As I wrote in Part I, in 1989, I lived in Vermont with my wife. While there, we often played backgammon and Scrabble. Sometimes, I had an intuition to make a prediction, and the prediction was realized. There are two notable examples from the Scrabble games.
Scrabble 1:
Prediction:
Soon after the game had started, I had the intuitive impulse to say, “I will now withdraw all the remaining E’s from the bag without looking.” I then made the statement.
Outcome:
Before selecting any E’s, My wife and I checked the board and our trays to figure out how many E’s were available to pull out of the bag. Out of 12 E’s in the game, 1 was used, none were on our trays, leaving 11 in the bag. This meant I had to pull out 11 E’s from the number of letters remaining in the bag, which numbered 83.
I then proceeded to withdraw 10 E’s in a row. At the 10th tile, I was overcome with the enormity of how improbable the prediction and outcome were, and stated, “I won’t get the final E. My eleventh draw was not an E.
Probability (provided by Bard chatbot):
Steps:
Total E's in the bag: 12
E's already used or on trays: 1 (played)
Remaining E's in the bag before drawing: 12 - 1 = 11
Probability of drawing 10 E's in a row:
First E: 11/83
Second E: 10/82
...
Tenth E: 2/74
Probability of drawing a non-E after the 10th E: 72/73 (since only 1 E and 72 non-E tiles remain)
Multiplying probabilities:
(11/83) * (10/82) * ... * (2/74) * (72/73) ≈ 2.76 * 10^-13
Interpretation:
The probability of drawing 10 E's in a row followed by a non-E is approximately 1 in 46.3 billion. This is much less likely than selecting all six winning New York Lotto lottery numbers, which is about 1:45,000,000.
Scrabble 2:
Prediction:
In this game, I had the sudden impulse to say to my wife, and said, “you will now play a seven letter word on each of your next three turns.”
Outcome:
She did exactly as predicted, playing: “surfeit,” “colorize,” and “reasoned.” I commemorated the feat with a photo (see top of post).
It is normal in Scrabble to occasionally play all 7 letters, but it doesn’t happen in every game. I have played hundreds of games for which I still have score sheets and can say that this is the only game where three 7 letter plays were made during the game, regardless of player or consecutive plays. For the same player to accomplish this in one game is impressive. To do it on consecutive turns is even more impressive.
To get an idea of the probability, I consulted the Bard chatbot. In this case, I didn’t have enough data to produce an accurate probability value. To know the actual probability, I would have to know how many 7 letter plays were possible based on the letters played, and the likelihood of drawing the right 7 letters after each play. The first can be estimated, but the second is unknown because I did not record which letters were in the bag when my wife chose her letters.
Probability (provided by Bard chatbot):
Turn 1 (SURFEIT):
Drawing SURFEIT: 1/35,000 (approximate number of playable 7 letter words in Scrabble dictionary)
Utilizing any S-starting word: 1/4 (assuming 4 S-starting words available on the board)
Board Placement: 69/225 (playable on 69 of 225 squares)
Combined Probability: (1/35,000) * (1/4) * (69/225) ≈ 1/4,754,285
Turn 2 (COLORIZE):
Drawing COLOR(I)ZE: 1/80,000 (approximate number of playable 8 letter words in Scrabble dictionary)
Utilizing specific I from SURFEIT: 1/1 (only one valid placement)
Board Placement: 1/225 (only one square for COLORIZE)
Conditional Probability for I-Placement: 1/32 (5 open squares above, 2 below)
Combined Probability: (1/80,000) * (1/1) * (1/225) * (1/32) ≈ 1/55,296,000
Turn 3 (REASONED):
Drawing REASONE(D): 1/80,000 (approximate number of playable 8 letter words in Scrabble dictionary)
Matching specific D from FIND: 1/1 (only one valid placement)
Board Placement: 1/225 (only one square for REASONED)
Combined Probability: (1/80,000) * (1/1) * (1/225) ≈ 1/18,000,000
Overall Probability:
(1/4,754,285) * (1/55,296,000) * (1/18,000,000) ≈ 1/4,705,615,616,000,000,000
Discussion
I asked Bard to find any example in published Scrabble games of three consecutive 7 letter plays by the same player. It found none. This doesn’t mean it doesn’t happen. I have read about rare occasions when two players have managed four 7 letter plays in a row, two per player. These tend to be distinctive once-in-a-lifetime events. I have found no examples of three in a row from the same player.
Again, this doesn’t mean it doesn’t happen, but it is genuinely rare. I suspect it is less rare than the 1:4 quintillion chance calculated by Bard. A more realistic probability might be 1:100,000 or so. This is considerably different from the probability calculation. The reason for the difference is that the letters in the bag are unknown, as are the words that could be made from them. In addition, player skill plays a role as well. With the two prior examples: blind draws from a bag and dice rolls, the entire process was random. Actually playing the words utilizes player skill in addition to chance draw.
This incident is interesting because of the prediction that preceded it, not the exact rarity.
There will be a part III and IV to this series, both of which are, to me, quite shocking. For now, these three examples should be enough to show that supposedly impossible events can and have happened immediately after a prediction they would occur. This implies a causal connection, though what that might be is difficult to determine.
WOW
Thank you!
Looking forward to the rest~