# Bingo Stems

A bingo is a play in which all seven letters on your rack are used – and it yields both the points on the board AND a fifty-point bonus. In most cases, a bingo involves a seven– or eight-letter word (although longer words can be created by utilizing two or more tiles already on the board). So if you want to improve your ability to play bingos, that leaves a pool of around 53k words to learn (there are 24,029 seven-letter words and another 29,766 eight-letter words).

Some smart people started thinking about how to approach this pool of words. One idea was to focus on words that could be formed from high-frequency letters. This thinking produced what are known in Scrabble circles as the 3%ers. 3%ers are all the seven-letter words that can be formed from the letters ADEGILNORSTU using a maximum of 3 As, 1 D, 4 Es, 1 G, 1 I, 1 L, 2 Ns, 2Rs, 2S, 2Ts, and 1 U (with the exception of the number of esses, these numbers represent the maximum number of groups of three that can be formed of each letter using the tiles in a standard 100-tile set). For example, there are twelve Es, so four groups of three can be formed. This group of words is referred to as the 3%ers because each of these letters has at least a 3% probability of being randomly drawn from a fresh Scrabble bag (i.e. all these letters appear on at least three tiles in a standard 100-tile Scrabble set). Here are the letter frequencies (arranged by point value). A handy way to remember these letters is the phrase “U DATE NO GIRLS.”

2 blank tiles (scoring 0 points)

1 point: E ×12, A ×9, I ×9, O ×8, N ×6, R ×6, T ×6, L ×4, S ×4, U ×4

2 points: D ×4, G ×3

3 points: B ×2, C ×2, M ×2, P ×2

4 points: F ×2, H ×2, V ×2, W ×2, Y ×2

5 points: K ×1

8 points: J ×1, X ×1

10 points: Q ×1, Z ×1

There are 2476 “3%er” seven-letter words. Based on tile probability, these words are the most likely to appear in your rack, so it’s not a bad way to start learning the words that will increase your ability to score bingos. It’s certainly better than learning seven-letter words randomly or alphabetically.

But WAIT. Don’t start memorizing yet. It would be useful for a player to have a way of identifying whether or not the seven letters on his or her rack could be used to form a bingo BEFORE the player spent his or her time trying to “find” the word. It would also be helpful if some structure or mnemonic could be developed that would aid a player in memorizing relatively large groups of seven-letter words.

Bingo stems accomplish both of these objectives.

Here’s how Bingo Stems work. Six-letter combinations of letters are identified and ranked based on TWO criteria: 1) the probability of the six-letter combination of letter appearing on a player’s rack, and 2) the probability of drawing a seventh tile that can be combined with the first six tiles to create a bingo or bingos. For example, the combination of QXKJZP is relatively unlikely and none of the 94 remaining tiles will combine with these tiles to form a bingo. On the other hand, the combination of AEINST has a relatively high probability of being drawn and any one of a remarkable 90 of the remaining 94 tiles could be combined with AEINST to for a bingo (only the letters J, Q, and Y cannot be combined with AEINST to form a bingo).

The top 100 six-letter combinations (or bingo stems) based on probability and likelihood of combining with a remaining tile to form a bingo have been identified. Mnemonics have been developed for these bingo to aid in identifying whether or not a bingo exists. Here is how it works.

A player looks at his rack and sees the six letter combination AEINST – or TISANE (a herb-flavored tea). She notes that the seventh letter is a K. She remembers the associated mnemonic: TUCKSHOP WIZ FIXES MEDICINAL BEVERAGE. Every letter in this phrase can be combined with TISANE to form a bingo, so she now knows that there is a bingo on her rack (or multiple bings). She can now take the time to find it. Had her seventh letter been a J, Q or a Y, should would have immediately known that no bingo was possible.

Bingo stems work for two reasons. First, six letter words are much easier to spot that seven-letter words, so this approach give a player the ability to stair-step into a bingo. Second, it provides a structure to aid in memorizing words.

So how much overlap is there between the words derived from bingo stems and the 3%ers? A total of 2022 words can be derived from the top 100 bingo stems. These word are known as Type I bingos by Scrabble afficionados. There are a total of 2476 3%ers. Only 890 words appear on both lists. That means that 1132 of the 2022 Type I words are not 3%ers. This should make sense, given that in many cases, the letter being combined with the high probability stem (i.e. the originial six tiles) is not a high frequency letter (a J, or an X, for example) and the resultant bingo, therefore, does not qualify as a 3%er. All the remaining 3%ers (i.e. all the 3%ers that are not on the bingo stem or Type I list) are known at Type II seven-letter words. There are 1586 Type IIs. The total number of 3%ers on the Type I list (890) plus the total number of Type IIs, all of which are 3%ers (1586) equals the total number of 3%ers (2476), as it should. Type III words are those words with the same or greater probability of appearing in a player’s rack as the lowest probability word that can be derived from one of the top 100 bingo stems and that do not already appear on either the Type I or Type II lists (i.e. they are not derived from one of the top 100 bingo stems and contain a low-frequency tile). The lowest probably word that can be derived from one of the top 100 bingo stems is HUNTERS. The word EROTICA, for example, is a Type III word. There are 2789 Type IIIs. Type IV words are all remaining seven-letter words. There are 17,632 Type IVs. If the number of Type Is (2022), Type IIs (1586), and Type IIIs (2789) are subtracted from the total number of seven-letter words (24,029), the result is 17,632, as expected. The majority of seven-letter words are Type IVs.

More information on bingo stems can be found in Mike Baron’s *Scrabble Crossword Game Wordbook* and on John Chew’s “Canonical List of Anamonics.”

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