關於 comparing game ，我們在網路上蒐集到這些相關的討論、資訊與評價

#Eugene讀的300多本myON電子書記錄
(此圖不包含同myON的『Kaite Woo』和『Dino』系列)
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大概是從5月中疫情爆發的時候，
SJE女孩兒門關在家防疫課時哪兒也不去，
沒上學的自學生Eugene則維持學習的步調，
卻增加了 #myON電子書 的量!
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延伸上一篇文 ‧ 傳送門https://www.facebook.com/ingrid.ing.1024/photos/a.1661247717465782/3058233677767172
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這張圖是5月~7月底的myON電子書+AR測驗記錄，
部分介紹找時間將截圖在留言處，
其他還有很多橋梁書套書、小說的閱讀同時進行~
#SJE閱讀記錄 #Eugene6Y7M #英文閱讀 #英文有聲書
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以下是Eugene讀『myON電子書記錄』書名提供給大家，
字數不多，並且很精彩!
Eugene讀的共有300多本，
字數約在1千上下，
而且精彩的說書人真是讚!
超多好看的書讓小E會想一讀再讀呢!
很多書小E看完就不測AR了，
所以列書單如下：

◆ The Elves Help Puss in Boots
◆ Quest for the Unicorn's Horn
◆ Medea Tells All: A Mad, Magical Love
◆ Medusa Tells All: Beauty Missing, Hair Hissing
◆ Three Blind Mice Team Up with the Three Little Pigs
◆ The Tooth Fairy
◆ Seriously, Snow White Was SO Forgetful!
◆ Trust Me, Hansel and Gretel Are Sweet!
◆ Snow White and the Seven Robots: A Graphic Novel
◆ Red Riding Hood Meets the Three Bears
◆ Red Riding Hood Meets the Three Bears
◆ The Robo-battle of Mega Tortoise vs. Hazard Hare: A Graphic Novel
◆ Medea Tells All: A Mad, Magical Love
◆ Helen of Troy Tells All
◆ Pandora Tells All: Not the Curious Kind
◆ Robin Hood, Time Traveler
◆ The Ugly Dino Hatchling: A Graphic Novel
◆ Keep It Simple, Rapunzel!
◆ Mermaid Midfielders
◆ Hansel and Gretel
◆ Say "Cheese"!
◆ Big Pig
◆ Cass the Monkey
◆ Rapunzel
◆ Honestly, Our Music Stole the Show!: The Story of the Bremen Town Musicians as Told by the Donkey
◆ The Recess Bully
◆ The Runaway Robot
◆ Alice, Secret Agent of Wonderland
◆ Frankly, I'd Rather Spin Myself a New Name!
◆ Sleeping Beauty, Magic Master
◆ Quest for the Unicorn's Horn
◆ Secret Matter
◆ Truthfully, Something Smelled Fishy!: The Story of the Fisherman and His Wife as Told by the Wife
◆ Pandarella
◆ Hansel and Gretel Stories Around the World
◆ Red Riding Hood, Superhero: A Graphic Novel
◆ Beauty and the Beast Stories Around the World
◆ Goldiclucks and the Three Bears
◆ Believe Me, Goldilocks Rocks!
◆ Believe Me, I Never Felt a Pea!
◆ Poodle and the Pea
◆ Kitten Who Cried Dog
◆ Ack's New Pet
◆ Pandarella
◆ Goldilocks and the Three Vampires
◆ The Silver Spurs of Oz
◆ Rapunzel vs. Frankenstein
◆ Peter Pan in Mummy Land
◆ Mouse Says "Sorry"
◆ Mouse Says "Sorry"
◆ Hippo Says "Excuse Me"
◆ Monster Knows Table Manners
◆ Monster Knows Excuse Me
◆ Party Problems
◆ Miles McHale, Tattletale
◆ Yasmin the Chef
◆ Truthfully, Something Smelled Fishy!: The Story of the Fisherman and His Wife as Told by the Wife
◆ The Robo-battle of Mega Tortoise vs. Hazard Hare: A Graphic Novel
◆ Max Goes to the Dentist
◆ Listen, My Bridge Is SO Cool!: The Story of the Three Billy Goats ◆ Gruff as Told by the Troll
◆ Buzz Beaker and the Speed Secret
◆ Buzz Beaker and the Growing Goo
◆ Marconi the Wizard
◆ Hair-pocalypse
◆ Little Tiger Picks Up
◆ Penguin Says "Please"
◆ Little Dinos Don't Push
◆ Little Dinos Don't Hit
◆ Dino Hunt
◆ Prize Inside
◆ Pizza Palace
◆ What's That Sound, Cinderella?
◆ Pet Costume Party
◆ Even Fairies Bake Mistakes
