A crazy cat lady wants to give away some cats. Five prospective owner arrive at her home, and agree to her rather eccentric method of judging them worthy of owning some of her beloved kitthes. There are six cats, either black or white, that the owners have never seen. The owners are arranged in a circle and a cat lady secretly places a cat on each of their heads (they are docile enough to stay there, as they are trained to be kitthe hats). Each owner can see the color of each cat except his own.
The cat lady instructs the awkwardly cat-laden individuals that at a specified time, they will all either simultaneously guess the color of their kitthe hat or remain silent. Should no-one be incorrect, but at least one person have the correct cat color, everyone gets their cat. She doesn't specify what will happen if someone *is* incorrect, but the last group that tried to obtain some cats never returned, and she never leaves to buy cat food.
Thankfully, the cat lady wanders away to another room, leaving the participants to devise an optimal strategy. Assuming they are not distracted or unnerved by the strained mewling being emitted from the room - and the sound of her cats meowing as well - what is the probability of successful kitthe acquisition for an optimal strategy?
(Bonus: What is the probability tend to as the number of participants approaches infinity?)
