First, the Axis will typically have 2 BH to fire onto the US units there. Every Allied player I have seen until you have used the Naval Bombardments to clear out the UK beaches to try and save the tanks from being destroyed, as it happened in this game. Because why would anyone not want to protect 3 of 14 available tanks, most of which do not get onto the board until the middle part of the game?
That, in my opinion, shows some difference in experience since the allied tanks are a valuable resource to protect.
The main point here is that, with your math, the odds of the US having more than 1 arty walk into Omaha are 50% at best. And the Axis mostly have 2 BH to fight with, which changes your numbers.
Second, there is approximately a 33% chance that 6 dice rolling for a 1 will miss, which is common enough to say your attack into Omaha, at least with the inf, was not getting hosed by missing. But the Germans getting slightly warm dice, added to the lack of hits.
Third, I did not have 6 more units on the board. Those 6 units were on the board from the start, and Omaha Beach is not set up for the Allies to walk over like Juno and Sword Beach. Using your logic, those units walking away from the beach also led to more Allied units surviving later in the game to fire more since you did not have to fight through them on the first few turns. As you would have in most other games. Your math also fails to consider that I can bring a tank, inf, or arty in on G1 to help push the odds in my favor to get those units free from the locked battle at Omaha. Which again changes your math and leads to their escape or the UK having to come in to bog them down again which affects you ability to power project to Caen.
Yes, I had fewer German units on the board. But my play was also based on what resources I had available. Should I have had fewer units at my disposal, I would not have made the earlier attacks that I did since I could see from the board state at round 5, I was in a winning position.
This was one game, so how can you say the game is balanced? Based on the results thus far the game is 100% in favor of the Germans as they are 1-0 right now. Why don’t we play another to put your money where your mouth is to see if you can make it 1-1?