◆ Counting Money!
◆ Maybe When I'm Bigger
◆ Traveling Shoes
◆ When Thomas Edison Fed Someone Worms
◆ The Swim Race
◆ Ruth's Pink Pajamas
◆ Me and My Cat
◆ Boo Bat
◆ Incredible Rockhead and the Spectacular Scissorlegz
◆ Truly, We Both Loved Beauty Dearly!
◆ Poodle and the Pea
◆ Marshmallow Mermaid
◆ Green Queen of Mean
◆ Evil Echo
◆ Yum!
◆ My Body
◆ My Day
◆ My Neighborhood
◆ Marvelous Me
◆ Paid to Game
◆ Mr. Bones
◆ Little Dinos Don't Yell
◆ Do Not Let Your Dragon Spread Germs
◆ Friends All Day
◆ Field Day Rules!
◆ The Goose that Laid the Rotten Egg: A Graphic Novel
◆ Plans Gone Wrong
◆ The Ants and the Grasshopper
◆ The Boy Who Cried Wolf
◆ The Boy Who Cried Vampire: A Graphic Novel
◆ Frankly, I'd Rather Spin Myself a New Name!
◆ Little Red Riding Hood Stories Around the World
◆ Rapunzel Stories Around the World
◆ Hansel and Gretel Stories Around the World
◆ Beauty and the Beast Stories Around the World
◆ Little Red Riding Duck
◆ Goldiclucks and the Three Bears
◆ Kitten Who Cried Dog
◆ Princess Harper Gets Happy
◆ Pandarella
◆ How Do We Stay on Earth?
◆ Scary Night
◆ Aliens and Energy
◆ The Big Mistake
◆ The Black Hole Report
◆ Ack's New Pet
◆ Ooze Slingers from Outer Space
◆ Eek Discovers Earth
◆ Tap Dance Troubles
◆ First Base Blues
◆ Soccer Switch
◆ Snow Dance
◆ Jack and the Beanstalk
◆ Lacey Walker, Nonstop Talker
◆ Crabby Pants
◆ Eleanore Won't Share
◆ Clara's Crazy Curls
◆ The Perfect Birthday Recipe
◆ The Little Bully
◆ You Get What You Get
◆ Zombies and Meatballs
◆ Boy Under the Bed
◆ Welcome to Third Grade, Gus!
◆ Going on a Field Trip
◆ Honestly, Red Riding Hood Was Rotten!
◆ No Lie, Pigs (and Their Houses) Can Fly!
◆ Seriously, Snow White Was SO Forgetful!
◆ Really, Rapunzel Needed a Haircut!
◆ Ninja-rella: A Graphic Novel
◆ Farms
◆ A Nature Walk on the Farm
◆ Bree's Bike Jump
◆ The Lion and the Mouse and the Invaders from Zurg: A Graphic Novel
◆ Lucille Gets Jealous
◆ Terrible, Awful, Horrible Manners!
◆ First Day of Unicorn School
◆ Trust Me, Hansel and Gretel Are Sweet!
◆ Clara's Crazy Curls
◆ Cat That Disappeared
◆ Super Billy Goats Gruff: A Graphic Novel
◆ Day of the Field Trip Zombies
◆ Shark in the Library!
◆ Sleeping Beauty
◆ Robin Hood, Time Traveler
◆ Red Riding Hood
◆ Rapunzel
◆ Puss in Boots
◆ Medusa Tells All: Beauty Missing, Hair Hissing
◆ Freestyle Fun
◆ Pandora Tells All: Not the Curious Kind
◆ Punk Rock Mouse and Country Mouse: A Graphic Novel
◆ Hansel and Gretel
◆ Chicken Little Saves the Moon Base: A Graphic Novel
◆ Johnny Slimeseed and the Freaky Forest
◆ The Goose that Laid the Rotten Egg: A Graphic Novel
◆ Believe Me, Goldilocks Rocks!
◆ No Lie, I Acted Like a Beast!
◆ Morning Mystery
◆ Johnny Slimeseed and the Freaky Forest
◆ Curse of the Red Scorpion
◆ Rapunzel
◆ Jak and the Magic Nano-beans: A Graphic Novel
◆ Goldilocks and the Three Vampires
◆ The Silver Spurs of Oz
◆ Peter Pan in Mummy Land
◆ Hansel and Gretel
◆ Rapunzel vs. Frankenstein
◆ Private Eye Princess and the Emerald Pea
◆ First Day, No Way!
◆ Beauty and the Dreaded Sea Beast
◆ Cinderella Stories Around the World
◆ Frog Prince
◆ Do Not Bring Your Dragon to Recess
◆ For Real, I Paraded in My Underpants!
