bananagrams

Bananagrams is a speed-skill-based word game. Think of it as a Scrabble with no board, no interconnected words between players, no turns or point values, and the ability to change what’s already on your board. You flip over 21 tiles to start the game and, in my household, this is anything but a casual competition.

Of course, as I learned in the book Word Freaks, the most obsessive and competitive folks will gravitate toward Scrabble. Pitting two expert Bananagrams players against each other will result in such a whirlwind of a game that it won’t be all that fun. Truly, the bottleneck becomes finger dexterity and some other factors that I’ll detail later.

I’ve been playing Bananagrams with my mom and grandmother for the last five years. I would say we are likely the best tri-generational team out there. The games are very competitive and we are always testing new strategies. Here are some of the strategies that I’m willing to reveal.

Two-Letter Words

The mid and late games are dominated by two-letter word knowledge. On the other hand, your early game can be stunted by overreliance on short words, since you’ll have fewer openings for later combinations and rearrangements. There are about 106 two-letter words. To win a game against experienced players, and especially to be the aggressor in the late game, you should know at least 60% of these words. Personally, I’d say I regularly deploy about 80% of them, and if you’re playing in a group that hasn’t dug into this word list, you’ll force others to adopt them quickly in order to remain competitive.

The crucial words are: jo, za, qi, gi, ma/pa, em/en/ex, xi/xu, ka/ki and what I call “the H’s”: ah/eh/uh/oh/ha/he/hi/hm/ho. Adding these to the words that are probably already in your vocabulary–ab, am, an, as, at, ax, aw, by, do, go, if, in, is, me, my, no, of, on, or, ow, pi, sh, to, up, us, we, yo–you’ve covered a respectable portion of this list.

Two-letter word knowledge is required for an aggressive player to maintain his desired tempo of the game. One benefit of these short, throw-away words is that you can often pop a letter later in the game that can be used to form 3 and 4 letter words though you’re only drawing one at a time. In fact, any two-letter words should be among the first things you attempt to deconstruct when you’re in the driver’s seat, having just peeled.

The Letter Q

Q is awful to deal with as a beginner. It’s common to dump the letter if you don’t have an accompanying “u” and I don’t think this is a bad strategy. Dumping isn’t always sustainable, especially if you’re playing with other aggressive, frequently-dumping, opponents. If you get stuck with a Q in the late game, you’ll lose. Here are the Q words you need to know.

2 letter: qi

3 letter: qat, qin, qis, qua, suq

4 letter words you should know: aqua, quad, quid, quiz, quit, quip

4 letter words without U that you should adopt: qaid, qoph, qats

5 letter words you should know: quack, quads, quaff, quark, qualm, quant, queen, quasi, quiff, quill, quiet, quest, quilt, quite, quirk, quake, quick, quota, quote, equip

5 letter words without U that you should adopt: qadis, qaids, qibla, qajap, qapik, qorma, qophs, qanat

Sleight of Hand

This is where younger players have a large advantage over older players, so I rarely fully capitalize on these optimizations since the combined age of my two playing partners is 155.

This is a real-time, organized chaos type of game. Everything takes time. So whether it takes you a little bit longer to turn tiles over when you’re forced to peel, when you decide to dump, or when the game starts, you’re at a disadvantage. There’s no way around it.

Likewise, there are a few tricks and rules I recommend to eke out some extra wins over time.

In the parts of the game where speed matters, put your hands and fingers in turbo mode. 200-1000 millisecond delays here and there really add up over the course of the game. In the beginning, when someone yells “split,” that’s when the game begins. Don’t wait for others to turn, don’t try to make decisions while you’re turning. You want to have as much information available as possible as quickly as possible. I’ve seen it suggested that pre-split you group your letters into bundles of 4, then press the tiles together and flip them in groups, but if your fingers are fast, you have options.

The most important “house rule” in the game is that you cannot begin reaching into the bunch until after you’ve called “peel. I hate it when someone calls “peel” while her right hand is already hovering over the bunch. It’s a huge advantage to the most aggressive player, so we ban it. Other players should have ever-so-slightly less time to peel since they’re reacting to someone calling it out. It should be impossible to glean an advantage here any other way.

