The pattern of hats on three heads can be 8 different permutations:
red, red, red
red, red, blue
red, blue, red
red, blue, blue
blue, red, red
blue, red, blue
blue, blue, red
blue, blue, blue
The trick is to “see” that 2 of these 8 permutations have a distinguishing characteristic: they involve all three hats being the same color.
Think about it ….. 1/4 of the time, the hats are all the same. 3/4 of the time they are NOT all the same ….. 1 is red and 2 are blue, or 2 are red and 1 is blue.
So if the players all make the assumption that the colors are split 1 and 2, and vote appropriately, they will win 3/4 of the time, by following this strategy:
If you see 2 hats of the same color, make a “guess” that your own hat is of the opposite color. But if you see hats of opposite colors, write “pass” on your slate.
EST's 3HP 
Hey Ernie. I found this great online video of a dad explaining the Three Hat Problem to his kid using Legos http://www.youtube.com/watch?v=Oh9b6Yij_Zs
David ….. The first reply I’ve gotten! Thank you so much. But this is not the same 3-hat problem. Your problem is interesting too, but it involves a limit on the numbers of each color of hat, whereas the first 3-hat problem from the 2001 N.Y. Times article states that there’s no limit to the number of each color hat. So seeing two blue hats on the other players doesn’t give you any certainty about the color of your own hat.