Can somebody explain why we are justified in making the assumption that:

y2 = Rx1 ==> x3 = Ry2            (?)

In other words, why does R remain constant over the nth bet?  

I see absolutely no reason for this to be true, or not to be true. 

They give absolutely no explanation, except for a vague "X is now in the same position Y was in".  I don't understand how that is anything close to a tangible argument.