(1) Opening racks

(1.1) Typical racks with assortment of good and bad tiles

In this position, you have the opening rack that is mixed between good and bad tiles. You have four good tiles on your rack, namely the H for both scoring and bingoing with number of potential pairings, as well as the ING synergy for potential -ING words, and the H also goes really well with the ING combination as well, especially for the consonant-heavy pickups. But you also have three bad tiles, namely three U's, which the U duplicates terribly in both long and short words, and three U's together is especially horrific, with very few words can be made with three or even four U's (as in MUUMUU). The best of the non-exchange play on equity is 8G HUG for 14 points, retaining the awful INUU leave. This play is nowhere near optimal since both the score and the rack leave are poor, so let's talk about the two choices mentioned. As we can see, both Quackle and Macondo rates exchanging UUU as the best choice, rating roughly at 6 points on equity better than the empty rack. On the other hand, the INUU leave is actually quite dreadful, since not only being vowel-heavy, it also contains duplicated U's, which is very difficult to work with. So in this case, you're much better off taking the automatic exchange, as opposed to playing HUG for only 14 points and plod through garbage combinations.

(1.2) Duplicate-heavy opening racks

The rationale is exactly the same as in the previous opening rack of GHINUUU. However, exchanging five keeping IT is significantly better than exchanging all seven tiles in this position, since with way too many I's on the opening rack already, it could potentially dilutes the bag and makes it much less likely to redraw more vowels and arguably multiple I's from the bag.

(1.3) The worst possible opening racks

This is one of the worst possible opening racks to draw in the game of Scrabble. There are surplus of garbage tiles, including three U's, both V's, and the W combined each other together. There are not a single plays that score a reasonable number of points and/or keep a reasonable rack leave, so exchanging is the only real way to go. I list some of the possibilities below (including a handful of suboptimal exchanges) below. Try to rank them from worst to best.

• Exchange six, keep V

• Exchange six, keep U

• Exchange five, keep AV

• Exchange six, keep W

• Exchange five, keep AW

• Exchange six, keep A

• Exchange all seven

Here are some explanations:

• Exchange six, keep V: Holding onto the V may be defensible in the later part of the game where you need to take a defensive advantage of preventing potential overlaps due to the lack of two-letter words. But the V combines very poorly with most high-pointers (also applies to the C, G, and T to the lesser-extent), and especially the U as well as the U-less Q, being reliant on excess of vowels, and severe underrepresentation in three- and four-letter words when compared to other four-pointers as well as the five-point K, creating an unhelpful blend while playing in the most spot they are most likely to be unloaded in the future turns, especially with consonant-heavy pickups, and permits some potentially nightmare draws such as the aforementioned U-less Q plus three or more additional consonants that are completely incompatible together. Not only that, the V is also very weak bingo tile, as in the early part of the game we should maximize some bingo chances, hence is not worth keeping here.

• Exchange five, keep AV: While holding onto the lone V is a little bit suicidal, when you add a key vowel in the A, things are not that really bad. Your chances of scoring decently are significantly improved as the V tends to prefer vowels (except the U) in terms of synergy. However, the danger of being forced to dump the V for hardly anything is still undoubtedly high, albeit being slightly reduced compared to the previous exchange.

• Exchange six, keep U: The U is slightly less clunky than the V, and functions differently from the V as a vowel rather than consonant. Holding onto the U can be an attempt to protect the Q pickup, but this practice is completely irrelevant due to the availability of Q words not followed by U, most arguably QI and QAT, and the U is the least helpful of vowels that anyone should not strive to make part of their rack leave. Not only that, holding onto the U on an exchange has significant drawbacks, including increased risk of getting a vowel-heavy rack and saddling with a low-scoring liability in the future turns. Again, it will frustrate you significantly more often than granting you a bingo or a nice scoring Q play.

• Exchange six, keep W; Exchange five, keep AW: The W is significantly less clunky than the V, but still undoubtedly more enemy than friend. Unlike the V, holding onto the W is benefical in the later game stages where the board is bingo-unfriendly and mid-valued tiles become far more important for taking advantage of triple-letter, double-word, and triple-word scores, or on other hotspots on the board. The W's synergy is completely different from the V, as the W tends to be found in English compound words, in which most of them tending to prefer synergistic consonants (such as the WH pairing), so the W goes poorly with excess of vowels. Again, but in the early part of the game we should maximize some bingo chances, and the W is not a good bingo tile for the factors mentioned here. It's not worth keeping here.

