91592097 in 16007560800 which is approximately 0.572% (or 1 in 175).
Some of what follows is already covered in @DenisS's answer and I have used the same dictionary of words (Collins Scrabble Words (2019))
for easy comparison. Note in particular in that answer the argument for discounting blanks when looking for valid combinations without words (i.e. that ...
I used the beginning of the program in @DenisS's answer to build the Scrabble dictionary, then I used it to write a small monte-carlo program to estimate the probability that no word can be formed with seven random tiles.
The result is a 0.58% +- 0.27% probability that no word can be formed.
$ python3 get_proba.py 1000 50
I'm going to make an estimate from the following assumption:
Any hand that contains at least one vowel, y, or a blank allows a valid move. Any hand that contains entirely consonants does not. Obviously there are exceptions, but they should be rare enough to have a negligible effect (and the false positives and false negatives work to cancel each other out).
This is the start of a much longer answer, but I'm putting it in here for now as a placeholder and as part of initial findings. This question will also be heavy on computer science, due to the fact that we can't brute force the answer because of the sheer size of the problem at hand
To start, a very weak, but easily proven upper bound for the percentage ...
It would make gameplay more frustrating
There is very little to gain, and a lot to lose from this tweak.
Because players have more information available, it will take longer to decide what the optimal play is.
Because other players can see what you have, they are more likely to make moves that will block your best possible play.
Rather than encouraging ...