◆ Olivia Bitter, Spooked-Out Sitter!
◆ Willy the Worm
◆ My Home
◆ Three Princesses
◆ The Frog Prince Saves Sleeping Beauty
◆ Sleeping Beauty
◆ Princess Bella's Birthday Cake
◆ Princess Addison Gets Angry
◆ The Tortoise and the Hare
◆ The Voice in the Boys' Room
◆ Servant and the Water Princess
◆ Because I Stubbed My Toe
◆ Yasmin the Builder
◆ New Kid from Planet Glorf
◆ Monster of Lake Lobo
◆ Golden Goose
◆ Dozer Strikes!
◆ Incredible Rockhead vs Papercut!
◆ Super-Powered Sneeze
◆ Up the President's Nose
◆ Blastoff to the Secret Side of the Moon!
◆ Hercules and the Pooper-Scooper Peril
◆ Witch's Brew
◆ Princess and Her Pony
◆ Day Mom Finally Snapped
◆ Boy Who Burped Too Much
◆ Secret of the Summer School Zombies
◆ Peek-a-Boo Dinosaurs
◆ My Little Bro-Bot
◆ Night of the Homework Zombies
◆ Max and Buddy Go to the Vet
◆ Invasion of the Gym Class Zombies
◆ Buzz Beaker and the Putt-Putt Contest
◆ Buzz Beaker and the Cave Creatures
◆ Lost Lunch
◆ Good, the Bad, and the Monkeys
◆ Frank 'n' Beans
◆ Little Lizard's New Baby
◆ Missing Monster Card
◆ Bus Ride Bully
◆ Buzz Beaker and the Cool Caps
◆ Eek and Ack vs the Wolfman
◆ Buzz Beaker and the Outer Space Trip
◆ Buzz Beaker and the Super Fast Car
◆ Snorkeling with Sea-Bots
◆ Buzz Beaker and the Race to School
◆ Jimmy Sniffles vs the Mummy
◆ Wright Brothers
◆ Double Trouble
◆ Dognapped!
◆ Fuchsia Fierce
◆ Do Not Bring Your Dragon to the Library
◆ My First Guide to Paper Airplanes
◆ Nose for Danger
◆ Helen Keller
◆ Thomas Edison: Physicist and Inventor
◆ People of the World
◆ Christopher Columbus and Neil Armstrong
◆ When Neil Armstrong Built a Wind Tunnel
◆ Jane Goodall
◆ Malala Yousafzai's Story
◆ Going to School: Comparing Past and Present
◆ Dinosaurs for Breakfast
◆ What Do You Think, Katie?
◆ Too Much RainRain
◆ A Is for Albatross
◆ Tricky Tooth
◆ The Best Baker
◆ Big Lie
◆ Jay-Z
◆ You Can Work in Music
◆ Spiders
◆ The Best Club
◆ I Can Reuse and Recycle
◆ How Effective Is Recycling?
◆ No Valentines for Katie
◆ Pony Party
◆ Piggy Bank Problems
◆ No More Teasing
◆ Moving Day
◆ Katie's Vet Loves Pets
◆ Drawing and Learning About Cats
◆ Moo, Katie Woo!
◆ Keep Dancing, Katie
◆ Katie's Spooky Sleepover
◆ Katie's Noisy Music
◆ Katie's New Shoes
◆ Katie Woo, Super Scout
◆ Katie Woo's Crazy Critter Jokes
◆ Katie Woo Has the Flu
◆ Katie Saves the Earth
◆ Katie Saves Thanksgiving
◆ Katie in the Kitchen
◆ Katie Goes Camping
◆ Mystery Coins
◆ Missing Trumpet
◆ Slime Attack
◆ Beach Bandit
◆ Crazy Clues
◆ Surprise Prize
◆ Ghost Sounds
◆ Katie Finds a Job
◆ Katie Blows Her Top
◆ Haunted House
◆ Alice in Wonderland
◆ Katie and the Haunted Museum
◆ Katie and the Fancy Substitute
◆ The Story of Ursa Major and Ursa Minor: A Roman Constellation Myth
◆ Katie and the Class Pet
◆ It Doesn't Need to Rhyme, Katie
◆ Helping Mayor Patty
◆ Goodbye to Goldie
◆ Nervous Night
◆ Good Morning, Farmer Carmen!
◆ Friends in the Mail
◆ Fly High, Katie
◆ Flower Girl Katie
◆ Daddy Can't Dance
◆ Cowgirl Katie
◆ Cartwheel Katie
◆ Boss of the World
◆ Boo, Katie Woo!
◆ Best Season Ever
◆ Happy Day
◆ Underworld Clash
◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆

