How does Zyzzyva calculate the probability of a word?
I don’t have a nice formula handy, but it’s basically a straight calculation of the number of possible combinations to get a particular set of letters from a full bag, including blanks. Separate combination values are calculated for drawing zero, one, or two blanks, and then the numbers of combinations are added together to get the total number of ways of drawing a word. If you’re interested, you can see the source code for yourself here (see LetterBag::getNumCombinations particularly). Are you sure the probability calculation is accurate? It seems unintuitive to me. Yep, it really is correct. The calculation of probability is notorious for violating human intuition. One useful guideline to remember is that doubled or tripled letters make a particular letter combination much more improbable than you might think. That’s because the number of ways to draw two identical letters out of the bag is generally much lower than the number of ways to draw two different letters out of the bag. If
