An approximate introduction to how zk-SNARKs are possible (part 1)
You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.
In the context of blockchains, this has 2 very powerful applications: Perhaps the most powerful cryptographic technology to come out of the last decade is general-purpose succinct zero knowledge proofs, usually called zk-SNARKs ("zero knowledge succinct arguments of knowledge"). A zk-SNARK allows you to generate a proof that some computation has some particular output, in such a way that the proof can be verified extremely quickly even if the underlying computation takes a very long time to run. The "ZK" part adds an additional feature: the proof can keep some of the inputs to the computation hidden.
You can make a proof for the statement "I know a secret number such that if you take the word ‘cow', add the number to the end, and SHA256 hash it 100 million times, the output starts with 0x57d00485aa". The verifier can verify the proof far more quickly than it would take for them to run 100 million hashes themselves, and the proof would also not reveal what the secret number is.
In the context of blockchains, this has two very powerful applications:
- Scalability: if a block takes a long time to verify, one person can verify it and generate a proof, and everyone else can just quickly verify the proof instead
- Privacy: you can prove that you have the right to transfer some asset (you received it, and you didn't already transfer it) without revealing the link to which asset you received. This ensures security without unduly leaking information about who is transacting with whom to the public.
But zk-SNARKs are quite complex; indeed, as recently as in 2014-17 they were still frequently called "moon math". The good news is that since then, the protocols have become simpler and our understanding of them has become much better. This post will try to explain how ZK-SNARKs work, in a way that should be understandable to someone with a medium level of understanding of mathematics.
Why ZK-SNARKs "should" be hard
Let us take the example that we started with: we have a number (we can encode "cow" followed by the secret input as an integer), we take the SHA256 hash of that number, then we do that again another 99,999,999 times, we get the output, and we check what its starting digits are. This is a huge computation.
A "succinct" proof is one where both the size of the proof and the time required to verify it grow much more slowly than the computation to be verified. If we want a "succinct" proof, we cannot require the verifier to do some work per round of hashing (because then the verification time would be proportional to the computation). Instead, the verifier must somehow check the whole computation without peeking into each individual piece of the computation.
One natural technique is random sampling: how about we just have the verifier peek into the computation in 500 different places, check that those parts are correct, and if all 500 checks pass then assume that the rest of the computation must with high probability be fine, too?
Such a procedure could even be turned into a non-interactive proof using the Fiat-Shamir heuristic: the prover computes a Merkle root of the computation, uses the Merkle root to pseudorandomly choose 500 indices, and provides the 500 corresponding Merkle branches of the data. The key idea is that the prover does not know which branches they will need to reveal until they have already "committed to" the data. If a malicious prover tries to fudge the data after learning which indices are going to be checked, that would change the Merkle root, which would result in a new set of random indices, which would require fudging the data again... trapping the malicious prover in an endless cycle.
But unfortunately there is a fatal flaw in naively applying random sampling to spot-check a computation in this way: computation is inherently fragile. If a malicious prover flips one bit somewhere in the middle of a computation, they can make it give a completely different result, and a random sampling verifier would almost never find out.
It only takes one deliberately inserted error, that a random check would almost never catch, to make a computation give a completely incorrect result.
If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? There is a clever solution.
see part 2
(Edited)
More on Web3 & Crypto

Koji Mochizuki
3 years ago
How to Launch an NFT Project by Yourself
Creating 10,000 auto-generated artworks, deploying a smart contract to the Ethereum / Polygon blockchain, setting up some tools, etc.
There is so much to do from launching to running an NFT project. Creating parts for artworks, generating 10,000 unique artworks and metadata, creating a smart contract and deploying it to a blockchain network, creating a website, creating a Twitter account, setting up a Discord server, setting up an OpenSea collection. In addition, you need to have MetaMask installed in your browser and have some ETH / MATIC. Did you get tired of doing all this? Don’t worry, once you know what you need to do, all you have to do is do it one by one.
To be honest, it’s best to run an NFT project in a team of three or more, including artists, developers, and marketers. However, depending on your motivation, you can do it by yourself. Some people might come later to offer help with your project. The most important thing is to take a step as soon as possible.
Creating Parts for Artworks
There are lots of free/paid software for drawing, but after all, I think Adobe Illustrator or Photoshop is the best. The images of Skulls In Love are a composite of 48x48 pixel parts created using Photoshop.
The most important thing in creating parts for generative art is to repeatedly test what your artworks will look like after each layer has been combined. The generated artworks should not be too unnatural.
