The rack leave is a crucial strategy for investing something well in the future turns. This strategy is primarily focused on various factors, including, but not limited to tile values, duplicate tiles, synergies, vowel-consonant balance, and bingo/scoring tendency.
You are more likely to create bingo words if you rid of some or all duplicate letters, as duplicate tiles often limit the number of words you can make on your rack by a fair margin, depending on the particular letter. That being said, this isn't usually the case. If forced to choose between keeping duplicate letters, they vary based on tolerance of duplication. However, there are several exceptions based on the other factors, such as keeping three consonants and three vowels where the two of three consonants are duplicate letters are significantly better than keeping four vowels and only two consonants due to the vowel-consonant imbalance (such as AEGINN versus AEGINO).
For instance, the E is unarguably the best vowel for duplication due to the flexibility of making words, with tons of both long and short words of two to nine letters in length in the lexicon you can make, with nearly one fifth in the entire list containing at least two of them. The S is also decent for duplication, not only due to the "plural" power that allows you to hook words and gives you some extra flexibility, but also creating the more flexible options to play with difficult fits and diversion on the board, thanks to the trend that the S starts more words than any other letters in English that also pluralizes with the another S at the end, making both the E and the S the two standout letters for duplication.
Outside of the standout point, there are multiple debatable letters for duplication. Let's talk about the vowels. First, AA is significantly more debatable to keep than II and OO, as there are significantly more short words that contain two A's than the others with two I's or two O's, and the A has significantly better synergies than the letter two. II and OO are also both debatable, especially when accompanied with multiple consonants that gel well together, albeit being lower than AA. II combination only limits the flexibility to make short words of five letters and below, not in longer words like seven- and eight-letter bingos and even longer words due to the word construction flexibility influenced by various prefixes and suffixes, as well as the spelling changes by suffixing. II tends to be better when accompanied with a handful of higher-scoring consonants that will help with the II combination, such as the C, D, F, H, K, M, P, and Z, as well as combinations like -ING words, since they are apt to absorb surplus of I's while also scoring decently in the process. OO on the other hand, makes a handful of short words that allow you to score consistently, but bingoing will be slightly more difficult than the AA and II combinations due to those words containing at least two O's have different formations in general. As for the UU combination, it is rarely advisable to hold onto it while not sacrificing more than 8-10 points unless you have the Q to pair with those U's or you have no good options to get rid of surplus of U's in the process. That being said, U duplicates extremely poorly overall when compared to any other vowels, as there are very few short words and there aren't that many long words like bingos that have at least two U's in them.
For consonants, their tolerance of duplication varies greatly. Duplicated one-point consonants aside from the S's, namely LL, NN, RR, and TT are all debatable due to various factors such as spelling, high in letter frequency without restrictions on prefixes, suffixes, and compound words. For high-point consonants, FF, MM, and PP stand out as three of the best high-point consonants for duplication due to their spelling flexibility that permits those two letters to gel together in an order, which will also increases the scoring potential in both long and short words. CC and HH are also fine, but less successfully when compared to the former three - CC makes more bingos starting with A, but making overlaps would be difficult, resulting in an unplayable seven-letter words on closed boards, while HH makes easy scoring options while unduplicating it, but bingoing with HH would be very difficult without some more specific words. DD is also questionable as well, especially for playing with something ending in -ED. YY and BB are significantly less preferable to the aforementioned letters, but not horrific if forced to keep them. As for GG without H or N, WW, and especially VV, they are rarely advisable to keep even if forced to hold onto them. While it is usually fine to keep duplicate tiles like TT, RR, FF, PP, and MM while also scoring a reasonable number of points, and trust to luck that you will get a good score next turn while unduplicating those letters, you should almost never hold onto the VV combination unless if you are scoring enough points to afford with the right accompanying letters like a slew set of bingo-friendly tiles like AER or EIR, or you know exactly where you are going to put them, as the VV combination permits numerous nightmare combinations that will force you to struggle with several unhelpful combinations or even result in an exchange with worst-case draws.
Let's take at the closer look at the number of bingos, there are 4,158 seven- and eight-letter words containing at least two R's, which stands out as one of the best non-E/S letter for duplication, compared to 3,351 for two T's, which is the next best. For higher-scoring tiles, there are 1,258 bingos containing at least two P's, 750 for the F, and 457 for the H. On the other hand, the V lags right at the bottom, with only a measly 138 bingos containing both V's.