• Exchange six, keep A: The A features in the highest number of short words of two to four letters in length, but its overall flexibility is slightly lower than the E. It is a great vowel when combined with strong bingo tiles and high-scoring consonants, appearing in a large number of English words alongside the E. While this exchange could potentially allow you to draw the second A, which is annoying at first glance, it's not actually a big deal, since there are a solid number of words that have at least two A's in them. In fact, there are well over 10,000 words of 2 to 9 letters in length that have at least two A's in them, most arguably AA, which is a Hawaiian word denoting a type of lava, plus a healthy dose of words starting with an A, which can also be found right at the very first page of the Scrabble dictionaries.

• Exchange all seven: Having decided to maximize some chances of drawing good tiles like ERS, AERST, the X, the Z, or the blank tiles, you may decide to go all out and throw everything back into the bag. You are also eliminating potential vowel problems while still ensuring that you will draw really good tiles from the bag, which also makes sense too.

As it turns out, there are only two standout exchanges in this position, exchanging six (keeping an A) and exchanging all seven tiles. It is worth saying that the difference between exchanging all seven and exchanging six keeping just an A are not that substantial, but rather a tiny one. Both of them are equally correct moves. With a small handful of suboptimal exchanges being undoubtedly mistakes, they are relatively small. Choosing not to exchange at all and attempting to be defensive from the very start by playing something like VAV for 18 points, leaving the outright horrible UUUW, would actually be much more damaging to your long-term chances of winning the game. The potential defense of VAV that prevents overlaps won't save you from a consequence of saddling with a serious liability in the future turns from the very start, as VAV scores only a measly 18 points (which as way below the average score for expert players of 35 points) and the UUUW leave would almost certainly force you to exchange in the second turn as you cannot manage your rack in the second turn without exchanging tiles. That being said, exchanging tiles allows you to net scoring 30 points better on average after a few future turns. As Scrabble games are decided by your average score, the good tiles like the S's, blanks, the X, the Z, and other stong combinations of bingo tiles such as EIRST, ACEHR, and AGILN. You better off making your better luck and try to maximize some winning conditions by exchanging tiles to maximize some chances of landing those good tiles, for instance, exchanging six tiles keeping an A followed by drawing a seven-letter bingo with multiple high-scoring tiles give you many more chances to land those key tiles, as opposed to only less than 7 after attempting to be defensive from the very start by playing something like VAV.

It is also worth noting that in the international CSW lexicon, UWU is also playable as a recently added word in the 2024 update, but this play is still not an optimal opening play. While it scores 6 fewer points than VAV, and the AUUV leave is far better than the UUUW leave due to the availability of bingos and other words that potentially allow bailouts such as UVULA, VACUUM, NOUVEAU, and VASCULUM, the AUUV leave is still undoubtedly horrific, as there will be way more instances when you have to settle for a mediocre plays that score in the 20-30 point range while keeping the awkward U combined with a slew set of good bingo tiles, a regular 10-15 point play that clearing out the rack, or just have no options to score anything while keeping a reasonable rack leave at all and be forced to exchange, hence is not worth playing here.

(2) A rack of power tiles

Modified from: Scrabble Handbook (PDF)

Our rack: JQUVVXZ

This would be a bizarre rack to draw in an actual game, but useful for talking about the relative values of "power" tiles. Here I will list a selection of possible exchanges, from foolish to wise.

• Exchange six, keeping Q - This is one of the worst moves it is possible to make in the game of Scrabble. Don't do it. Seriously. Although the face value of 10 points for the Q is equal highest of any tile (along with the Z), its "true" value is easily the lowest. For every meaty score you get in the 40-60 point range (e.g. QI/QI with the Q tripled twice) there will be many more times when you have to settle for a mediocre 20-something QAT, a regular 11-point QI, or just have no place to put it at all and be forced to either effectively play with five or six tiles or exchange back again.

