I'm still working on it, but I think a key idea is that 1) The "host" tells you he is going to eliminate one of the two losing options, and then allow you to choose from the two remaining options. 2) The host allows you, if you wish, to "protect" one of the options from being eliminated. If you choose to protect, you may still choose either of the remaining options after elimination occurs.

The correct solution is to protect one of the options and then choose the other option.

The real challenge is coming up with appropriate flavor text for this idea, but I think I'll get it eventually.