The full Scrabble tile set consists of 56 consonants, 42 vowels, and 2 blank tiles. Depending on the board position and the remaining tiles in the pool, a slightly consonant-heavy rack with multiple synergistic consonants is more conducive to bingo formation and scoring option diversity. If the pool is vowel-heavy, better off keeping extra consonants that are particularly synergistic (e.g. CEHPR is a much better leave than CEPR for the vowel-heavy pool), even if you are sacrificing a few points by doing so. There are multiple ideal vowel-consonant balance formulas as follows:
Sevens:
4 consonants + 3 vowels (e.g. AEINPRT => PAINTER/PERTAIN/REPAINT)
5 synergistic consonants + 2 vowels (e.g. ACMOPRT => COMPART, AGIMNRW => WARMING)
4 consonants + 2 vowels + S (e.g. AGILNST => LASTING/SALTING/SLATING/STALING)
4 consonants + 2 vowels + Y (e.g. ACHNOTY => TACHYON)
Eights:
5 consonants + 3 vowels (e.g. ACEIMPRT => IMPACTER)
4 consonants + 4 vowels (e.g. EIIMOPTZ => OPTIMIZE)
4 consonants + 3 vowels + Y (e.g. ACIMNORY => ACRIMONY)
6 synergistic consonants + 2 vowels (e.g. DEGINNRT => TRENDING, ACEHMNRT => MERCHANT)
5 consonants + 2 vowels + S (e.g. AAHMNPST => PHANTASM)
5 consonants + 2 vowels + Y (e.g. AGHINNTY => ANYTHING)
On the flip side, if you leave four vowels or leaving two vowels and only one consonant in the pool that is extremely vowel-heavy, you are likely run a high risk of having a rack that has too many vowels, known as the "vowelitis", possibly with six or all seven vowels on your rack, they don't score well and would risk an exchange in the future turns. Likewise, if you keep too many consonants, especially if they are incompatible together (such as BFGP and KNVW), you will have limited options with a rack filled with surplus of consonants that are incompatible together, making it very difficult or maybe impossible to form any words. Examples of five-consonant combinations that are incompatible together that makes the two vowel:five consonant rack considered to be "consonant-heavy" including BCFGP, CGLMW, and FHKTV.
Different letters have different tendency at making bingos. The S and the blanks are two of the most valuable tiles to keep on your rack, allowing you to play bingos or high-scoring non-bingo plays depending on the tiles you replenished from the bag. Some of the good bingo tiles including A, C, D, E, H, I, L, M, N, O, P, R, S, T. Leaves like ERS and EIRST are very good for bingoing since they go really well together, and they tend to have so many seven- and eight-letter words that include those bingo-prone letters. Whereas if you keep weaker bingo letters that don't mesh well with many letters, such as the V and the W, making it much less likely to result in a bingo, since there are far fewer seven- and eight-letter words containing those letters, and they have awkward synergies with many letters like high-scoring letters.
It is also worth talking about "synergies" as well as "anti-synergies", meaning that certain letters may mesh well together or not. Letters that go really well together, such as CH, CK, PR, ING, LPY, as well as scoring tile-heavy combinations like CHK, CHP, CPY, CHW, CKY, HPY, GHINW, and so on, have some good synergies since they go side-by-side in a word and they have a solid representation in terms of number of words that allows you to score consistently while preserving some outside chances of playing a bingo for many more points. But combinations like FP and MV are considered to be awkward to deal with, since they have far fewer words that contain both of those letters, creating an unhelpful blend while playing the very spot they would be most likely to be unloaded in the future. If forced to choose between keeping bingo-unfriendly pairs of high-point tiles, for instance, BY, FH, and KW are all preferable to almost anything that involves the V (possibly except CV, HV, MV, and PV), since they have some good scoring potential that allows you to score consistently without a bingo, especially if the rest of the consonants are good or the board is limited to non-bingo scoring options.
As for the UV and the UW combinations, they are rarely advisable to keep while scoring weakly, since not only they are very few short words that contain those combinations, they also lower the scoring opportunities with bad draws than most of the other anti-synergies, and also permits nightmare combinations that would likely force you to exchange.
The "anti-synergy" is also defined with low-scoring racks as well. For instance, if you keep good bingo letters like AEINRT, you will end up bingoing with many draws as the AEINRT leave makes 56 seven-letter bingos with 17 unique letters (CDEFGHIKLMNPRSTUW). Whereas if you keep multiple low-pointers that mesh very poorly together, even without duplicate letters, such as DGITU and ILORU, you would end up having a very high risk of low-scoring liability that would often force you to effectively play with many tiles as possible while clearing up the rack for minimal points or possibly result in an exchange when it fails to result in a bingo, making those rack leaves even far inferior to synergistic rack leaves that include high-scoring tiles like CEIPR and GHINT, since the last two rack leaves have some good scoring potentials and forms significantly more bingos.
Source: https://www.cross-tables.com/leaves.php
ACELR: +11.5
AERST: +29.0
CEHIR: +13.2
CINOT: +9.4
EIMPR: +11.1
ERS: +16.8
GHINT: +9.8
GINRS: +19.4
ACHP: +7.7
ALPRY: +6.1
ACHKW: +10.2
AHWY: +3.2
FILTY: +3.4
ABERZ: +16.3
ACJK: +5.0
AEQRU: +13.3
EIPRX: +11.0
AEGINN: +8.6
AEPRR: +6.0
EIRTT: +5.4
ADT: +0.5
CPT: -2.9
DENU: +1.9
ERRT: +1.7
IMR: +1.1
NOR: -0.5
AAWY: -2.6
AKW: +0.5
CHW: -0.4
CFR: -3.3
CKRT: -1.2
CPRT: -3.1
FLRTY: -2.6
GHNPY: -1.5
AGILU: -8.4
DGITU: -10.3
ILORU: -11.5
LNOU: -8.2
BFGP: -18.3
BGIPW: -15.1
CDGNW: -15.7
CGMW: -14.5
FKLMT: -12.2
GKMT: -13.7
AACIU: -14.8
ADIIU: -18.6
AEIO: -11.9
AIOU: -17.2
EUU: -18.7
LOOU: -16.2
OOUV: -19.3
BBOUU: -18.2
GGII: -16.0
IOOWW: -16.6
LLNNU: -22.4
QVW: -17.5
BGTUV: -21.7
CGUVW: -23.6
FGVV: -25.6
GKUUV: -23.6
IUUW: -27.0
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