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Scrabbling for Mastery

a patzer's journey

Calculating the probability of drawing JANITOR twice
me again
I know I have some mathematically inclined LJ friends, and I was wondering if you would be willing to check my math. I've received an email containing a story about someone in the UK who drew JANITOR to begin a game at age 19, and then at age 59 did the exact same thing again. It didn't specify whether there were any blanks involved. He was wondering what is the probability of this happening.

Here is what I'm planning to write in response. Does this look about right to you? All these numbers only pertain to the very first draw (once per game), not all the draws during the course of an entire game. Also, I think I should be able to figure out how to calculate the answers to the two unanswered questions near the end, but if you have any pointers I would appreciate it!

I'm not showing my work at the moment, but if necessary I will detail all the steps I took to get these numbers. Note that the "number of combinations" numbers that I quote were calculated by Zyzzyva; I didn't calculate those by hand. All numbers assume a 100-tile bag with 2 blanks. And of course, I'm using CSW07 since the emailer is from Britain.

Zyzzyva has the ability to display the relative probability rankings of words compared to each other. For example, it can tell you that if you draw 7 tiles out of a full bag of Scrabble tiles, the most likely word you could form is OTARINE (pertaining to an otary, a big-eared seal).

Zyzzyva doesn't display absolute probabilities, but I'm happy to calculate these for you. Below are some questions and answers you may find useful. If you have more questions, please let me know.

- What is the probability of drawing the word JANITOR on a single try?

There are 16,007,560,800 distinct ways to draw 7 tiles from a full bag of 100 Scrabble tiles. There are 5,423,112 distinct ways to draw tiles that will allow you to play OTARINE, so the absolute probability is about 0.034%, or about 3 chances in 10,000. There are 817,236 ways to draw JANITOR, so its probability is about 0.0051%, or about 5 chances in 100,000. Therefore JANITOR is about 6.6 times less likely than the most probable word, OTARINE. Overall, the probability of JANITOR gives it a ranking of 2,391 out of 32,909 total 7-letter words. In other words, even though it contains the unlikely J, JANITOR is among the top 10% most probable words to draw on a single try.

- What is the probability of drawing the word JANITOR twice in only two tries?

The odds of drawing JANITOR in 2 out of 2 tries is 0.0051% squared, or about 0.00000026%, about 2 chances in a billion.

- What is the probability of drawing the word JANITOR twice over the course of many hundreds of games?

The email you received stated that the person has played Scrabble many hundreds of times over 40 years or so. For simplicity, let's assume that he has played 1000 games of Scrabble, or about 25 games per year. Over the course of 1000 games, the probability of drawing JANITOR at least one time is about 5%, or about 1 chance in 20. The probability of drawing JANITOR at least twice is about 0.25%, or about 1 chance in 400.

Here are a couple more questions for which I haven't calculated the answers yet.

- What is the probability of drawing any word (not particularly JANITOR) twice in a row?
- What is the probability of drawing any word (not particularly JANITOR) twice over the course of many hundreds of games?

These are actually key questions, since the coincidence may have been equally astonishing if the word had been any other word besides JANITOR. However, adding the possibility that it could have been *any* word significantly increases the likelihood of the coincidence. I haven't yet calculated exactly how the probability is affected, but I wouldn't be surprised to learn that the total likelihood becomes greater than 50%. In other words, over the course of 1000 games a truly astonishing occurrence might be that one *never* draws the same word twice!

This is similar to the well-known birthday problem, where the likelihood that two people in a room share a birthday becomes greater than 50%, counterintuitively, when there are only 23 people in the room.

Of course, not all valid words are as likely to be spotted as JANITOR, since JANITOR is a word in common use. For example, someone might have twice drawn the word TRIAXON (a sponge spicule with three axes), which has exactly the same probability as JANITOR. But it would probably go unnoticed, since TRIAXON is a very uncommon word.

Here are a couple other tidbits you might find interesting:

There are three 7-letter words that are absolutely impossible to play. These words are BEZZAZZ, PAZZAZZ, and PIZZAZZ. These words all mean the same thing; they are variations of the spelling of PIZZAZZ, meaning panache or flamboyance. They are unplayable because the standard set of Scrabble tiles only contains one Z and two blanks, so a word with four Zs cannot be formed.

