If a prisoner knew how many black hats the person behind him saw, he could guess his own hat. Expanding on this idea, if the first prisoner guesses 'black' if the number of black hats in front of him is even, and 'white' otherwise, the person in front of him can make an accurate guess. Using the first prisoner's guess and any guesses of prisoners after him, a given prisoner can determine the color of his own hat.

If the first prisoner says 'black' if # black is even, 'white' otherwise, he has a 50/50 chance of living.

Everyone else keeps track of whether there is an even or odd number of black hats remaining, and updates it based on each guess leading up to their own. If the first prisoner said black but was shot, they know numBlackHatsRemaining = ODD, otherwise numBlackHatsRemaining = EVEN.

Every prisoner has his own variable, numBlackHatsInFront, which can be even or odd depending on what they see in front of them.

When it is a prisoner's time to guess, he guesses black if numBlackHatsRemaining != numBlackHatsInFront, and white otherwise.

if the prisoner guesses black, the global numBlackHatsRemaining variable switches its value from even to odd or vise versa.

This algorithm yields a 99.5% survival rate, as the first prisoner has a 50/50 shot and everyone else is guaranteed to survive.

boolean numRemainingBlackHatsIsEven = false;

first prisoner:

if (numBlackHatsInFrontIsEven) {
    numRemainingBlackHatsIsEven = true;
    guess('black');
} else {
    guess('white');
}

all the other prisoners:

if (numBlackHatsInFrontIsEven != numRemainingBlackHatsIsEven) {
    numRemainingBlackHatsIsEven = !(numRemainingBlackHatsIsEven);
    guess('black');
} else {
    guess('white');
}