How Many Parts Should You Create?
Are you wondering how many parts you should create to avoid duplication as much as possible when generating your artworks? My friend Stephane, a developer, has created a great tool to help with that.
Generating 10,000 Unique Artworks and Metadata
I highly recommend using the HashLips Art Engine to generate your artworks and metadata. Perhaps there is no better artworks generation tool at the moment.
GitHub: https://github.com/HashLips/hashlips_art_engine
YouTube:
Storing Artworks and Metadata
Ideally, the generated artworks and metadata should be stored on-chain, but if you want to store them off-chain, you should use IPFS. Do not store in centralized storage. This is because data will be lost if the server goes down or if the company goes down. On the other hand, IPFS is a more secure way to find data because it utilizes a distributed, decentralized system.
Storing to IPFS is easy with Pinata, NFT.Storage, and so on. The Skulls In Love uses Pinata. It’s very easy to use, just upload the folder containing your artworks.
Creating and Deploying a Smart Contract
You don’t have to create a smart contract from scratch. There are many great NFT projects, many of which publish their contract source code on Etherscan / PolygonScan. You can choose the contract you like and reuse it. Of course, that requires some knowledge of Solidity, but it depends on your efforts. If you don’t know which contract to choose, use the HashLips smart contract. It’s very simple, but it has almost all the functions you need.
GitHub: https://github.com/HashLips/hashlips_nft_contract
Note: Later on, you may want to change the cost value. You can change it on Remix or Etherscan / PolygonScan. But in this case, enter the Wei value instead of the Ether value. For example, if you want to sell for 1 MATIC, you have to enter “1000000000000000000”. If you set this value to “1”, you will have a nightmare. I recommend using Simple Unit Converter as a tool to calculate the Wei value.
Creating a Website
The website here is not just a static site to showcase your project, it’s a so-called dApp that allows you to access your smart contract and mint NFTs. In fact, this level of dApp is not too difficult for anyone who has ever created a website. Because the ethers.js / web3.js libraries make it easy to interact with your smart contract. There’s also no problem connecting wallets, as MetaMask has great documentation.
The Skulls In Love uses a simple, fast, and modern dApp that I built from scratch using Next.js. It is published on GitHub, so feel free to use it.
Why do people mint NFTs on a website?
Ethereum’s gas fees are high, so if you mint all your NFTs, there will be a huge initial cost. So it makes sense to get the buyers to help with the gas fees for minting.
What about Polygon? Polygon’s gas fees are super cheap, so even if you mint 10,000 NFTs, it’s not a big deal. But we don’t do that. Since NFT projects are a kind of game, it involves the fun of not knowing what will come out after minting.
Creating a Twitter Account
I highly recommend creating a Twitter account. Twitter is an indispensable tool for announcing giveaways and reaching more people. It’s better to announce your project and your artworks little by little, 1–2 weeks before launching your project.
Creating and Setting Up a Discord Server
I highly recommend creating a Discord server as well as a Twitter account. The Discord server is a community and its home. Fans of your NFT project will want to join your community and interact with many other members. So, carefully create each channel on your Discord server to make it a cozy place for your community members.
If you are unfamiliar with Discord, you may be particularly confused by the following:
What bots should I use?
How should I set roles and permissions?
But don’t worry. There are lots of great YouTube videos and blog posts about these.
It’s also a good idea to join the Discord servers of some NFT projects and see how they’re made. Our Discord server is so simple that even beginners will find it easy to understand. Please join us and see it!
Note: First, create a test account and a test server to make sure your bots and permissions work properly. It is better to verify the behavior on the test server before setting up your production server.
UPDATED: As your Discord server grows, you cannot manage it on your own. In this case, you will be hiring several moderators, but choose carefully before hiring. And don’t give them important role permissions right after hiring. Initially, the same permissions as other members are sufficient. After a while, you can add permissions as needed, such as kicking/banning, using the “@every” tag, and adding roles. Again, don’t immediately give significant permissions to your Mod role. Your server can be messed up by fake moderators.
Setting Up Your OpenSea Collection
Before you start selling your NFTs, you need to reserve some for airdrops, giveaways, staff, and more. It’s up to you whether it’s 100, 500, or how many.
After minting some of your NFTs, your account and collection should have been created in OpenSea. Go to OpenSea, connect to your wallet, and set up your collection. Just set your logo, banner image, description, links, royalties, and more. It’s not that difficult.
