I haven't looked at the comments yet. Two minutes was enough thinking time to get me to one-box, put not enough time to verbalize my intuition. There was a post earlier on lw about making decisions with imperfect memory that is relevant, I think.

My intuition is something along the lines of 'my decisions only affect whether omega gives me a million dollars or not, so the lottery doesn't matter'.

Further thoughts: your strategy when numbers match change the information that numbers matching conveys. If you one box, it tells you that the particular round loses the lottery. If you two box, it tells you that the particular round wins.

Since you win the lottery just as often regardless of when you know that you win the lottery, the value of this information is zero. All two-boxing does is move the coincidences to coincide with winning the lottery. That, and lose you nearly a million dollars per coincidence.