• Exchange six, keeping J - The J is far less awkward than the Q due to the flexibility to play without the U, but still undoubtedly more enemy than friend. Again, it will frustrate you more often than it will grant you a nice plays like 50-point JO/JO, 60+ point five- and six-letter J plays, and even 100+ point bingos.

• Exchange six, keep X - The X features in the most two-letter-words of any of the power tiles (five, namely AX, EX, OX, XI, and XU), but its overall flexibility is still lower than the Z. It's far more debatable than the J or Q, but I would still throw it back most of the time.

• Exchange five, keep QU - Although holding on to a lone Q is a bit suicidal, when you add a U things aren't so bad. Your chances of scoring decently are vastly increased. However, the danger of being forced to dump the Q for hardly anything is still present, especially if you have too many consonants, the rest of the letters go poorly with the QU combination, or there is no feasible scoring potentials for the QU combination, albeit greatly reduced.

• Exchange all seven - With this rack full of alleged power tiles, it is interesting that three of the possible exchanges mentioned (keeping either QU/X/Z) are better than keeping nothing at all.

• Exchange six, keeping Z - The Z is easily the best of the so-called goodies. It's the least likely to have to be dumped, and its versatility makes it the most likely to get a good score with. It appears not only in more short words, but also more bingos and 5-6 letter words than any other power tile (1,575 seven- and eight-letter words, and 722 five- and six-letter words containing the Z in the NWL lexicon, compared to 1,290 7s and 8s and 594 5s and 6s for the X, which is the next best).

So, the Z is the only power tile that is unarguably worthy of the name, and is often worth keeping when you exchange tiles. The X and the QU combinaation are pretty much neutral. As for the J and especially the U-less Q, it is rarely advisable to hold onto them in an exchange. While it's usually fine to keep the Z, and maybe X and QU, and trust to luck that you'll get a good score next turn, you should never hold on to the J or especially the U-less Q unless you know exactly where you are going to put them, for instance, the J is worth keeping on an exchange along with the CK combination together for the potentially high-scoring words like JACK words or something.

(3) Your second move

The same principle of exchange on your second move (after your opponent's opening move) is very similar to your first move, except it greatly varies on the opening word, whether the opening move is a bingo, a five- or six-letter opening word, or short defensive words like VAV and CWM (as seen in an example diagram below).

In this diagram, the only obvious play is I6 BU(M)F for 16 points, retaining the utterly unpleasant BGIV combination for next turn. This move is nothing appealing because both score and rack leave are very poor, so trading is in order as a sensible automatic alternative. Here are some potential exchanges ranked from worst to best.

• Exchange six, keep V: (see diagram 1.3)

• Exchange five, keep IV: While holding onto the lone V is a little suicidal without vowels, when you add the lone non-U vowel, things aren't so bad. The V has the tendency to prefer vowels, not a surplus of consonants for other high-scoring tiles like the H, K, W, and Y, so it makes sense to keep the I and the V together. However, the danger of being forced to dump the V for hardly anything is still undoubtedly high due to the factors mentioned in the previous exchange, albeit reduced.

• Exchange six, keep U: (see diagram 1.3)

• Exchange four, keep FGI: Now we move onto the four-tile exchange. Keeping FIG is also a sensible alternative for scoring with something like FRIG, FEIGN, FIGHT, FUNGI, GRIEF, and longer words like -ING words, but the F and the G together are not particularly synergistic. It's not an optimal exchange, but it's okay.

• Exchange five, keep BI: Now let's talk about the B. The B tends to combine better with the A than the I for potential -ABLE words and AB- words that appear right near the very first page of the Scrabble dictionaries. It's not as good as AB or BE, but it's just fine. But I'm going to cover the 

• Exchange six, keep G: The G has the lowest point values of the consonants on your rack, but again, still undoubtedly more enemy than friend. With bad draws that don't involve the friends like the N (as explained for keeping GI on an exchange below), H, L, R, or even the J and the Z, you're very vulnerable to settle for a mediocre 20-30 point plays, a regular 15-20 point plays, or just have to exchange again in order to create a bingo on your own rack, and the N-less G goes poorly with many letters in the alphabet, like the C (without the H), the K plus the T or another G together, the V with excess of consonants, and even the U-less Q (QIGONG and MBAQANGA don't count due to the inclusion of the N). Again, it will frustrate you far more often with bad draws than granting you some flashy bingos

