4

While studying Scrabble word lists through Zyzzyva, I came across the term playability order. I understand the term probability order, which lists the most probable tile combinations on a rack of 7 tiles. However, I was unable to understand what criteria orders the words based on playability order.

The first three words in the playability order for 3 letter words are

QIN
QAT
QIS

Which according to me is quite absurd to be most playable, as one is more likely to draw two E's (out of 12) and one R (out of 6) to play ERE or REE, rather than drawing the only Q.

Can someone explain to me in simple words the meaning of playability order of words in Scrabble?

3

"Playability" refers to the expected benefit from playing the word. That is, the actual benefit times the expected chances of getting to make the play.

Q is a very high-valued letter, so any word made with a Q will give you a large benefit. QIN, QIS, and QAT, also have pretty good chances of being played, because you can tack on the Q to common words such as in, is, and at, or tack on Q and N or T around a vowel.

A word with two E's actually has a decidedly better chance of being played, but the value of the two Es is much less than that of one Q. It is this factor that makes the "Q" combinations more playable.

  • But how is the "actual benefit" calculated? Is it not through examining real games, as I state in my answer? How else can it be done, since the score depends on context? Plus the "benefit" is not just about score, it is about balancing your rack etc. – user2390246 Jul 6 '16 at 6:43
  • @user2390246: Yes, a rough calculation of actual benefits would be point benefits, adjusted for the impact of rack balance, as you said. But replacing a Q with another letter generally helps your rack balance, replacing two Es could hurt (depending on the situation). And it could be calculated by examining real games, as you said, or estimated through e.g. a Monte Carlo simulation. – Tom Au Jul 6 '16 at 11:13
3

"Playability" refers to how often these words crop up in real games. Someone will have made a database of all the words played across a large number of "high-standard" games (e.g. club level and above) and ranked how often certain words crop up.

QIN ranks highly because it is a very common way of getting rid of a Q (since there are relatively few Q words to choose from). In addition, it can be formed by hooking -N onto QI, which itself is a very commonly played word. Thus QIN can be considered a useful word to know.

In your example, it might be quite common to have the option of playing ERE, but in most situations that won't score you many points, and there will be better combinations present on your rack.

Note that "playability" is a slightly more subjective concept than "probability". The latter can be calculated precisely, whereas playability will depend on the set of games chosen to average across, and ultimately the decisions of the players taking part in those games.

1

Playability of a word indicates how useful it is to know a word in a Scrabble game because it is likely to be playable as the best move in a particular situation. It is measured by how much worse off you are if you don't know that word. The difference in equity point between that word and the next best play (i.e. equity loss) is tallied over many games to calculate its playability score; the higher the better. (For an explanation on equity loss, see my other answer here)

See here for further explanation http://crosstables.livejournal.com/24367.html

Taking your Q example, it's easier to understand the concept from the reverse angle: your Q will be unplayable if you don't know QIN and it will severely hamper you (i.e. big equity loss), so QIN has high playability score. On the other hand, not knowing ERE is not as bad if you know RE (for example), so even if that situation happens more often, the cumulative effect will not be as bad as that one time you had Q and don't know QIN, hence the lower playability score of ERE.

Another thing to note is that words with more anagrams tend to have lower playability score. Take the highly valued RETINAS rack, high in probability and (deservedly) must be learnt. However RETINAS itself has low playability score, because most likely most of the time if you don't know RETINAS but you know RETAINS (or any of the other anagrams) and the other anagram can be played, no big damage done and equity loss is small.

  • Indeed, "the best move". And one factor which makes one play better than another is your leave (i.e. what tiles it leaves on your rack). QIN scores the same as QIS and ZIN, and you're as likely to draw QIN as ZIN, but QIN has most playability because Z is better to keep than Q, and S better than N. Your leave is important because it is correlated with the expected equity of your next turn. – Rosie F Dec 23 '16 at 9:49

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.