I think I was slow coming up with this, but basically I wrote a lot of tables out and came up with...SPOILER... Alice always guessing the same as what she flip

I think I was slow coming up with this, but basically I wrote a lot of tables out and came up with...SPOILER... Alice always guessing the same as what she flips and Bob always guessing different. But - my question is this: Are there any other possible solutions to this puzzle? Either way, I'm pretty sure this is just an Illuminati code plot from the White House to find the world's top coders and recruit them into some CIA program.