At the 2020 yearly black- and white- hatted logician gathering, the following fun activity is organized.
$N$ logicians will sit around a table, each wearing a black or a white hat the color of which is chosen for them randomly at the flip of a fair coin. Everybody sees the other hats but ignores the color of his own.
Every 15 seconds a bell rings and the logicians must immediately do one of 3 actions: say "black", say "white" or say nothing.
If at any time a logician claims a color that is not the color of his hat, the building collapses and they all die in great pain. They know how to have fun.
When all logician have correctly claimed the color of their hat, the game concludes and they are served a delicious meal.
If one or more logicians can't make up their mind and never say anything, well, they all die first of boredom figuratively and then of hunger literally.
They can discuss freely to decide a strategy before the game starts. But once it has started and the hats get chosen, the communication is limited to seeing the other's hats colors and hearing the other's answers.
Can they guarantee too all survive? If not, how can they maximize the probability to survive and eat the delicious meal? Assume $N$ is large.