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It's generally easier to get a low score in Scrabble than a high one. But is it easier to get a really low score?

Suppose you play a game of Scrabble by yourself in which you only make legal plays (that is, they'd withstand a challenge). You eventually play all of the tiles.

The order of play is important - if you make two words, you count them both. If you play on a double word score, the word that you formed is doubled (so you might want to start by playing a short word). Also remember that if you play all 7 tiles in your hand you get 50 points, so don't do that.

A lower bound on the score is 187. This is obviously not possible, as you're going to have to overlap words a fair bit. What is the lowest possible score you can get?

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  • $\begingroup$ I added italics because I think that having to play all tiles is the most important constraint in the problem. Also, (to attempting solvers) I have an idea that it would be best to play very long words, so that overlapping is minimal. Also also, overlapping should probably be done with 1-point letters if possible (all while avoiding extra-point squares). $\endgroup$ – Brandon_J Mar 22 at 16:39
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    $\begingroup$ Here's a link to a 1981 paper outlining the lowest possible scoring Scrabble games. No formal proof is given for their final answer, but it might be a good starting point. $\endgroup$ – DqwertyC Mar 22 at 17:54
  • $\begingroup$ NOOOOOOOOO I didn't get to answer :( Cracks knuckles Time to bring out the weird words $\endgroup$ – North Mar 22 at 22:36
  • $\begingroup$ So we have to use every single tile? LIke we can't make a game where it would be impossible to place a z or q anywhere? $\endgroup$ – North Mar 22 at 22:53
  • $\begingroup$ @North Deusovi has you beat with weird words :P $\endgroup$ – noedne Mar 22 at 22:59
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I started with the solution given in a paper found by DqwertyC in a comment. Unfortunately, it contains several errors, including invalid words, incorrect scoring, and the wrong tile distribution. Finding ways to resolve these errors gave me the following board.

scrabble board

The opening play is es, using both blanks. The next 3 plays of voicers, epigram, and thirties overlap only in blanks. Each of the subsequent $19$ plays forms one of the remaining $19$ visible words, overlapping in exactly one 1-point tile. The bonus squares used are $10$ 1-point tiles on double letter squares (at G3, I3, A4, I7, M7, D8, M9, A12, H12, and D15). Every play uses at most 6 tiles, so no bingos occur. This incurs a total penalty of $19+10=29$ on the total tile score of $187$, resulting in a final score of $187+29=216$.

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I've managed a score of $225$. I'm sure a better score is possible, since there were a few places where I was not optimal.

It's impossible to avoid all the "special" squares on the board, so I chose only to hit a few of the Double Letter squares, which are no more penalizing than creating an extra join between words (i.e. it's probably more beneficial to cross a few Double Word squares and get a lot of longer words than it is to squeeze my way in between the "special" square using 3-letter words).

I started out using both blanks to negate the automatic Double Word that occurs on the starting square.

Here is the final board:
enter image description here

And here is the sequence of moves (they could go in many other orders without affecting the score):
(format is (Word score)(Cumulative score) Word (Uppercase indicates new tiles))

  1. (0)(0) IN (both blanks) (Double word)
  2. (1)(1) Rin (add the R)
  3. (15)(16) IMPrinTING (Double letters - I and N)
  4. (7)(23) iRING (Double letter - G)
  5. (23)(46) REACQUiring (Double letter - A)
  6. (15)(61) EXIgENT
  7. (8)(69) eBBS
  8. (8)(77) LOOsED (Double letter - O)
  9. (8)(85) tAKE
  10. (13)(98) SWeATY (Double letter - A)
  11. (8)(107) AUDiTOR
  12. (5)(112) IDEa
  13. (10)(122) MOOiNG (Double letter - O)
  14. (11)(133) AJAr
  15. (10)(143) FLaILS (Double letter - I)
  16. (16)(159) UNSaVVY
  17. (6)(165) ECRu
  18. (22)(187) WHEeZE (Double letter - E)
  19. (7)(194) TAUnTER
  20. (4)(198) tOIL
  21. (10)(208) POOlED (Double letter - O)
  22. (7)(215) rIFE
  23. (6)(223) HAe
  24. (2)(225) At
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  • $\begingroup$ Whoops! Just noticed that there should be an extra 50 pts added, because I had one bingo. Will try to rework. $\endgroup$ – GentlePurpleRain Mar 22 at 18:34
  • $\begingroup$ If you play Tournament rules, and (incorrectly) challenge each word, then you subtract 5 points each turn for 120 point discount. $\endgroup$ – Chris Cudmore Mar 22 at 19:18
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    $\begingroup$ playing 'print (5)' instead of 'rin (1)' avoids the bingo and gives a total score of 229 $\endgroup$ – Daniel Mathias Mar 22 at 19:42
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    $\begingroup$ Out of interest, what's the Scrabble board editor you're using? $\endgroup$ – ZanyG Mar 22 at 20:30
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    $\begingroup$ @ZanyG I just googled and found this one. $\endgroup$ – GentlePurpleRain Mar 22 at 21:16
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It is in fact possible to do an entire Scrabble game without ever using bonus tile besides the mandatory one in the front. enter image description here

I started of with in, then print, then printer (I borrowed GPR's idea)

The circled/boxed i and n in the middle are blanks, btw.

Here's an interesting note to point out: just because this set-up doesn't use any bonuses doesn't actually make it the lowest scoring game. I screwed up with using the k twice (in OAK and KEG). Even disaccounting for that, there are over thirty different reuses from just my initial count. I actually lost count... If anyone wants to waste their life, feel free to count it up, but regardless, it takes some obscure words and many different tile placement that ends up creating more points rather than just taking the double letter on the 1 point-er.

*Please note that no bingos were actually scored in this run. **All words are valid words in Scrabble. Yes, "cwm" is a word. Yes, "joe" is a word. Yes, every single word here is a playable word. If you don't believe me, go ahead and look up every single word and waste your life

enter image description here

That one's just a joke boad that I made, by techinical rules of Scrabble, if no one challnges it, it's valid. Another way to make a board, without any use of the bonues tiles.

Final Point It's physically impossible to achieve 187, as the OP stated. In fact, it's impossible to get 188, 189, etc... you have to cross tiles. I think the only way to get the lowest possible score isn't to use the least number of bonus tiles. Rather, it's the least number of crossings: and those crossings need to be on a 1 tile for minimal effect on the points.

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    $\begingroup$ That moment when you disprove the GPR @GentlePupleRain I have blasphemed! Please forgive me! Don't use that banhammer! $\endgroup$ – North Mar 23 at 3:03
  • $\begingroup$ If it wasn't for the fact that you had to use all your tiles I could've also made a board where the Z, Q, X, J, K, V, and V stayed on the rack... :( That would've been 50 points off by the end, and wouldn't have been that hard to pull off. There are no two letter words including V, K only has 2, Z, J, and Q only have 1, and X... X actually has 5. But it's worth 8 points so $\endgroup$ – North Mar 23 at 3:13

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