[f97tosc]

This was actually how I started to think about the problem but after I solved for "ROR" I realized that I don't think it is true that you initially "pass" the integer with 50% chance. And indeed, when I solved for the approach side as well, the answer I got was different. Of course I could have made an error somewhere when solving those equations, but I am quite skeptical of the 50% pass claim now.