To date, this substack has been exclusively focused on my more interesting dreams. I have also had some statistically unlikely experiences that do not involve dreams. In this post, I will present one such experience from 1989. This event involved dice rolls, making it very easy to perform a valid statistical analysis of the outcome.
The event:
Prediction
My wife and I moved to Vermont in 1989. While there, we developed the habit of playing board games, primarily backgammon and Scrabble. On one evening, we were playing backgammon. For those who are unfamiliar with backgammon, an essential element is to roll dice, two per player. The first player rolls his dice by shaking them in an opaque cup and tossing them on the backgammon board. Player 2 then does the same thing.
During this game, I suddenly had an intuition. The intuition came in the form of a prediction along with the admonition that if I stated the prediction out loud, it would be realized. This was the prediction, which I did state aloud to my wife:
“We will now roll matching descending doubles, from sixes to ones.”
This is about as concise as this particular prediction could be made, and it came to mind fully formed, like poetry. It predicted that immediately after saying it, the following sequence of 24 numbers would be rolled:
6, 6, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1.
Not only that, but that my wife would start the sequence with double sixes, then I would roll sixes, and the rolls would continue to alternate between us so that my wife and I would each be responsible for one half of the prediction.
Outcome
My wife rolled double sixes. I then rolled double sixes. She rolled double fives, I also rolled double fives. She rolled double fours, and I did also. She rolled double threes, and then I rolled double threes. She rolled double twos, and I rolled double twos. At this point, I got spooked by the sheer improbability of the event and said aloud, “we won’t roll the double ones.” My wife then rolled two non-matching numbers, and I did the same.
I used the Bard Chatbot to calculate the probability*. Here is what it came up with:
Part 1: Probability of the specific descending doubles in sequence
First roll (wife, double 6s): 1/36
Second roll (you, double 6s): 1/36
Third roll (wife, double 5s): 1/36
... and so on, for each of the 20 rolls: 1/36 * 1/36 * 1/36 * ... * 1/36 = (1/36)^20
Part 2: Probability of the final 4 non-doubles
Same as in previous calculations:
(35/36 * 35/36) * (35/36 * 35/36) = (1225/1296)^2 ≈ 0.886
Combined probability:
(1/36)^20 * (1225/1296)^2 ≈ 7.38e-46
Interpretation:
The probability of the specific sequence of rolls, considering each roll's independence and specificity, is incredibly small, approximately 1 in 1.35 sextillion.
*Note that I do know how to make these calculations without the chatbot, but I like the way it presents the information.
Discussion
A friend once told me “that didn’t happen,” after I told him of this event. He is a gifted mathematician and programmer. From his perspective, the rolls were so improbable that they could not have occurred ever, even without the prediction. He was wrong, as my wife and I can both attest.
The normal accepted scientific standard for a non-random result is 0.05 (1:20), which is “statistically significant” or 0.01 (1:100), “statistically highly significant.” In this case, we are looking at a probability value with 24 zeroes. In other words, by any reasonable scientific standard, there is no chance that my prediction and the outcome are unrelated.
How then, are they related? As far as I am aware, I did nothing to cause the outcome beyond making the prediction. I don’t believe the prediction was precognitive because I was able to interrupt the sequence at the end by saying, “we won’t roll the ones.” Also, it didn’t feel precognitive, as odd as that may sound. It was as if my saying what the rolls would be caused them to follow suit.
This isn’t the only example I’ve got where I’ve said improbable things and they have immediately happened. Sometimes, like this one, the notion just comes to mind. Other times, I say something and am totally surprised when it happens, because it hadn’t occurred to me that it might.
Very interesting!
Actually, fascinating!