photo Stephen took tells it all.  Ned is there, wings in raging-hawk stance, tail feathers spread in a clear show of aggression.  Laka, on the other hand, is looking relaxed and playful, not even quite in the "Beaky-Beak" stance yet.

I still cringe when I see this.  It's that half second before disaster.

But she reached him.  Hook, release, hook, release.  Then hook with her top beak and the lower beak closed on him.  Had she wanted to hurt him, Ned would be dead.  She was just playing.  But Ned's lower beak was pushed out slightly on the right side.  He was able to eat (thank heavens) but it was a couple of weeks before his beak moved back in to normal position.

My husband was mortified.  He learned a really tough lesson and since then is careful.  Ned, however, has learned nothing from the experience at all.  He still occasionally goes on his stupid kamikaze missions.