Solution to BEEMOTY rack:

There are two lessons to be learned from this rack: how to reevaluate your leave values, and how to react to a bizarre play from a strong opponent.

Let’s start off with the basic analysis of the position.  You’re down 10 points with a strong rack. The T and Y are both very strong tiles, and against a random rack, you’re easily the favorite. The Y is probably worth about 8 points here, while the T is probably worth between 15 and 20.  Both a14 and n10 are very lucrative, but more importantly, both spots are probably going to stay open. The Y is a guaranteed 35, but can potentially score anywhere from 40-60 points!  Saving one or both of these tiles (especially the T) can be extremely lucrative on future turns.

Based on this analysis alone, you should probably be favoring YEP, although plays like BYTE and MOTE are reasonable. Based on pure equity and potential, I think YEP is going to result in the best spread and point differential over the next few turns, against a random rack and a random player.

How does WO fit into this equation, especially given the fact that it was played by a top player? It’s very difficult for any player to figure out what is going on from an x6 followed by WO here, but let’s analyze some of the potential reasons that someone might play WO, and how that affects potential options:

1. WO is a diversion for an existing bingo line or scoring spot. WO is made to protect something already on the board. In this case, we should lean towards playing elsewhere outside of the bottom left, especially potentially lucrative spots such as columns g and h.

2. WO is a bait designed to draw out the T that could block a future bingo or scoring spot. This is a further reason to distance yourself from column a plays.

3. Opponent has concluded that you rarely have a T. In this case, you should further the story and not play the T: that spot is very likely to remain open if this is the case.

You should avoid: especially BYTE. You should *really* want to keep the T both because of an increased adjusted valuation and because there is a more than reasonable alternative in YEP. I’d suggest that players only play the T here if it has the highest valuation by a very large margin: probably over 25 points in equity for all of the reasons listed.

You can certainly consider other plays: however, I just don’t think we have enough information. Any good blocking play just gives up over 15 points in valuation, and often gives our opponent a decent scoring option back some of the time, and I just don’t think that trade is worth it most of the time. If your opponent keeps fishing, THEN start blocking, but we’re not in a favorable enough position to block what look to be fairly unlikely bingo lines at this point.

Remember, we are losing the game: if the opponent is going to draw well enough to hit a fish or a play they didn’t already have last turn, we probably weren’t going to win this game anyway, and making a blocking play means we are small favorites even if we managed to block a potential bingo or high scoring play opportunity. YEP scores significantly more points than anything else that doesn’t use the T, and most of the other options don’t block well either, and therefore, I think it should be the preferred play.

As for what our opponent has after WO? Well, you’ll have to wait for a new position on that one… stay tuned for part 3!

Before we examine these options, as always it’s useful to note the other factors: the score (0-24, not really a factor) and his range. Your opponent’s range after AZO is fairly strong, likely containing an N, often containing an A, and containing more ?/S than random. They are fairly unlikely to have an E, as well as many clunky tiles (C, G, P, X, etc. are unlikely)

AWN and NAW are very similar plays. Both close the board about equally well, while AWN scores two point less but creates a slightly better board because of your S hook. It’s really a tossup between these plays.

WAN looks good because of the NE possibility, but this possibility isn’t nearly as good as it first appears. First of all, your opponent is likely to have an N themselves, and while they don’t have an E, they might draw one, or have a D/S/T already or could draw one next turn. Even if they don’t, your opponent will sometimes have a G/P/X/S to underlap WAN, substantially weakening the utility of that hook. WAN does open some possibilities for you, but it also opens possibilities for your opponent that hits their likely range fairly hard. The openings are better for your opponent than they are for you.

However, the strongest play is WEAN, scoring two more points than NAW/WAN and severely limiting your opponent’s scoring options since they can no longer underlap WEAN as easily. Computer analysis shows that WEAN decreases the opponent’s score by 4 points more than AWN/NAW and 7 points more than WEAN. While the E is a welcomed addition to ANS, it’s not nearly as significant as the superior defense and 2 additional points.