Word & Board Utility: Capping, Crossing, Spacing

Listen, I’m not going to draw a bunch of diagrams for you. If you have a 3 letter word, say, “act,” on your board, there are right moves and wrong moves. Different words have different utility, a term I’m using to refer to how easy it is to build additional words off of them. If I took a random sampling of 2500 words and pitted a few “machine learning” bot players against each other, over time we’d see a few words bubble up to the top in use in competitive play. Those words would have high utility.

Don’t get me wrong, some 2 letter words have high utility, but I’m trying to focus on more nuanced cases like “goof” versus “fog.” Goof uses more letters, but in my opinion it has lower utility. The right way to play “act” is to build something off the ‘a,’ proceeding to the right, and another word ending on the ‘t.” Building something on the ‘c,’ in the middle of the word, essentially (but not completely) blocks off the ‘a’ or the ‘t,’ which are each letters that are otherwise quite easy to build off.

Along this line of reasoning, I prefer a lot of 3-letter words over four-letter words. With four-letter words, it’s too tempting to use the 2nd or 3rd letter to build a new word, whereas for a three-letter word, with an odd number of letters, you’re more-or-less guided into placement around what I call the “caps,” the first letter and the last letter.

Then, we have the concept of spacingThis tends to be more intuitive. You always–always want to build your board as wide and spacey as possible. During the mid and late game, you want your rapid-fire brain to snap tiles into place without having to do any searching, shuffling, or dumping. If you don’t do that, and have many short words, you’ll find that you have very few options to create two-tile words later in the game.

Especially in the longest games (2 players), the player’s board whose covers the largest area is often going to be the winner. It’s deceptively easy to fall into the trap of blocking yourself in with short words that all start running into each other. This concept of spacing means you need to think a few turns ahead–and you can disregard it if you know you don’t have a few turns before the end of the game.

For example, if I play “coffee,” let’s think a few moves ahead. I then create “crawl” from the c, “freedom” from the first f, and “enigma” from the last e. Sounds good, right? No. Because I built three words down from “coffee,” it’s going to be tough to expand on them. The letters in crawl can be used to end words without an issue. But building something starting with the “a” in crawl? Not going to happen–I’m going to be blocked by “freedom.” Even two-letter words are off the table!

Meanwhile, “freedom” isn’t very free, now is it? The base utility is pretty high (a lot of popular letters), but the spacing is awful. If the game is going to continue for some time, I’m going to want to place the word elsewhere.

These concepts get extremely nuanced with tons of exceptions so this is more of something to keep in mind than hard and fast rules. If I was to pit two bots with the same playing speed against each other, could I determine “optimal” play? No, probably not. But I could determine highly-efficient play, which is if the time it takes you to imaginatively build a word is not a factor but the time it takes you to physically build that word is a factor, then a bot with a full dictionary and playing the largest possible words would probably not need to make more than 4 moves to the first peel. After a day of “learning,” we’d be seeing just a few massive words and it’s likely that the use of spacing patterns would be learned, too.

Humans do take time to figure out what words they can or want to build. They also take time to click the tiles together to actually form those words in front of them.

“Quickdump”

Here’s the letter distribution:

  • 2: J, K, Q, X, Z
  • 3: B, C, F, H, M, P, V, W, Y
  • 4: G
  • 5: L
  • 6: D, S, U
  • 8: N
  • 9: T, R
  • 11: O
  • 12: I
  • 13: A
  • 18: E

My “Quickdump” strategy relies on statistics. Kind of like how the quants beat the traders in liar’s poker when they sped the pace of the game up. If you look at the letter distribution above, after each player has taken 21 tiles, two things are clear. First thing is that there’s not that much random chance. If everyone randomly selects 21 tiles, it’s hard to have a vastly superior initial group of letters. Further, there are a few awful (low-utility) letters remaining in the bunch, but they are outnumbered by “good” letters, considering the average person’s vocabulary.

When a player calls “dump” in Bananagrams, they exchange one of their own tiles for three from the bunch. There’s no limit to how many times you dump. There is also no strict rule on whether the face-down tiles in the bunch can or should be mixed up. The implication here is that a player could aggressively dump their bad letters, placing them in a “known” area in the bunch where they could selectively peel or dump for them later, or simply avoid them until the very very late game. Also, there is no rule against taking back the one tile you are giving up for your dump.

