If you answered 1/3 to the original Sleeping Beauty Problem, I do not think that there is any sensible answer to this one. I do not however consider this strong evidence that the answer of 1/3 is incorrect for the original problem.

To also expand on this: 1/3 is also the answer to the "which odds should I precommit myself to take" question and uses the same math as SIA to yield that result for the original problem. And so it is also undefined which odds one should take in this problem. Precommitting to odds seems less controversial, so we should transplant our indifference to the apparent paradox there to the problem here.