Promoting Your Project
After all, promotion is the most important thing. In fact, almost every successful NFT project spends a lot of time and effort on it.
In addition to Twitter and Discord, it’s even better to use Instagram, Reddit, and Medium. Also, register your project in NFTCalendar and DISBOARD
DISBOARD is the public Discord server listing community.
About Promoters
You’ll probably get lots of contacts from promoters on your Discord, Twitter, Instagram, and more. But most of them are scams, so don’t pay right away. If you have a promoter that looks attractive to you, be sure to check the promoter’s social media accounts or website to see who he/she is. They basically charge in dollars. The amount they charge isn’t cheap, but promoters with lots of followers may have some temporary effect on your project. Some promoters accept 50% prepaid and 50% postpaid. If you can afford it, it might be worth a try. I never ask them, though.
When Should the Promotion Activities Start?
You may be worried that if you promote your project before it starts, someone will copy your project (artworks). It is true that some projects have actually suffered such damage. I don’t have a clear answer to this question right now, but:
- Do not publish all the information about your project too early
- The information should be released little by little
- Creating artworks that no one can easily copy
I think these are important.
If anyone has a good idea, please share it!
About Giveaways
When hosting giveaways, you’ll probably use multiple social media platforms. You may want to grow your Discord server faster. But if joining the Discord server is included in the giveaway requirements, some people hate it. I recommend holding giveaways for each platform. On Twitter and Reddit, you should just add the words “Discord members-only giveaway is being held now! Please join us if you like!”.
If you want to easily pick a giveaway winner in your browser, I recommend Twitter Picker.
Precautions for Distributing Free NFTs
If you want to increase your Twitter followers and Discord members, you can actually get a lot of people by holding events such as giveaways and invite contests. However, distributing many free NFTs at once can be dangerous. Some people who want free NFTs, as soon as they get a free one, sell it at a very low price on marketplaces such as OpenSea. They don’t care about your project and are only thinking about replacing their own “free” NFTs with Ethereum. The lower the floor price of your NFTs, the lower the value of your NFTs (project). Try to think of ways to get people to “buy” your NFTs as much as possible.
Ethereum vs. Polygon
Even though Ethereum has high gas fees, NFT projects on the Ethereum network are still mainstream and popular. On the other hand, Polygon has very low gas fees and fast transaction processing, but NFT projects on the Polygon network are not very popular.
Why? There are several reasons, but the biggest one is that it’s a lot of work to get MATIC (on Polygon blockchain, use MATIC instead of ETH) ready to use. Simply put, you need to bridge your tokens to the Polygon chain. So people need to do this first before minting your NFTs on your website. It may not be a big deal for those who are familiar with crypto and blockchain, but it may be complicated for those who are not. I hope that the tedious work will be simplified in the near future.
If you are confident that your NFTs will be purchased even if they are expensive, or if the total supply of your NFTs is low, you may choose Ethereum. If you just want to save money, you should choose Polygon. Keep in mind that gas fees are incurred not only when minting, but also when performing some of your smart contract functions and when transferring your NFTs.
If I were to launch a new NFT project, I would probably choose Ethereum or Solana.
Conclusion
Some people may want to start an NFT project to make money, but don’t forget to enjoy your own project. Several months ago, I was playing with creating generative art by imitating the CryptoPunks. I found out that auto-generated artworks would be more interesting than I had imagined, and since then I’ve been completely absorbed in generative art.
This is one of the Skulls In Love artworks:
This character wears a cowboy hat, black slim sunglasses, and a kimono. If anyone looks like this, I can’t help laughing!
The Skulls In Love NFTs can be minted for a small amount of MATIC on the official website. Please give it a try to see what kind of unique characters will appear 💀💖
Thank you for reading to the end. I hope this article will be helpful to those who want to launch an NFT project in the future ✨

Jonathan Vanian
3 years ago
What is Terra? Your guide to the hot cryptocurrency
With cryptocurrencies like Bitcoin, Ether, and Dogecoin gyrating in value over the past few months, many people are looking at so-called stablecoins like Terra to invest in because of their more predictable prices.
Terraform Labs, which oversees the Terra cryptocurrency project, has benefited from its rising popularity. The company said recently that investors like Arrington Capital, Lightspeed Venture Partners, and Pantera Capital have pledged $150 million to help it incubate various crypto projects that are connected to Terra.
Terraform Labs and its partners have built apps that operate on the company’s blockchain technology that helps keep a permanent and shared record of the firm’s crypto-related financial transactions.
