It seems to me the answer becomes more obvious when you stop imagining the counterfactual you who would have won the $10000, and start imagining the 50% of superpositions of you who are currently winning the $10000 in their respective worlds.
Every implementation of you is you, and half of them are winning $10000 as the other half lose $100. Take one for the team.
If you count the amount of “wanting to switch” you expect to have because the cable guy hasn’t arrived yet, it should equal exactly the amount of “wishing you hadn’t been wrong” you expect to have if you pick the second half because the cable guy arrived before your window started.
I’m not sure how to say this so it’s more easily parseable, but this equality is exactly what conservation of expected evidence describes.