Last time we had out of sync, the AI moved 3 stacks on the strategic map, but my friend intercepted one of the stacks. However, before combat was initiated, on my screen the 3rd stack was in another position. On his screen, the stack was left alone (thus why he attacked). We couldn't not detect if lag cause this discrepancy or if it was independent from connection speed. He won a on auto combat and I crashed. After I logged back, I still saw the 3rd stack existing there. On his screen there was only 2 stacks. We reverted the turn, and similar thing happened again. This time he went for manual combat and after the win, the 3rd stack mysteriously disappeared from my screen, even though it was half a screen away.