This lecture was about tiles. The main concepts were:

- Special tiles (?, S, Q, J, Z, X)
- Tile tracking
- Bag awareness
- Setups

1. Special tiles

We discussed 2 particularly good tiles and 4 particularly problematic tiles.

Blanks: there are 2 of these in the bag, and you should value them at about 25
points each. Why are blanks worth so much? Well, by nature, they are already an
amazing asset - like having 1 of each letter in your rack. That opens up a lot
of possibilities. In particular, blanks make it a lot easier to get bingos,
which are a key element of scoring well in Scrabble. Take a look at the
examples in the slides to see two situations when it is and isn't worth using a
blank for more points.

S: there are 4 of these, and they're worth about 8-10 points each. You probably
can guess why S's are particularly valuable - they're extremely hookable. You
can hook them onto many nouns and verbs to hit bonus spots or find lanes to
place bingos. Especially in combination with a blank, an S makes a rack much
easier to bingo with. See the slides for some examples about using (or not
using) S.

NB: The value of these declines significantly the more closed the board is and
the less bingo lanes are available. Duplicates are also not worth much: it's
very hard to anagram with two blanks, and you only need one S to hook. But
never exchange a blank or S: instead, use it to get some points if you don't
need it in your rack right now, so your opponent doesn't draw it. But be
careful: using a blank or S trivially usually signals to your opponent that you
have another.

QJZX: these are really grouped together, and the same concepts generally apply
to all. These tiles, often referred to as the ``power tiles'', are anything
but. They're difficult to use, and usually sit on the rack for a long time,
blocking your chances of playing bingos. Q is the worst by far, and the slides
show the short list of words with Q without U, and an example of when my
opponent was stuck with the Q on their rack at the end of the game and lost 20
points because of it. You should almost always aim to get rid of these tiles as
soon as feasible. DON'T wait for a ``good spot'' to come along - they rarely
do, and you're wasting turns and points waiting for one. However, this all
depends on several other factors: the advancement of the game (later in the
game, you should be even more focused on disposing of these tiles ASAP, as
they're harder to place at this point and you don't want to risk getting stuck
with them), the score (the more you're down, the quicker you want to get rid of
them to free your rack for big opportunities (i.e. bingos)), the bag's
composition, and the particular shape and opportunities of the board (if there
are multiple open I's next to DLS, then holding onto Q for an extra turn or so
isn't so bad, because you have a place to get rid of it reserved). These 4
tiles vary in the degree of badness. If I had to rate them on a scale of 1-10
where 10 is the worst, it would be something like Q=10, J=5, Z=3, X=1. (This
doesn't mean X is a good tile - it's just the best among these 4.)

2. Tile tracking

We also talked about tile tracking. On the score sheets, there is a frequency
chart of all the tiles in the bag on the right side. You can use this chart to
cross off the tiles that have been played as the game goes on. This allows you
to know the exact composition of the remaining tiles at all times, which is
particularly helpful during the endgame (when the bag is empty), because you'll
know your opponent's tiles exactly. For this reason, it's important to reserve
adequate thinking time for the endgame, when you'll need a lot of time to think
about your choices and what your opponent will play in response, and what
you'll play in response to that, and so on. I recommend trying to having 5 full
minutes left by the time you get to the endgame (the bag is empty).

Tracking is deceptively difficult to do correctly without a lot of practice.
One technique that I've recently begun using which helps a lot is to make a
small mark in the corner of the box for each play after you track it. This way,
when you inevitably forget to track a play, you'll easily be able to find which
one you missed and correct your tracking.

3. Bag awareness

Besides at the endgame, having an accurate record of the tiles remaining is
helpful for general bag awareness. How does this impact your playmaking?
Before, we assumed that the bag always had the roughly 60:40 CV ratio whenever
we evaluate our leaves. But this is often not the case: if we know the bag is
actually 50:50 CV, we would want to keep more consonants, since we're more
likely to draw vowels than usual. So our awareness of the bag informs how we
evaluate leaves. Sometimes, estimating the CV ratio of the bag is easier to do
by glancing at the board and estimating based on the apparent CV ratio of the
board (more visually intuitive than looking at the lists of crossed-off letters
on the frequency chart).

Beyond just the CV ratio, pay close attention to which special tiles are left
in the bag. For instance, knowing how many blanks are left can inform our
estimate of the probability of playing a bingo in coming turns. If there are
only a few tiles left in the bag and QJZX are among them, we might try to play
fewer tiles so we don't draw a deadly rack right before the endgame. These are
a few examples of how we can use our knowledge of the tile distribution to
inform our play.

It's also important to always be aware of how many tiles are left in the bag.
You can't exchange once there are fewer than 7 tiles in the bag, so if you find
yourself with a moderately bad rack close to the endgame, you should make sure
you get an exchange in before you lose the option to.

4. Setups

Another way to apply our bag awareness is with setups. Besides the overall CV
ratio, tile tracking provides us with useful information about how many of each
particular tile is left - we especially care about the distribution of the 6
mentioned above. When we hold the last of a particular tile, we can often use
this to our advantage in setups. Look at the slides for a particularly common
example: using the knowledge that we hold the last S to set ourselves up for a
nice bonus play that our opponent can't take from us.