You can dump a high-value tile, like an “a,” but in the same hand-motion can pick it back up along with two random tiles, thus growing the tiles in your possession while only sacrificing time.

Okay, so giving up a Z and getting three random letters before there’s been excessive dumping makes sense. Though it breaks your concentration, it’s a useful move. But why would we want to expand our holding so early in the game?

Thanks to the Law of Large Numbers or whatever you want to call it, as you get more free letters, the potential number of words you can make grows significantly. In the Quickdump strategy, you often don’t have to look at your letters and try to determine what words you should make, you think of a few words and then arrange the letters.

For example, if I peel to the point that I have 40 unused letters, there’s a really good chance that I can make 1-2 huge, high-utility words without even thinking about them. They’re right in front of me, I just need to find the letters. When I explain this strategy, people find it to be hard to believe, but it works.

To prove my point, I’ve devised a simulation that evaluates how the chances of me being able to play any of 10 preselected 10-letter words grows as I accumulate more tiles. These words are somewhat arbitrary but I picked ones that I’ve actually played in games and that have varying extensions and word composition.

If you play 1000 games where you draw 21 tiles, here is the percentage chance of each word, with ‘cat’ thrown in for reference:

Abandoning: 3.4%
Earthquake: .6%
Allegories: 5.7%
Bespeckled: .1%
Coffeecake: 2.2%
Freestyler: 2.0%
Obligation: 1.8%
Pestilence: 1.4%
Supportive: 2.6%
Upchucking: 0%
Cat: 24.5%

Huh? You can only make “Cat” in 24.5% of your initial draws? There are only 3 occurrences of the letter c, so this makes sense. But it’s quite surprising that some of our arbitrary selection of monstrous 10-letter words are able to be played with some frequency!

Here’s where Quickdump comes into play. Let’s say I start each game by gaining ten tiles by executing 5 back-to-back privileged dumps:

Abandoning: 18.3%
Earthquake: 4.4%
Allegories: 24.6%
Bespeckled: 1.9%
Coffeecake: 9.0%
Freestyler: 10.4%
Obligation: 13.3%
Pestilence: 8.0%
Supportive: 8.1%
Upchucking: 1.7%
Cat: 43.3%

Wow, suddenly it’s feasible to keep some of these words in our back pocket. Excluding the word cat, my results show that you would be able to play one of these ten words in 55% of games where you dumped for ten extra tiles at the start of the game.

If we adopt an extremely aggressive Quickdump strategy where we attempt 10 privileged dumps for 20 extra tiles, the numbers are boosted further:

Abandoning: 35.7%
Earthquake: 12.0%
Allegories: 48.8%
Bespeckled: 7.5%
Coffeecake: 21.0%
Freestyler: 26.0%
Obligation: 32.9%
Pestilence: 25.7%
Supportive: 27.4%
Upchucking: 5.8%
Cat: 61.9%
Chance we can make one of the ten-letter words: 85%

 

If you have a large vocabulary, fast playing speed, and are against opponents who are slow, dump-adverse starters, Quickdump is really useful and extremely frustrating to the unsuspecting player. You’ll win a lot of games. Even if an opponent begins peeling while you only have a few words constructed, you have high guaranteed utility. So as long as you maintain discipline in spacing out your board, you should be able to keep pace with the most aggressive player even if you are braindead, at least for a few moves.

The only way to counter a privileged dumper of a similar skill level is to also rapidly privileged dump which will most likely result in a local rule being established that forbids privileged dumping. I find that the speediest players have trouble outrunning a Quickdumper (me) in most games. You’re sacrificing control over early tempo of play, while the usefuless of your monster words begins to be realized is in the very late game,. You realize you have tons of unexplored nooks and crannies on your board while others are boxed in. You’ll always be wishing that the game was longer. The problem with multiple people dumping frequently is that the pool and quality of the pool will be degraded rapidly, so the strategy loses effectiveness.

Winning Strategies for Bananagrams