In the comments on the linked site several people refer to the Monty Hall problem, which is not relevant in this problem. When I first heard of the Monty Hall problem years ago, I modelled it with playing cards, and by actually doing the experiment I was quickly convinced of the obviousness of the not-so-obvious correct solution.
With this problem also, it is very easy to model. Flip a coin. If it is heads, wake up SB on Monday and ask her the odds of flipping heads. It is 50/50. If it is tails, wake her up on Monday and on Tuesday and ask her on both days the odds of flipping heads. It is 50/50. "Thirders" are incorrectly assuming that each of the three outcomes is equally likely. Ain't so.
Chance that upon awakening it is Monday is 75% (50% Monday and heads, 25% Monday and tails). Chance upon awakening that is Tuesday is 25%.