What if, no matter what happens, Chris always chooses to pass, essentially taking himself out of the game. Then you have two people with two possible hat combinations. If Ann then always chooses the hat that Bob is wearing, and Bob always chooses the hat that Ann isn't wearing, one of them will always be right.

In case 1: Ann will see Bob wearing a red hat and she will guess that her hat is red (the one Bob is wearing), thus winning the game. Bob will guess his hat is blue (the one Ann isn't wearing) and will get it wrong.

Case 2: Ann will see a red hat and guess a red hat, winning the game. Bob will see a red hat and guess blue but it won't matter as Ann has already won.

Case 3: Ann will see a blue hat and guess that she is wearing a blue hat, however, Bob will see Ann's red hat and guess that he is wearing a blue hat, winning the game.

In this way, they can guarantee a victory. If Ann and Bob are wearing the same hat, Ann will win. If they are wearing different hats, Bob will win but they can always ensure that at least one of them will guess correctly and win the game.