What is the probability of a Scrabble player making two seven letter words on their first two turns?

by Jeremy Lewis
(Nova Scotia, Canada)

Hi Jeremy - thanks for a very interesting question.

First let me explain why there is no 'exact' answer to your question, and then I'll give you a realistic ball-park figure.

The probability of a Scrabble player making a bingo (that's what many players call it when you use up all seven of your letters) depends on...

1. The Scrabble dictionary being used
2. The players' word knowledge, anagramming skills, and strategic styles

So let me make a couple of assumptions...

Assumption 1: The Scrabble dictionary being used is the Official Scrabble Players Dictionary used in North America (which seems reasonable since you are from Canada, after all).

Assumption 2: Both players have perfect word knowledge, perfect anagramming skills, and follow a conventional Scrabble strategy. (Without this assumption, you just can't go anywhere really.)

In that case, the probability that the first player can play a bingo from their first rack can be computed exactly using the known distribution of letters in a standard tile bag, along with the known list of allowable words. It turns out to be about 15%. (That surprises many lounge-room players!)

Now, the probability of getting a bingo on the second move is not possible to work out exactly, since it depends on what the other player decides to play in response to the opening bingo.

However, since on the second move a player has additional bingo opportunities (i.e. they can now play eight-letter words through the opponent's letters), the likelihood of another bingo is probably a little higher than the first - let's say 20% (which I suspect overestimates things a little).

Multiplying these values together gives a probability of about 3%. In other words, if two 'perfect' players were to play each other in 100 Scrabble games, you would expect that in about three of those games the opening player will play two consecutive bingos.

The only way to get a more accurate answer is to have a Scrabble program play itself thousands and thousands of times, which several serious gamers do from time to time. If I can get access to the results of such a simulation, I'll update this answer and we can see how far off my estimate is.

I suspect the result would be a little less than 3%, since my 20% figure is probably an over-estimate.

In the meantime, thanks again for the interesting question Jeremy. And feel free to comment below if you'd like me to follow up on anything.


P.S. Even though your question refers to seven-letter words, I've assumed you really mean bingos, which can be eight letters long, or even longer.

P.P.S. Was this question triggered by someone doing this to you? ;-)

Comments for What is the probability of a Scrabble player making two seven letter words on their first two turns?

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Four in a row
by: Anonymous

I'm playing a game of scrabble online with an old friend, and they just got three bingos in a row, and then one smaller word, and then a fourth bingo. I know this person is very, very smart - but four in five turns? Is it possible? I don't want to think they are cheating - but I've never seen anything like it, and I've been playing a long time...

In expert level Scrabble games, or when you are playing against a computer, it does occasionally happen, but it really does require a superb knowledge of the Scrabble dictionary and an excellent anagramming ability.

That is, it would be very unusual to see four out of five bingos where all the bingos are common and easy-to-find Scrabble words.

Were the four words 'common' English words, or highly obscure Scrabble words? Were the words easy to anagram (like HOPPING), or were they brilliant finds (like TIRAMISU)? Does your friend study Scrabble words seriously (e.g. using Scrabble software? These are things you would want to know before suspecting him/her of cheating.

Over the years I've had four-in-five bingos played against me a reasonable number of times, but always by an expert player, or a computer program. Never by a casual player.

by: Anonymous

Yesterday (May 3rd, 2011) with three of us playing we had four 7-letter words in, I believe, our 1st five plays! I don't have the the score sheet with me tonight. I'll double check it tomorrow. I took a photo of the board because nothing like this had ever happened before. I wonder if any one can figure the odds on this one. Thanks

Beat the record
by: Bernard

Today, February 17, 2011, I played with an opponent, started with the word BELCHER. He added PHRASES to make belchers. Then I added VICTION below E to make eviction. Then he added IGAMOUS below B to make bigamous. That's 4 consecutive 7-letter words, then I added fawns to S of bigamous and he added hydro to R of phrases. I added GENESES above H of hydro and he added AITATOR to G of geneses to make AGITATOR. That's six 7-letter words in 8 turns. Could it be a record?

by: Anonymous

Thanks Derek we had 4 players playing. My first word was SETTING and my second word was LOCATED.

I don't imagine this will happen again any time soon.

Thank you for your help and effort.

Kind regards, Jeremy Lewis.

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