今天, 應該是最炫最酷的一家公司, Robinhood, 上市的一天. 它獲利了嗎? 我想沒有多少投資人會care. 最關心的, 應該是它的營收成長率, 還有股價.

在我們一直追逐科技成長股, 被他們的高營收成長率, 潛在的高報酬昏眩的時候, 會不會忘記他們醜得要命的財務報表?

而在今年, 大家追逐的這些趨勢股表現不佳的時候, 是不是也給了我們一些省思?

其實美股中, 還有很多財務報表漂亮, 但聽起來一點也不有趣(甚至很無聊)的公司, 但他們股價穩定, 長期下來, 也給了投資人很大的回報. 像之前介紹過的POOL, 過去幾年也是平均一年翻一倍的漲幅.

而在IPO中, 也有這類的好公司.

Carrier Global(CARR), 2020年4月上市的IPO, 算是工業類股, 漲了快5倍. 有在獲利. (開利冷氣應該有聽過?就是這家公司)

Academy Sports and Outdoors (ASO), 民生消費股, 也有獲利, 2020年10月上市的IPO, 目前也漲了3倍.

下面這篇文章挺好. 與大家分享. 就像文章作者所提的, 龜兔賽跑, 穩(漲)的烏龜, 不一定會輸.

也祝福大家找到&培養自己的能力圈, 穩穩獲利.

Jim Cramer: The Biggest Thing That Happened Thursday Was the Boring Stuff

No, it wasn't Robinhood or the mega-cap tech companies, it was names we depend on like Carrier Global.
By JIM CRAMER Jul 29, 2021 | 03:38 PM EDT

Stocks quotes in this article: HOOD, FB, PYPL, CARR, RTX, NUE, AGCO, ZM, ALGN, AAPL, EBAY, AMD, XLNX

One of the most glorious things I have seen involving the stock market in ages happened today.

Was it Vlad Tenev ringing the opening bell for his breakthrough, disruptive Robinhood (HOOD) , representing 22 million mostly young new investors? Was it the free-for-all decline in the stock of the "F" in FAANG, Facebook (FB) ? Or the clobbering that Paypal (PYPL) took after what looked to be a good quarter?

Nah. I was bumping into Dave Gitlin, CEO of Carrier Global (CARR) , and his charming daughter, a college student at the University of Wisconsin. They were calmly waiting for me to finish "Squawk on the Street" to say, "Hi," and I couldn't be more thrilled. Because unlike the much ballyhooed Robinhood deal, which seems like a bust, Carrier Global came public back in April 2020 at $12 and today, after tremendous earnings, not sales, but earnings, it made an all-time high at $53, after reporting a terrific number with tremendous HVAC sales, up 31%, and an earnings surprise of 55 cents vs. the 30 cents that Wall Street was expecting.

Carrier, which was spun off when United Technologies merged with Raytheon (RTX) had some tailwinds, like the need to have clean air inside, because of the pandemic and clear air outside because office buildings are responsible for 40% of carbon emissions. But the huge upside surprise and the gigantic buyback belonged to Dave and his team and I that's what I told his daughter. I made sure she knew how proud she should be about how this man made so much money for people. Twelve to 53 in 15 months time is the name of the game.

Look, I am not trying to take away from anything that Robinhood and its co-founder and CEO Vlad Tenev have created. Far from it. They have created billions for themselves and are now letting people participate in their great sales growth. You got a chance to pay a fortune per share and many Robinhoodies did, as tons of stock was allocated to the 22 million people who joined Robinhood, because of a bang up app that every young person seems to know.

I am simply saying that HVAC, yep heating, ventilation and air conditioning is one of the most boring businesses on earth and at times like today, with all of the hoopla of Robinhood it is easy to forget is how lots of money can be made being boring, and I like that. The most exciting thing that happened this year is Carrier helped provide refrigeration for vaccines. That's just fine with me.

Unlike Robinhood, Carrier hasn't brought anyone into the stock market. It's more laser-like focus on air conditioning once spun off from Raytheon means nothing to people. Just Wall Street gibberish. But you have probably walked by a Carrier machine thousands of times and never thought anything of it. Yet, you could have bought it for a song at six times earnings instead of 25 times sales.