The very least likely 7-letter word that is not impossible to play is ZYZZYVA. There are only 18 distinct ways to draw ZYZZYVA, since you would need to draw both blanks, both Ys, one of two Vs, and the only Z. That makes the probability of drawing ZYZZYVA about 0.0000001%, or about 1 chance in a billion. Note that this is even less likely than drawing JANITOR twice in a row!

NSC 2011
me again
I hadn't played a Scrabble tournament in about a year and a half before this year's Nationals. In fact, I hadn't studied a single word during most of that time, and I only really studied, reviewing all 4s and 5s and some 7s and 8s, for about two weeks before the NSC. So I'm totally thrilled to have gone 15-16 with a big positive spread. I honestly didn't expect to win many games at all, and a near .500 record was way beyond my expectation.

At the same time, playing in Division 1 for the first time made me realize that I hate being the guy who has learned enough to be dangerous but not enough to be feared. I missed plenty of bingos, including ADGMNOOR, which I had down cold just a couple weeks ago because it showed up in the very first set of Aerolith Toughies, which I drilled the hell out of. I played plenty of phonies I thought were good, including the horrible CATLINE* which refuses to extricate itself from my brain. I hooked an E on JUGA, which I know better than to do, if only I had thought about it for half a second. I challenged words I certainly should have known, including INDUSIAL. And I let phonies go in critical situations, like a D hooked on COOMBE. Probably my worst moment was when I threw away a certainly won endgame by missing a simple out-in-two that would have blocked my opponent's best play. Instead I made one of the few plays that could lose, even though I had calculated that it would lose.

I'm not saying this to dwell on the negative. In fact, in general I'm pretty happy with how I played. However, I want to get to a point where I do not make these kinds of blunders, and it is going to take a lot of work. I felt like my wins were mostly luck and my losses were mostly skill. I had two 300-point blowout wins, and I lost two games by 1 point, including the botched endgame I just mentioned. I'm confident enough (or arrogant enough) to believe that I am capable of becoming a world-class player, but it is going to take a lot of hard work. I think this Nationals has finally kicked my butt into gear. I have a year to prepare for the next NSC, and I'm not going to squander it. Obviously I'm not going to become a Nigel or a Wiegand in a year, but maybe I can take the first step.

Overall the experience was great, and I'm glad I went. It was excellent to see so many friends I have not seen in a long time. I also thought the experience of running a vendor table was interesting, though I don't know if I'll do it again. I do have a bunch of extra T-shirts and things that I'll list on the Zyzzyva web site in case anyone is interested. And I discovered that Dallas in summer isn't so bad if you just never leave the hotel.

So now it's back to work on the iPhone app and making my way through the dictionary. Although I'm a Collins player, I think I need a stronger base in OWL2 first. So that's what I'm going to concentrate on this year. If there's a Collins division at next year's NSC, I'll probably play in it because I want to support Collins play in North America. Otherwise, I'll be diverting my personal study stream through the OWL2 tunnel and plan to emerge much stronger in a year.

Anyone going to both NSC and Causeway?
me again
I have a small package of Zyzzyva goodies that I've been asked to get to Karen Richards at Causeway in November. It's an envelope, about 14" x 11" weighing a little more than a pound. Is there anyone going to both the NSC and Causeway, who would be willing to deliver the package for me? If so, let me know and we can make arrangements for me to give you the package at the NSC. Thanks!

Zyzzyva 2.1.5 released
I've released a new version of Zyzzyva, 2.1.5. You can get the latest version here:


This is a bug-fix update. I would especially like to thank Leighton 'Sandy' Gelling for going far beyond what could reasonably be expected in helping me track down and fix a number of irksome issues on 64-bit Linux. Thank you!

Here is the full list of changes in this version:

- Account for screen size when displaying Word Judge
- Add user preference for hyphens to denote inner hooks
- Enlarge CSW copyright notice
- Fix a bug when loading saved searches and quizzes containing umlauts
- Fix a bug that caused blank lexicon names to appear in lexicon list
- Fix multiple bugs that caused failures on 64-bit Linux
- Word definition fixes

This will probably be the last update for a few months as I'm trying to focus my efforts on the Zyzzyva iPhone project. However, if any critical bugs are found, I will fix them.

Sharing a room at the NSC?
me again
Anyone out there who will be going to the NSC but hasn't finalized lodging plans yet? I'll be registering for the NSC today (last minute, natch) but don't have a reservation at the hotel yet. If any of you are interested, I'd love to split the cost of a room. (Males only or my wife would be quite unhappy.) I know about the rides/roommates list, but I thought I should ask my friends first.