• Exchange five, keep GI: While holding on to the lone G on an exchange can be somewhat alienating, when you add an I, things becomes better. Your chances of hitting synergistic combinations like -ING or -IGHT- words are significantly increased, allowing you to absorb an excess of consonants more effectively since those combinations tend to prefer consonants. Again, with bad draws that don't involve those combinations like something I just mentioned, the danger of being forced to dump the G for hardly anything is still present.

• Exchange six, keep B: Holding onto the B can be a sensible alternative for potential -ABLE words or something, and at least have some synergies with the L and the R, as well as the Z for something like BLAZE, ZEBRA, BAZAAR, ZOMBIE, etc. for big score. But the B is not a great bingo tile to keep on an exchange unless we're keeping something like ABELR, which have a great synergy.

• Exchange six, keep F; Exchange five, keep FI: The F is far less awkward than the V among the four-pointers, but still undoubtedly little more enemy than friend. While holding onto the F may be defensible in the later part of the game where the board is more closed and mid-value tiles become more important for taking advantage of multiple premium squares like the triple files and the TLS-DWS hotspots, and the F goes much better with the I than the B. Just like the B, the F goes relatively well with the L and the R. But in the early part of the game we should be maximizing our bingo chances, and the F is not a good bingo tile. Again, it's not worth keeping here.

• Exchange six, keep I: Now we decide to throw all the bingo-unfriendly tiles back and keep just one bingo-friendly letter that appears in "RETAINS" seems sensible. But keeping a lone vowel that is not an E, or maybe an A still leaves things too imbalanced. If the pool is still heavily skewed in favor of consonants, there are way too many floating consonants on the board, or there are very few I's left, or we are keeping some extra consonants, this is definitely alright. But keeping an I can be vulnerable to drawing a duplicate I, which duplicates poorly in short words, but reasonably well in bingos, creating an unhelpful blend with excess of vowels, which can be particularly toxic, and drawing even more than four vowels with three or more copies of I's could potentially lead to a repeated exchange. But overall, this is the second best exchange of all, just barely behind exchanging all seven. It's definitely in the right direction now, and it makes total sense.

• Exchange all seven: With all the suboptimal exchanges being out of the debate, exchanging all seven tiles is technically the correct move in this position. You are also maximizing the chances of drawing some good tiles like the aforementioned ERS or some blank tiles for this defensive opening board to potentially S-hook onto CWM. This is perfectly the right call here.

It is also worth noting that while both Quackle and Macondo rates the play of BUMF for 16 points being barely better on static equity, with only nearly 2 points better on equity. But when taking into account the simulation after a few hundreds of iterations, then Quackle rates exchanging all seven as the correct play, marginally ahead of keeping just an I. This shows that the best leave from a particular rack is not the same every time, but also depends on factors such as board position/remaining pool. Again, choosing not to exchange at all and take the 16-point BUMF instead, leaving the horrible BGIV, would actually be much more damaging to your long-term chances of winning the game on this defensive opening board. In this case, after BUMF, for every extremely rare instances you can draw into miracle bingos (in fact, there are only a meager of three sevens and seven eights that can be drawn into the BGIV leave. Sevens including BRAVING, OVERBIG, and the newly added VERBING, eights including GIVEABLE, GIVEBACK through the C of CWM, VERBIAGE, as well as four -ING eights (BEHAVING, BEHOVING, BEVELING, and BRAVOING), save for the only recently added six-letter VIBING), there will be far more typical instances when you have to settle for a play scoring in the 20-30 point range retaining the horrible rack leaves like something involving the U-less Q with minimal chances to use the Q productively in the future turns, a weak-scoring play in the 10-20 point range, or just have no good way to score anything while keeping a reasonable leave and be forced to exchange to prevent dealing with horrible racks further.

(4) The "nearly" opening racks

(5) The borderline case

(6) The really wide open board

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