The Carriers, with CEOs who pay themselves lavishly but perhaps not excessively, or the Nucor's (NUE) the steel company that's also well managed and sells at six times earnings, represent valuable properties, especially when the U.S. government is about to agree on a trillion dollar infrastructure bill and the country has more than 6% GDP. We don't know why they are re-opening trades or closing trades, delta-variant trades or building and bridge investments. Forgive me, though for comparing the company of Robinhood, with something that may stay special for a while vs. companies that get described as venerable, solid and built to last.

These companies are not rarities. You know people have to eat, right? You know that there would be famine without farming. So why not buy the stock of Agco (AGCO) , No. 2 farm equipment, which went from $40 to $130 in a year and a half without ever being expensive. Combines too boring? Again fine with me. Now that the masks are off -- or at least in some places, although Zoom (ZM) is still crushing it -- I, like many others, including my daughter, didn't like how her teeth looked even as, to me, they were perfect. Dentists tell you to get Align (ALGN) . I wanted them on "Mad Money" but the show was just too darned jammed. The stock's up the most in the S&P 500, with a product that, again, like the Purloined Letter, is right in front of you.

I love tech. Created the term FANG, added the "A" when it was clear that Apple (AAPL) had to take the acronymic stage between another "A" and an "N." I am proud that those who bet against me on Twitter, the legion, are betting against FAANG. I wrote obituaries for a goodly time in my career as a reporter but I never wrote as many as have been penned to talk about the group has already made the ultimate measure on behalf of shareholders.

Oh and it's not like I don't like tech or fin tech. I felt the slings and arrows of Facebook and PayPal today. Facebook's management once again lowered the boom on its future talking about real deceleration in growth. I thought it was too dire. PayPal's Dan Schulman talked about how the separation with its former partner, eBay (EBAY) gets done now and earnings will be hurt. This was one of the least revelatory surprises ever. I think both are practicing UPOD, Underpromising to Overdeliver, and, sure this time might be different, but it's sure been the way they have handled it in the past.

Far better to be in the straight out blow outs like Advance Micro (AMD) which had still one more banner day, this time because the company it is buying, the dowdy Xilinx (XLNX) , a sleepy semiconductor company, had tremendous earnings. The two together could be unassailable and even as AMD is now richly valued it is deservingly so.

I can't wait to hear Vlad Tenev's reflection on Robinhood's debut as a public company and about the novel offering that gave millions of shares to his clients. Vlad's not so much a rags to riches American story. He's a poor Bulgarian to insanely rich American because of his on ingenuity. That's a story with celebrating in itself.

I am simply pointing out that unlike Vlad, whom you would have had invested with when you weren't allowed or able to, Dave Gitlin sure didn't keep you out of the better bet, the stock of HVAC king Carrier.

You did.

📜 [專欄新文章] Uniswap v3 Features Explained in Depth

✍️ 田少谷 Shao

📥 歡迎投稿： https://medium.com/taipei-ethereum-meetup #徵技術分享文 #使用心得 #教學文 #medium

Once again the game-changing DEX 🦄 👑

Image source: https://uniswap.org/blog/uniswap-v3/

Outline

0. Intro1. Uniswap & AMM recap2. Ticks 3. Concentrated liquidity4. Range orders: reversible limit orders5. Impacts of v36. Conclusion

0. Intro

The announcement of Uniswap v3 is no doubt one of the most exciting news in the DeFi place recently 🔥🔥🔥

While most have talked about the impact v3 can potentially bring on the market, seldom explain the delicate implementation techniques to realize all those amazing features, such as concentrated liquidity, limit-order-like range orders, etc.

Since I’ve covered Uniswap v1 & v2 (if you happen to know Mandarin, here are v1 & v2), there’s no reason for me to not cover v3 as well ✅

Thus, this article aims to guide readers through Uniswap v3, based on their official whitepaper and examples made on the announcement page. However, one needs not to be an engineer, as not many codes are involved, nor a math major, as the math involved is definitely taught in your high school, to fully understand the following content 😊😊😊

If you really make it through but still don’t get shxt, feedbacks are welcomed! 🙏

There should be another article focusing on the codebase, so stay tuned and let’s get started with some background noise!

1. Uniswap & AMM recap

Before diving in, we have to first recap the uniqueness of Uniswap and compare it to traditional order book exchanges.

Uniswap v1 & v2 are a kind of AMMs (automated market marker) that follow the constant product equation x * y = k, with x & y stand for the amount of two tokens X and Y in a pool and k as a constant.

Comparing to order book exchanges, AMMs, such as the previous versions of Uniswap, offer quite a distinct user experience:

AMMs have pricing functions that offer the price for the two tokens, which make their users always price takers, while users of order book exchanges can be both makers or takers.

Uniswap as well as most AMMs have infinite liquidity¹, while order book exchanges don’t. The liquidity of Uniswap v1 & v2 is provided throughout the price range [0,∞]².

