Slitherine

I've got to say, the Luck of the Draw scenario really sucks for the Allies. It's hard enough for them already, and this just makes it worse. First, there's a good chance some of your better units will be lost in hopeless positions from the outset. (Nothing like seeing an elite infanry in Schonberg.) Worse, there's always a chance your reinforcements won't arrive on time; the risk of them not arriving on time hobbles Alied play far more than any benefit they may get from something arriving early. Allied defense is always hard-pressed, and a lot of the key decisions revolve around knowing how much you have to leave to defend a space, and knowing that a unit will be appearing in Liege or Verviers on Fosse the next turn is often key. If this suddenly becomes unreliable, Allied chances go right out the window IMO.

What's also depressing is how many random Game Center games now turn out to be Luck of the Draw, and it's always someone who's taken the Axis who's picked that scenario. Cowards. It's gotten to the point I just resign from these immediately.

The same thing happened to me during a Game Center match, I was playing the Allies and already on the 20th there wasn't much to do than wait for replacements.
I did get to battle 1 SS Pz in Huy and force it to retreat, but lost the game on 23rd (Axis had 57 VPs). I couldn't shake the feeling of "wait, what happened?" at the end of this game, after losing in the initial turns units that normally had a fighting chance in other scenarios.
By changing only the reinforcements table, the Luck of the Draw scenario would have its degree of randomness while still keeping some of the gameplay balance.
The initial unit deployment looks like a more sensitive area to modify, especially when the Axis has the initiative and upper-hand in troops strength.

While I absolutely understand your frustration, still I have played a decent number of games as the Allies in Luck of the Draw and managed to pull out my fair share of wins. The random placement can also hurt the Germans, though I agree it is more likely to benefit them. Same with the reinforcements. You really have to use a different approach to the scenario since you can't take anything for granted. What I like about Luck of the Draw is that you have to put more thought into your game play.