In this position, its essential to realize the primary existential threat to your lead: bingos. You’re up by 44 and turn: it’s going to be hard for your opponent to outrun you by simply scoring, as there really aren’t all that many scoring options possible. Quackle simulation shows that the average score is 20 points with a standard deviation of about 12, indicating that a 44 point lead + turn is quite safe in terms of this position’s future scoring potential.
The major existential threat to your lead is bingos: fortunately, you’re on a board where it is difficult to bingo. Unfortunately, it is also very easy for your opponent to create bingos and bingo lines.
One approach is to outrun these potential bingos. A play like KERNEL/KERNED, RELENT or RETTED scores decently and plays off bad tiles on this board (since the bingo prospects are so bad, tiles like E, N, T, etc. drop in value considerably) in hopes of drawing good tiles (such as the S, H, and Q). Another option is to play TAEL (which sets up the S, but the S is going to score anyway, and can be blocked by row 13 parallels: you can also play the row 13 parallel like NE first to “protect” TAEL).
There are two spots to create bingo lines: one in bottom left quadrant, but more noticeably, bingo line hooks can be created at n5 with plays such as PARE, TARE, HARE, and especially CARE/CRAM. These threats are not only immediate: they are recurring, and your opponent can (and often should) make these plays even without the S in hand, and are very difficult to stop in general. For this reason, a reasonable option is playing TRAM immediately for 6 points, blocking the potential S setup immediately.
But for this same reason, the D is a quite useful tile because of the five letter word DIRAM. This allows you to block many of those setups (all of them except CARE), and prevents a recursive bingo line that can easily overcome your lead. For this reason, the D is a very useful tile to keep: enough so that RELENT becomes a better play than RETTED, and KERNEL is a better play than KERNED.
While KERNEL scores more points, it is also less flexible, keeping 3 consonants and two Ts (with 3 Ts unseen). Thus, RELENT has a higher valuation. Similarly, when you compare RELENT and TAEL, both have a nearly equivalent leave (DT is a trifle better than DENT, but not much) but the VINYLS hook is a slight negative since it introduces an outscoring threat (VINYLS isn’t a threat immediately, but after the CARE/TARE setup, it could easily become one with some other scoring tiles). I slightly prefer RELENT.
Really though, it just comes down to the fact that we’re going to have to deal with the n5 setups eventually, and we’re going to have to sacrifice points to do so: even if our opponent makes a 25 point play next turn, that setup is still going to be a priority for turn after turn after turn, and there’s never going to be a good option to block it. Your opponent will almost always make this setup in future turns and you’re going to need to block it. For this reason, it’s best to stop this setup in its tracks and block it immediately by playing TRAM to preemptively kill the potential open flower that will be very difficult to stop.

With this rack, there are only 4 real options: VIE 8g, AVE 8h, VITAE, and -E.

The first comparison that we should make is between VIE and AVE. Both plays imply very strong leaves, which are likely to induce closed board responses from a strong opponent assuming that they don’t have a strong rack. VIE will often prompt plays through the E or preceding the I and E, while AVE is harder to block, although it can still be blocked with G-AVE or E-AVE (if they have those tiles). (AVE 8f can be considered as well, but it gives your opponent a lot better scoring and lowers the score of your bingos dramatically, even though it results in more playable bingos on future turns.)
This factor decreases the worth of both leaves, but has a greater effect on VIE. While the leave in somewhat stronger after VIE, AVE will result in a more bingo friendly board for your range, making it a slightly stronger play even though it retains a slightly worse leave.
-E might initially seem good until you realize that bingos occur somewhat rarely. Less than 1/3 of the bag will result in a 7 letter word, and many times a good opponent will not give you letters to play an 8 letter word (or play anything at all) or play a word that will make some of your 7s unplayable. AVE results in nearly as many bingos as -E while also scoring 12 points, making AVE a stronger play than -E.
Finally, we must compare VITAE and AVE. VITAE scores 24 and keeps ER (which is worth about 5) but does also give your opponent options in the form of increased parallels and bingo potential. From a valuation standpoint, it’s pretty easy to peg VITAE right around 27, which means AVE has to get there, and honestly, it’s hard to see how AVE gets there. EIRT isn’t worth 15 in a standard situation, and given that your opponent has a very firm grasp of your range after AVE and that many racks can result in blockier plays, it’s difficult to see how EIRT can make up the 15 points, especially since the rack can turn problematic on future turns when it fails to bingo in the immediate future.

I do feel as though it’s important to note what can be learned from this rack in general. I hope that readers come away with two important themes from this rack and racks like this in general:
1. Racks that are near a bingo (that don’t contain an S) are not very good opening racks in general. When you end up fishing, a good opponent is going to be able to put you on a range and play very well against that range, not just next turn, but often on future turns. We’re often trained that the objective of Scrabble is to bingo, but when you fish with AAEILNT or AEEGINT, you’re not doing it because “you’re excited and you almost have a bingo”, you’re mostly doing it because there really aren’t any reasonable alternatives. At the end of the day if you can get out of these racks by either scoring 30+ points or scoring 20+ and keeping a decent leave rather than 10 points and a very good leave, you’re actually often better off scoring unless the board is extremely conducive to bingos, especially against good opponents who are capable of leave inference.
2. Opening racks in general are actually better thought of as closed board situations that are very permutation-heavy. A lot of times on opening racks the board will be empty or near empty and there won’t be a ton of room to play bingos etc. in the immediate future. A big problem with this rack specifically is that VIE isn’t parallel-able and AVE is hurt because of the front-hooks that kill AVE-R: without both of these factors, AVE and VIE become viable and are quite possibly the best play. A similar rack like AEEHIRT is actually a lot more viable in this case, since HIE/HAE make it much more difficult for your opponent to close bingo lines profitably since there are no hooks or parallels that severely hamper the board for bingos next turn.