Uniswap as well as most AMMs have price slippage³ and it’s due to the pricing function, while there isn’t always price slippage on order book exchanges as long as an order is fulfilled within one tick.

In an order book, each price (whether in green or red) is a tick. Image source: https://ftx.com/trade/BTC-PERP

¹ though the price gets worse over time; AMM of constant sum such as mStable does not have infinite liquidity

² the range is in fact [-∞,∞], while a price in most cases won’t be negative

³ AMM of constant sum does not have price slippage

2. Tick

The whole innovation of Uniswap v3 starts from ticks.

For those unfamiliar with what is a tick:

Source: https://www.investopedia.com/terms/t/tick.asp

By slicing the price range [0,∞] into numerous granular ticks, trading on v3 is highly similar to trading on order book exchanges, with only three differences:

The price range of each tick is predefined by the system instead of being proposed by users.

Trades that happen within a tick still follows the pricing function of the AMM, while the equation has to be updated once the price crosses the tick.

Orders can be executed with any price within the price range, instead of being fulfilled at the same one price on order book exchanges.

With the tick design, Uniswap v3 possesses most of the merits of both AMM and an order book exchange! 💯💯💯

So, how is the price range of a tick decided?

This question is actually somewhat related to the tick explanation above: the minimum tick size for stocks trading above 1$ is one cent.

The underlying meaning of a tick size traditionally being one cent is that one cent (1% of 1$) is the basis point of price changes between ticks, ex: 1.02 — 1.01 = 0.1.

Uniswap v3 employs a similar idea: compared to the previous/next price, the price change should always be 0.01% = 1 basis point.

However, notice the difference is that in the traditional basis point, the price change is defined with subtraction, while here in Uniswap it’s division.

This is how price ranges of ticks are decided⁴:

Image source: https://uniswap.org/whitepaper-v3.pdf

With the above equation, the tick/price range can be recorded in the index form [i, i+1], instead of some crazy numbers such as 1.0001¹⁰⁰ = 1.0100496621.

As each price is the multiplication of 1.0001 of the previous price, the price change is always 1.0001 — 1 = 0.0001 = 0.01%.

For example, when i=1, p(1) = 1.0001; when i=2, p(2) = 1.00020001.

p(2) / p(1) = 1.00020001 / 1.0001 = 1.0001

See the connection between the traditional basis point 1 cent (=1% of 1$) and Uniswap v3’s basis point 0.01%?

Image source: https://tenor.com/view/coin-master-cool-gif-19748052

But sir, are prices really granular enough? There are many shitcoins with prices less than 0.000001$. Will such prices be covered as well?

Price range: max & min

To know if an extremely small price is covered or not, we have to figure out the max & min price range of v3 by looking into the spec: there is a int24 tick state variable in UniswapV3Pool.sol.

Image source: https://uniswap.org/whitepaper-v3.pdf

The reason for a signed integer int instead of an uint is that negative power represents prices less than 1 but greater than 0.

24 bits can cover the range between 1.0001 ^ (2²³ — 1) and 1.0001 ^ -(2)²³. Even Google cannot calculate such numbers, so allow me to offer smaller values to have a rough idea of the whole price range:

1.0001 ^ (2¹⁸) = 242,214,459,604.341

1.0001 ^ -(2¹⁷) = 0.000002031888943

I think it’s safe to say that with a int24 the range can cover > 99.99% of the prices of all assets in the universe 👌

⁴ For implementation concern, however, a square root is added to both sides of the equation.

How about finding out which tick does a price belong to?

Tick index from price

The answer to this question is rather easy, as we know that p(i) = 1.0001^i, simply takes a log with base 1.0001 on both sides of the equation⁴:

Image source: https://www.codecogs.com/latex/eqneditor.php

Let’s try this out, say we wanna find out the tick index of 1000000.

Image source: https://ncalculators.com/number-conversion/log-logarithm-calculator.htm

Now, 1.0001¹³⁸¹⁶² = 999,998.678087146. Voila!

⁵ This formula is also slightly modified to fit the real implementation usage.

3. Concentrated liquidity

Now that we know how ticks and price ranges are decided, let’s talk about how orders are executed in a tick, what is concentrated liquidity and how it enables v3 to compete with stablecoin-specialized DEXs (decentralized exchange), such as Curve, by improving the capital efficiency.

Concentrated liquidity means LPs (liquidity providers) can provide liquidity to any price range/tick at their wish, which causes the liquidity to be imbalanced in ticks.

As each tick has a different liquidity depth, the corresponding pricing function x * y = k also won’t be the same!