My first live poker session ever
me again
My wife and I bought a Daily Deal for the Wendover Fun Bus several months ago. It normally costs $18 (we got it for $10); you get free transportation to Wendover and back, $5 cash, and a bunch of vouchers for the buffet and match play. It's a pretty slick deal. Anyway, the Daily Deal expired today so naturally today was when we used it.

I was excited because I basically haven't played any poker since February, and obviously I haven't been playing any at all since April 15. But I was also really nervous because I've never played live poker at a casino, and only very rarely played live poker even with buddies. Long story short, I was unsure of how it would go but I did really well. Read on for details. This is pretty long, probably much longer than it deserves, but hey, it was my first time.

NOTE: At the end I have a question about a hand for my poker-playing friends - see the last hand described behind the cut.

Read more...Collapse )

Anyway, that was pretty much the best possible introduction to live poker. Total luckbox. My winning percentage at showdown was nearly 100%. I outdrew everyone and I don't think I was outdrawn even once. I ended up turning my $50 into $196 in less than three hours. Honestly I wouldn't ever expect that to happen again, which is one reason I wrote it up in so much detail. If you read the whole thing, I hope you enjoyed it almost as much as I did.

Zyzzyva 2.1.3 released
I've released a new version of Zyzzyva, 2.1.3. Zyzzyva is a program for studying words, practicing anagramming, and adjudicating challenges. It runs on Windows XP, Vista, Windows 7, NT, 2000, 98, and Me; Linux; and Mac OS X 10.3.9 or later. You can get the latest version here:


This update includes the CSW12 word list, thanks to WESPA and HarperCollins. After installing Zyzzyva 2.1.3, if you are interested in using CSW12, make sure to click the Preferences button, then the Edit button next to Load Lexicons, then activate the checkbox next to CSW12. You will also probably want to rebuild all your lexicon databases to get updated word definitions and lexicon symbols.

Here is the full list of changes in this version:

  • Add CSW12 lexicon
  • Add FISE2009 (Spanish) lexicon
  • Rename several lexicons:

    • CSW to CSW07
    • OWL2+LWL to OWL2
    • OSPD4+LWL to OSPD4
    • OWL+LWL to OWL

  • Many word definition fixes, including help from David Sutton and Tapani Lindgren
  • Display lexicon on Word Judge adjudication screen
  • Change inner hook character from hyphen to center dot

One clarification about the Spanish FISE2009 lexicon. Zyzzyva is still unable to translate the digraphs CH, LL, and RR as single characters, so these are encoded as 1, 2, and 3 respectively. Also, Ñ is encoded as 4. I apologize that I haven't been able to fully implement a user-friendly Spanish solution, but I also felt that continuing to leave out the FISE lexicon would be unacceptable. I hope this solution will work for now, and I will improve it in future releases.

Please give me feedback about how you think Zyzzyva could be improved! I'm always trying to make it the best word study program it can be. If you would like more information about Zyzzyva, please join the Zyzzyva Users list here:


I hope you enjoy using Zyzzyva, and most of all, have fun with it!

Zyzzyva iPhone officially used at the club
me again
I wish I had more progress to report on the Zyzzyva iPhone app, but it's been a really busy week and I've mostly been working on Word Judge UI enhancements. I'm currently working on Search and hope to have basic Anagram/Pattern searches functional by this weekend. In the meantime, I finally used the app for adjudication during an actual game yesterday at the club. Happily, I find myself 1-0 on challenges so far when using the Zyzzyva app.

Now we're talking - more Zyzzyva Word Judge screenshots
These screenshots are more like what I envision for the final Zyzzyva word judge on the iPhone. Pretty nice, eh? It actually works and the look feels very familiar, which is probably why I like it so much. Phase 1, a functional word judge that looks pretty, is in the books. I'm sure there are many improvements to be made, and I'm looking for beta testers, so if you're interested in testing let me know. Sometime this week I'll be moving on to Phase 2, search. Are you excited? I am.

Word Judge minimally functional
These screenshots are definitely NOT what the final Zyzzyva word judge will look like on the iPhone. But it took me several hours of work to get this much, so to me it looks pretty damn cool. The buttons actually work, and the actual words are actually being looked up from an actual word source. Like, actually. I've learned a lot so far and I'm excited to hook up much cooler things than this.