Here’s what you need to know about Terra and the company behind it.
What is Terra?
Terra is a blockchain project developed by Terraform Labs that powers the startup’s cryptocurrencies and financial apps. These cryptocurrencies include the Terra U.S. Dollar, or UST, that is pegged to the U.S. dollar through an algorithm.
Terra is a stablecoin that is intended to reduce the volatility endemic to cryptocurrencies like Bitcoin. Some stablecoins, like Tether, are pegged to more conventional currencies, like the U.S. dollar, through cash and cash equivalents as opposed to an algorithm and associated reserve token.
To mint new UST tokens, a percentage of another digital token and reserve asset, Luna, is “burned.” If the demand for UST rises with more people using the currency, more Luna will be automatically burned and diverted to a community pool. That balancing act is supposed to help stabilize the price, to a degree.
“Luna directly benefits from the economic growth of the Terra economy, and it suffers from contractions of the Terra coin,” Terraform Labs CEO Do Kwon said.
Each time someone buys something—like an ice cream—using UST, that transaction generates a fee, similar to a credit card transaction. That fee is then distributed to people who own Luna tokens, similar to a stock dividend.
Who leads Terra?
The South Korean firm Terraform Labs was founded in 2018 by Daniel Shin and Kwon, who is now the company’s CEO. Kwon is a 29-year-old former Microsoft employee; Shin now heads the Chai online payment service, a Terra partner. Kwon said many Koreans have used the Chai service to buy goods like movie tickets using Terra cryptocurrency.
Terraform Labs does not make money from transactions using its crypto and instead relies on outside funding to operate, Kwon said. It has raised $57 million in funding from investors like HashKey Digital Asset Group, Divergence Digital Currency Fund, and Huobi Capital, according to deal-tracking service PitchBook. The amount raised is in addition to the latest $150 million funding commitment announced on July 16.
What are Terra’s plans?
Terraform Labs plans to use Terra’s blockchain and its associated cryptocurrencies—including one pegged to the Korean won—to create a digital financial system independent of major banks and fintech-app makers. So far, its main source of growth has been in Korea, where people have bought goods at stores, like coffee, using the Chai payment app that’s built on Terra’s blockchain. Kwon said the company’s associated Mirror trading app is experiencing growth in China and Thailand.
Meanwhile, Kwon said Terraform Labs would use its latest $150 million in funding to invest in groups that build financial apps on Terra’s blockchain. He likened the scouting and investing in other groups as akin to a “Y Combinator demo day type of situation,” a reference to the popular startup pitch event organized by early-stage investor Y Combinator.
The combination of all these Terra-specific financial apps shows that Terraform Labs is “almost creating a kind of bank,” said Ryan Watkins, a senior research analyst at cryptocurrency consultancy Messari.
In addition to cryptocurrencies, Terraform Labs has a number of other projects including the Anchor app, a high-yield savings account for holders of the group’s digital coins. Meanwhile, people can use the firm’s associated Mirror app to create synthetic financial assets that mimic more conventional ones, like “tokenized” representations of corporate stocks. These synthetic assets are supposed to be helpful to people like “a small retail trader in Thailand” who can more easily buy shares and “get some exposure to the upside” of stocks that they otherwise wouldn’t have been able to obtain, Kwon said. But some critics have said the U.S. Securities and Exchange Commission may eventually crack down on synthetic stocks, which are currently unregulated.
What do critics say?
Terra still has a long way to go to catch up to bigger cryptocurrency projects like Ethereum.
Most financial transactions involving Terra-related cryptocurrencies have originated in Korea, where its founders are based. Although Terra is becoming more popular in Korea thanks to rising interest in its partner Chai, it’s too early to say whether Terra-related currencies will gain traction in other countries.
Terra’s blockchain runs on a “limited number of nodes,” said Messari’s Watkins, referring to the computers that help keep the system running. That helps reduce latency that may otherwise slow processing of financial transactions, he said.
But the tradeoff is that Terra is less “decentralized” than other blockchain platforms like Ethereum, which is powered by thousands of interconnected computing nodes worldwide. That could make Terra less appealing to some blockchain purists.

CyberPunkMetalHead
3 years ago
Developed an automated cryptocurrency trading tool for nearly a year before unveiling it this month.
Overview
I'm happy to provide this important update. We've worked on this for a year and a half, so I'm glad to finally write it. We named the application AESIR because we’ve love Norse Mythology. AESIR automates and runs trading strategies.
