I just finished reading 'War of the rats' by David Robbins; a partly ficticious account of the sniper duel in the ruins of Stalingrad, between Sgt. Vasily Zaitsev, and a crack German sniper, who may not have actually existed, according to Wikipedia. But it reminded me of a favourite AH idea I came up with years ago; what if, when Manstein's relief column got to its closest point to the surrounded German pocket in Stalingrad, WI Paulus decided to just go for it, and try to break out, join up with Manstein, and save the sixth army? Now, you can say that he would never have done it, but let's just assume that he did. Maybe he did it just because it was the right thing to do, and to hell with der Fuhrer's orders.
So do they successfully fight their way out, albeit taking horrific casualties, or do they just get completely chopped up in the attempt? I can just imagine an exhausted and bedraggled Paulus, walking up to Manstein somehere on the Russian steppe, and something like' Into your hands I entrust the sixth army', then he wanders off and sticks his pistol in his mouth before he can be arrested.
Whatever happens, Hitler goes completely apeshit, maybe so much so that he has a stroke, or a seizure or something and is hospitalised. Of course, most of the survivors of the breakout would likely wind up getting killed in other battles, but this would have been preferable to starving to death in Stalingrad, or in a POw camp, or being worked to death, or maybe even better than being worked almost to death, until finally being released about 1955.