Each tick has its own liquidity depth. Image source: https://uniswap.org/blog/uniswap-v3/

Mmm… examples are always helpful for abstract descriptions 😂

Say the original pricing function is 100(x) * 1000(y) = 100000(k), with the price of X token 1000 / 100 = 10 and we’re now in the price range [9.08, 11.08].

If the liquidity of the price range [11.08, 13.08] is the same as [9.08, 11.08], we don’t have to modify the pricing function if the price goes from 10 to 11.08, which is the boundary between two ticks.

The price of X is 1052.63 / 95 = 11.08 when the equation is 1052.63 * 95 = 100000.

However, if the liquidity of the price range [11.08, 13.08] is two times that of the current range [9.08, 11.08], balances of x and y should be doubled, which makes the equation become 2105.26 * 220 = 400000, which is (1052.63 * 2) * (110 * 2) = (100000 * 2 * 2).

We can observe the following two points from the above example:

Trades always follow the pricing function x * y = k, while once the price crosses the current price range/tick, the liquidity/equation has to be updated.

√(x * y) = √k = L is how we represent the liquidity, as I say the liquidity of x * y = 400000 is two times the liquidity of x * y = 100000, as √(400000 / 100000) = 2.

What’s more, compared to liquidity on v1 & v2 is always spread across [0,∞], liquidity on v3 can be concentrated within certain price ranges and thus results in higher capital efficiency from traders’ swapping fees!

Let’s say if I provide liquidity in the range [1200, 2800], the capital efficiency will then be 4.24x higher than v2 with the range [0,∞] 😮😮😮 There’s a capital efficiency comparison calculator, make sure to try it out!

Image source: https://uniswap.org/blog/uniswap-v3/

It’s worth noticing that the concept of concentrated liquidity was proposed and already implemented by Kyper, prior to Uniswap, which is called Automated Price Reserve in their case.⁵

⁶ Thanks to Yenwen Feng for the information.

4. Range orders: reversible limit orders

As explained in the above section, LPs of v3 can provide liquidity to any price range/tick at their wish. Depending on the current price and the targeted price range, there are three scenarios:

current price < the targeted price range

current price > the targeted price range

current price belongs to the targeted price range

The first two scenarios are called range orders. They have unique characteristics and are essentially fee-earning reversible limit orders, which will be explained later.

The last case is the exact same liquidity providing mechanism as the previous versions: LPs provide liquidity in both tokens of the same value (= amount * price).

There’s also an identical product to the case: grid trading, a very powerful investment tool for a time of consolidation. Dunno what’s grid trading? Check out Binance’s explanation on this, as this topic won’t be covered!

In fact, LPs of Uniswap v1 & v2 are grid trading with a range of [0,∞] and the entry price as the baseline.

Range orders

To understand range orders, we’d have to first revisit how price is discovered on Uniswap with the equation x * y = k, for x & y stand for the amount of two tokens X and Y and k as a constant.

The price of X compared to Y is y / x, which means how many Y one can get for 1 unit of X, and vice versa the price of Y compared to X is x / y.

For the price of X to go up, y has to increase and x decrease.

With this pricing mechanism in mind, it’s example time!

Say an LP plans to place liquidity in the price range [15.625, 17.313], higher than the current price of X 10, when 100(x) * 1000(y) = 100000(k).

The price of X is 1250 / 80 = 15.625 when the equation is 80 * 1250 = 100000.

The price of X is 1315.789 / 76 = 17.313 when the equation is 76 * 1315.789 = 100000.

If now the price of X reaches 15.625, the only way for the price of X to go even higher is to further increase y and decrease x, which means exchanging a certain amount of X for Y.

Thus, to provide liquidity in the range [15.625, 17.313], an LP needs only to prepare 80 — 76 = 4 of X. If the price exceeds 17.313, all 4 X of the LP is swapped into 1315.789 — 1250 = 65.798 Y, and then the LP has nothing more to do with the pool, as his/her liquidity is drained.

What if the price stays in the range? It’s exactly what LPs would love to see, as they can earn swapping fees for all transactions in the range! Also, the balance of X will swing between [76, 80] and the balance of Y between [1250, 1315.789].

This might not be obvious, but the example above shows an interesting insight: if the liquidity of one token is provided, only when the token becomes more valuable will it be exchanged for the less valuable one.

…wut? 🤔

Remember that if 4 X is provided within [15.625, 17.313], only when the price of X goes up from 15.625 to 17.313 is 4 X gradually swapped into Y, the less valuable one!

What if the price of X drops back immediately after reaching 17.313? As X becomes less valuable, others are going to exchange Y for X.

