53 vs 54 point word rarity in 5x5

[BoggleOtaku]

Hi Naboka,

When you mentioned excitement at finding 37 point words, I was confused as to why.
Then I started thinking about how excited my daughter would be at 67 point words.
And, finally, I realized you were obviously talking about 4x4 games.

Brutally faced with my ignorance of the most basic of facts regarding 4x4 and in abject apology at any mistakenly inferred slight, I present to you in meagre recompense a dynamic heat histogram of 4x4 words shown with and at same scale as the 5x5 plot.

Enjoy!

Wordtwist 5x5 Word Point Competition trends.png

[Naboka]

Hi Naboka,

When you mentioned excitement at finding 37 point words, I was confused as to why.
Then I started thinking about how excited my daughter would be at 67 point words.
And, finally, I realized you were obviously talking about 4x4 games.

Brutally faced with my ignorance of the most basic of facts regarding 4x4 and in abject apology at any mistakenly inferred slight, I present to you in meagre recompense a dynamic heat histogram of 4x4 words shown with and at same scale as the 5x5 plot.

Enjoy!

Wordtwist 5x5 Word Point Competition trends.png

Thanks. Definitely seem to be different universes, 4X4 and 5X5--and probably 6x6.

Long ago I concluded that playing the highest-point-value best words in 4x4 would require finding the q/z combination. Those two letters immediately truncate the board, resulting in a much lower number of available words. Perhaps I'm wrong but I don't think a board exists in 4x4 where a player could reliably get 701 points, which are required to retire it. In other words, playing those boards wreak havoc on average total word scores.

Playing the lower-word-availability boards has opened a new world of possibilities. I keep finding boards with words used in chemistry that have to be the unique ones that you're interested in. Long words that it's likely no one has found before. Words probably even more rare than coelenterazines.

Your comments about your wife and daughter remind me of my life. Though my wife often finds me to be a tedious bore, (not that yours finds you as such) she's been hearing too many comments from friends about how much they or their husbands enjoy conversations with me. She's beginning to reassess the value of ideas that to her are utterly meaningless. She's a pragmatist and has little patience with the physics that belie our sensory grasp of reality. If she has no immediate practical use for it, goodbye.

Since I often have a reader's rather than listener's grasp on word pronunciation, my pronunciations can sometimes be off. English is a weirdly inconsistent language with spelling and pronunciation.

I remember a while back rolling my eyes when artistic types started pronouncing homage with a silent h. I looked through several dictionaries to see if that version of pronunciation was an option and couldn't find it. Nope. But that's the way so many people are pronouncing it now.

What's really interesting is to monitor the spelling of kindergarteners. When I first started working with my wife, a very smart kid had used chree in a written sentence. ??? Tree. Our tongues are positioned so closely to the same spots when making both sounds. Almost every 5 year old I've worked with has been shocked that tree begins with t rather than ch. Same with chrain and so many others. It's often how we speak, but not how we spell.

Because the schwa sound can be confusing, I often have the correct word on a board, but am frantically trying to spell it correctly. Mostly I'm doing educated guesses for long words from arranging word elements so I'm not visually following the letter paths on the actual board.

Do 5x5 boards follow the pattern of very high point best words existing primarily on boards with fewer words?

Time to get on the bike and enjoy beig physical.

[Naboka]

ps: I did a head slap about my comment. I meant the Fibonacci spiral not the sequence. One of those senior moments of conflation. (Not that I wasn't guilty of being prone to the same stuff in my teens, 20's, 40's etc.)

I've done a lot of painting and drawing since retiring, and the application of the Fibonacci spiral or golden spiral too artwork was a revelation.

Also, I forgot to admire your color choices for the data spread.

Also, being lazy, I only gave the spread a cursory view. One thing that strikes me is the spacing of ultrarare unique words on both graphs. It seems that the spacing on the bottom row of the 5x5 is greater than the 4x4. This suggests a higher frequency of finds in 4x4. Makes me wonder if this is partially due to commonization of words that would otherwise be unique such as z/q words or -izations words. When a player familiar with 4x4 triggers on -izations, only 8 letters need to be reconfigured to arrive at a 16/33 outcome. And that can take seconds or less. I guess such combinations exist in 5x5.

Part of my wondering is the existence of words in both formats that have never ever been found. Words of unknown length that no one has discovered. It would be interesting to know which format has more.

Here are some examples of the spiral. Nature is filled with them.
OIP-1345991439.Fn8I3GuVff2OXN9yrIWWPwHaEv.jpg

OIP-2032695211.VXMk0fgIY0siUV28uLiwcAHaHa.jpg



OIP-2200272153.BCEbysFA0KcxfETj7k8U6gHaE_.jpg

OIP-2821235551.SjboxF5XFo8UYia7F47zxwHaHa.jpg

[BoggleOtaku]

Nice pictures! It's a reasonable conflation: Just like DNA encodes the sequence of the protein, Fibonacci series provide the pattern of its namesake spiral, which approximates the golden spiral. Of course you have to still correctly fold the protein from 1D to 3D (nontrivial) and the pattern into the spiral 1D to 2D (trivial in comparison).

There's likely only one 54-point word in 5x5, as has been discussed previously, whereas there are at least three 37-pt in 4x4 (I saw three looking through some of the monthly competition records. So that would suggest more max word length boards in 4x4 leading to high frequency of finds. That seems like at least one more reason for your observation in addition to your thought on it.

I agree with your comments in the "next next" to last post (as one might literally put it in Japanese) regarding ultra rare words in small word-number boards. Take the 54 point ultra rare QUINQUASEXAGINTILLIARDTHS: so many special letters suck the capability of the board to have huge numbers of words. That seems pretty common in 5x5--you often see boards with very few words, maybe 7 or less letters, except for one or two 9+ ultra rare words, and these can often be 15+ letters. The board was apparently handcrafted to contain that word. Once that one long word (with perhaps special letters) is forced into the board, it seems like probabilities of having lots of words decreases. (Maybe further letters are randomly chosen to populate the board instead of choosing remaining ones to maximize word count, since the purpose for that board has already been fufilled by putting in the extra long word.)

Between 2016-2021, 5x5 had higher frequency top word points relative to 4x4 then and 5x5 now. There were many high scoring words there and then that ended commonly with -izations. I think this supports your comments about why 4x4 may have higher frequency than 5x5 currently.

What I found most striking in comparison of the two plots:
1. The statics for word points pre-2015 are almost identical between 4x4 and 5x5. It made me think that not only the same dictionary was used for both boards, but also that perhaps the 4x4 boards were reused in 5x5 by embedding in a 5x5 board and adding extra letters around two edges . Now I am wondering what the commonality in the actual words in word point lists for 4x4 and 5x5. Neither goes up nearly to their potential, allowing the improved boards post 2016.

2. Where as the 5x5 has odd even word point parity almost everywhere, the post-2021 4x4 charts have a pattern that almost goes in groups of threes at high word point. At least it is not nearly as good a match to an odd/even pattern.

BTW, I liked you story about pronunciation. Our daughter when maybe 3 get really excited about cliff nests. I wondered how she even knew what a cliff nest was. Had she secretly been watching "The Swallows of Capistrano"? I told her that we don't have cliff nests around here. We only figured it out when she asked about cliff nest chrees.