Yes, Joe definitely shot and yes Ben, the gentleman mercenary, was always going to clean up in the final showdown.

Joe had the strength and coordination to spin his gun back into his holster after being shot.
If he was 100% bad, he'd have taken careful aim and killed Cooper.
The aim of practical politics is to keep the populace alarmed and clamorous to be led to safety.

I made me the same question.
Why Lancaster tries to take the Winchester, after jump of the balcony,
if had bullets in his gun ?
Many claim, Lancaster allows win to him (Cooper) on purpose.
Something strange happens in this final duel .

You would think Joe might have had that sentiment towards Ben for the booty.
Can you fly this plane?
Surely you can't be serious.
I am serious,and don't call me Shirley

Honestly, I think Joe tried to kill Ben, but Ben beat him, but not by much. I do NOT believe Joe allowed himself to be killed. I think Ben was in denial all along, hoping Joe wasn't really as bad as he 'put on'. Prob isJoe was.
If Joe's gun had been empty, Ben would've opened the cylinder & the camera would've trained on it, to accentuate that Joe tossed the fight.
Joe was bad & Ben was just a hair faster.
Carpe Noctem!

Maybe the Col. was upset thinking(knowing?)Joe deliberately missed?
Can you fly this plane?
Surely you can't be serious.
I am serious,and don't call me Shirley

Sara Montiel who is from Mexico
Not she was from Spain, it's an extended error.
Sara Montiel (1928-2013).

Trivia says Coop didn't like her, she smelled and never washed her hair. lol
Can you fly this plane?
Surely you can't be serious.
I am serious,and don't call me Shirley

There were two 'reports.'(pistols)
Can you fly this plane?
Surely you can't be serious.
I am serious,and don't call me Shirley

"After having shot Lancaster Cooper approaches his already dead body, then takes Lancasters gun in his hand and stares at it for a second. Then stares again at Lancaster with visible emotion. Why?
My guess is that perhaps Lancaster didnt fire his gun at all. In the last second he got remorses because Cooper was giving him the chance he had denied to everybody else before. "
"Lancaster definitely fired. But I know what you mean, there was something fishy about the shootout. They both drew and shot simultaneoulsy, so why did Lancaster miss? "
"I wonder if they were implying that something was wrong with Lancaster's pistol? "
I can't believe nobody has thought about this before. I always assumed Lancaster left his gun empty on purpose. Cooper was the only friend he ever had, he didn't want to shoot him. It was the only "good deed" he ever did in his life. Cooper realizes this when he picks up Lancaster's gun. There is definitively self-loathing in his eyes.
Jessica Rabbit
"I'm not bad. I'm just drawn that way."

or at least so close, that we'd not be sure, until Joe fell.
Carpe Noctem!

I think you are all reading too much into it. The gunfight was shot in such a way that the audience wouyld think that the bad guy had at first won. It was nothing to do with any ones ego

Don't be embarassed, rogerscorpion. We all err. That's why they put erasers on pencils.
If Ben thought Joe was redeemable, he was very stupid. They say the devil is charming.
He maketh His sun to rise on the evil and on the good St. Matthew 5:45

I'm embarrassed. It was Archie Savagenot Woody.
I think Ben liked Joe. Joe was charming & Ben thought Joe was redeemable. Ben was seriously sad, when he had to kill him.
Carpe Noctem!

Personally, I can't believe the story about the alternate endings being filmed. There can never have been any question Coop's character would win the gunfight. Lancaster's character was an total scumbag with no redeeming characteristics, and he was proud of it. If some actor other than Lancaster had played him, one who usually played villians, say Jack Lambert, you would all recognize this, and wouldn't be carrying on so. He definitely shot his revolver. I don't think Ben (Cooper) actually liked Joe (Lancaster). He just felt sorry for him because he had been raised in such a scummy way that helped turn him into an amoral killer. But each of us is ultimately responsible for his or her own behavior regardless of circumstances.
By the way Woody Stode was not in this movie.
He maketh His sun to rise on the evil and on the good St. Matthew 5:45

YeahI see it as Ben tossed the gun, because he really liked Joe & kept hoping Joe was only pretending to be as bad as he truly was.
Joe really had no loyaltyas exhibited by killing Strodewho was blindly loyal to Joe.
Burt died smiling, because he saw the humor in everything. He gambled & he lost.
Carpe Noctem

This scene struck me as fishy too.
Burt dies smiling, as if he got what he wanted. He made Cooper shoot him in a "fair" duel instead of just gunning Burt down for the murder of their colleague (the man of color). Burt challenged him to a draw to assuage Cooper's conscience, not because Burt wanted to survive. So I think he threw away the shot and let Cooper cut him down.
But the more I think about it the more I think that this impression was not intended by the script and director; it was the result of Burt Lancaster and his huge ego insisting on getting "the last laugh", or the last grin, as it were. He refused to die like a defeated villain, making the viewer think he had planned it that way. The ambiguity is the result of the clash between Burt's ego and the rest of the people involved in the production, which is evident throughout the movie.
Cooper's reaction is easier to read because it fits in with the intended plot: he gets tearful as he tosses aside Burt's gun because it is a "he who lives by the gun, dies by the gun" moment for him. He basically liked the guy but because Burt resorted to excessive force, getting carried away by his gunslinger lifestyle, Coop had to put a stop to it.

Sorry I can't help with the email addresses but Sara Montiel who is from Mexico is also alive even though she is about 80. She might be one that knows. She played Nina the love interest of Gary Cooper.

Ha, ha, hadnt thought about them, thank you. Now we only need to know their e-mails and send the question. Anyones got them?

Also Denise Darcel is still alive (I think) and she was an actual witness to the shootout. Maybe she has some thoughts on it too.

Good point jr. One wonders because as one remembers in an earlier scene with Maximilian both were fast and expert shots and both fired and should have hit each other. Of course everyone makes a mistake and misses once in a while and this may have been Burt's time to miss. Ernest?

Maybe we can ask Ernest Borgnine?
Hey Ernest!! What's the verdict?

Thank you, Jrogersdal, you just read my mind.
Sadly enough most of the people involved in the making of this movie - Aldrich, Cooper, Lancaster, screenwriters - passed away for some time, so we wont probably ever get to know if there was really something about this or if we are just having to much imagination.

Lancaster definitely fired. But I know what you mean, there was something fishy about the shootout. They both drew and shot simultaneoulsy, so why did Lancaster miss? It's not like Cooper's shot interrupted his, Lancaster even spun his gun and holstered it afterwards. Then when Cooper approaches and pulls Lancaster's pistol he gives it a hard look and throws it away in disgust, like he was angry that he ended up with some advantage and it wasn't fair to his sense of honor. I wonder if they were implying that something was wrong with Lancaster's pistol?
A puzzle