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Bingo Stems

2010 December 5
by admin

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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