Bingo in 38 straight Scrabble games

by W J
(Kennedy)

What are the odds of someone scoring a bingo in 38 consecutive Scrabble games?

Hi WJ - well, this is certainly an unusual question ;-) As with all questions about probability, we need to make some assumptions first before we can do a calculation.

You see, the odds of playing a bingo in a Scrabble game depend heavily on the skill of the player concerned, and on the skill of their opponent/s. A player who doesn't know ANY 7 or 8 letter Scrabble words, for example, would have a 0% chance of scoring a bingo in 38 games, because they can't get a bingo in a single game, let alone 38 games straight!

To answer your question, I'm going to assume that we're talking about two expert Scrabble players playing each other for 38 games. In this case, each player has about a 95% chance of playing a bingo in any individual game - that is, an expert player only fails to bingo in about 1 in 20 games.

In this situation, the probability of playing a bingo in 38 straight games is 0.95 to the power of 38. The result is about 0.15, so it will happen about 15% of the time.

However, if one player is an expert at Scrabble, and the other is a novice, the chances of 38 consecutive bingo games (for the expert) will be much higher than 15%. Why?

Because, among other things, the novice will fail to block the expert's bingos on many occasions, and will also tend to play shorter words, resulting in longer games, resulting in more bingos for the expert.

I could go on and on about other scenarios, but hopefully this is enough to give you a rough answer to your question.

All the best.