The below image illustrates the scenario of DAI/USDC pair with a price range of [1.001, 1.002] well: the pool is always composed entirely of one token on both sides of the tick, while in the middle 1.001499⁶ is of both tokens.

Image source: https://uniswap.org/blog/uniswap-v3/

Similarly, to provide liquidity in a price range < current price, an LP has to prepare a certain amount of Y for others to exchange Y for X within the range.

To wrap up such an interesting feature, we know that:

Only one token is required for range orders.

Only when the current price is within the range of the range order can LP earn trading fees. This is the main reason why most people believe LPs of v3 have to monitor the price more actively to maximize their income, which also means that LPs of v3 have become arbitrageurs 🤯

I will be discussing more the impacts of v3 in 5. Impacts of v3.

⁷ 1.001499988 = √(1.0001 * 1.0002) is the geometric mean of 1.0001 and 1.0002. The implication is that the geometric mean of two prices is the average execution price within the range of the two prices.

Reversible limit orders

As the example in the last section demonstrates, if there is 4 X in range [15.625, 17.313], the 4 X will be completely converted into 65.798 Y when the price goes over 17.313.

We all know that a price can stay in a wide range such as [10, 11] for quite some time, while it’s unlikely so in a narrow range such as [15.625, 15.626].

Thus, if an LP provides liquidity in [15.625, 15.626], we can expect that once the price of X goes over 15.625 and immediately also 15.626, and does not drop back, all X are then forever converted into Y.

The concept of having a targeted price and the order will be executed after the price is crossed is exactly the concept of limit orders! The only difference is that if the range of a range order is not narrow enough, it’s highly possible that the conversion of tokens will be reverted once the price falls back to the range.

As price ranges follow the equation p(i) = 1.0001 ^ i, the range can be quite narrow and a range order can thus effectively serve as a limit order:

When i = 27490, 1.0001²⁷⁴⁹⁰ = 15.6248.⁸

When i = 27491, 1.0001²⁷⁴⁹¹ = 15.6264.⁸

A range of 0.0016 is not THAT narrow but can certainly satisfy most limit order use cases!

⁸ As mentioned previously in note #4, there is a square root in the equation of the price and index, thus the numbers here are for explantion only.

5. Impacts of v3

Higher capital efficiency, LPs become arbitrageurs… as v3 has made tons of radical changes, I’d like to summarize my personal takes of the impacts of v3:

Higher capital efficiency makes one of the most frequently considered indices in DeFi: TVL, total value locked, becomes less meaningful, as 1$ on Uniswap v3 might have the same effect as 100$ or even 2000$ on v2.

The ease of spot exchanging between spot exchanges used to be a huge advantage of spot markets over derivative markets. As LPs will take up the role of arbitrageurs and arbitraging is more likely to happen on v3 itself other than between DEXs, this gap is narrowed … to what extent? No idea though.

LP strategies and the aggregation of NFT of Uniswap v3 liquidity token are becoming the blue ocean for new DeFi startups: see Visor and Lixir. In fact, this might be the turning point for both DeFi and NFT: the two main reasons of blockchain going mainstream now come to the alignment of interest: solving the $$ problem 😏😏😏

In the right venue, which means a place where transaction fees are low enough, such as Optimism, we might see Algo trading firms coming in to share the market of designing LP strategies on Uniswap v3, as I believe Algo trading is way stronger than on-chain strategies or DAO voting to add liquidity that sort of thing.

After reading this article by Parsec.finance: The Dex to Rule Them All, I cannot help but wonder: maybe there is going to be centralized crypto exchanges adopting v3’s approach. The reason is that since orders of LPs in the same tick are executed pro-rata, the endless front-running speeding-competition issue in the Algo trading world, to some degree, is… solved? 🤔

Anyway, personal opinions can be biased and seriously wrong 🙈 I’m merely throwing out a sprat to catch a whale. Having a different voice? Leave your comment down below!

6. Conclusion

That was kinda tough, isn’t it? Glad you make it through here 🥂🥂🥂

There are actually many more details and also a huge section of Oracle yet to be covered. However, since this article is more about features and targeting normal DeFi users, I’ll leave those to the next one; hope there is one 😅

If you have any doubt or find any mistake, please feel free to reach out to me and I’d try to reply AFAP!

Stay tuned and in the meantime let’s wait and see how Uniswap v3 is again pioneering the innovation of DeFi 🌟

Uniswap v3 Features Explained in Depth was originally published in Taipei Ethereum Meetup on Medium, where people are continuing the conversation by highlighting and responding to this story.

👏 歡迎轉載分享鼓掌

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