Volatility, technical analysis, oscillators, and other signals are currently supported by AESIR.
Additionally, we enhanced AESIR's ability to create distinctive bespoke signals by allowing it to analyze many indicators and produce a single signal.
AESIR has a significant social component that allows you to copy the best-performing public setups and use them right away.
Enter your email here to be notified when AEISR launches.
Views on algorithmic trading
First, let me clarify. Anyone who claims algorithmic trading platforms are money-printing plug-and-play devices is a liar. Algorithmic trading platforms are a collection of tools.
A trading algorithm won't make you a competent trader if you lack a trading strategy and yolo your funds without testing. It may hurt your trade. Test and alter your plans to account for market swings, but comprehend market signals and trends.
Status Report
Throughout closed beta testing, we've communicated closely with users to design a platform they want to use.
To celebrate, we're giving you free Aesir Viking NFTs and we cover gas fees.
Why use a trading Algorithm?
Automating a successful manual approach
experimenting with and developing solutions that are impossible to execute manually
One AESIR strategy lets you buy any cryptocurrency that rose by more than x% in y seconds.
AESIR can scan an exchange for coins that have gained more than 3% in 5 minutes. It's impossible to manually analyze over 1000 trading pairings every 5 minutes. Auto buy dips or DCA around a Dip
Sneak Preview
Here's the Leaderboard, where you can clone the best public settings.
As a tiny, self-funded team, we're excited to unveil our product. It's a beta release, so there's still more to accomplish, but we know where we stand.
If this sounds like a project that you might want to learn more about, you can sign up to our newsletter and be notified when AESIR launches.
Useful Links:
Join the Discord | Join our subreddit | Newsletter | Mint Free NFT
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Aure's Notes
2 years ago
I met a man who in just 18 months scaled his startup to $100 million.
A fascinating business conversation.
This week at Web Summit, I had mentor hour.
Mentor hour connects startups with experienced entrepreneurs.
The YC-selected founder who mentored me had grown his company to $100 million in 18 months.
I had 45 minutes to question him.
I've compiled this.
Context
Founder's name is Zack.
After working in private equity, Zack opted to acquire an MBA.
Surrounded by entrepreneurs at a prominent school, he decided to become one himself.
Unsure how to proceed, he bet on two horses.
On one side, he received an offer from folks who needed help running their startup owing to lack of time. On the other hand, he had an idea for a SaaS to start himself.
He just needed to validate it.
Validating
Since Zack's proposal helped companies, he contacted university entrepreneurs for comments.
He contacted university founders.
Once he knew he'd correctly identified the problem and that people were willing to pay to address it, he started developing.
He earned $100k in a university entrepreneurship competition.
His plan was evident by then.
The other startup's founders saw his potential and granted him $400k to launch his own SaaS.
Hiring
He started looking for a tech co-founder because he lacked IT skills.
He interviewed dozens and picked the finest.
As he didn't want to wait for his program to be ready, he contacted hundreds of potential clients and got 15 letters of intent promising they'd join up when it was available.
YC accepted him by then.
He had enough positive signals to raise.
Raising
He didn't say how many VCs he called, but he indicated 50 were interested.
He jammed meetings into two weeks to generate pressure and encourage them to invest.
Seed raise: $11 million.
Selling
His objective was to contact as many entrepreneurs as possible to promote his product.
He first contacted startups by scraping CrunchBase data.
Once he had more money, he started targeting companies with ZoomInfo.
His VC urged him not to hire salespeople until he closed 50 clients himself.
He closed 100 and hired a CRO through a headhunter.
Scaling
Three persons started the business.
He primarily works in sales.
Coding the product was done by his co-founder.
Another person performing operational duties.
He regretted recruiting the third co-founder, who was ineffective (could have hired an employee instead).
He wanted his company to be big, so he hired two young marketing people from a competing company.
After validating several marketing channels, he chose PR.
$100 Million and under
He developed a sales team and now employs 30 individuals.
He raised a $100 million Series A.
Additionally, he stated
He’s been rejected a lot. Like, a lot.
Two great books to read: Steve Jobs by Isaacson, and Why Startups Fail by Tom Eisenmann.
The best skill to learn for non-tech founders is “telling stories”, which means sales. A founder’s main job is to convince: co-founders, employees, investors, and customers. Learn code, or learn sales.
Conclusion
I often read about these stories but hardly take them seriously.
Zack was amazing.
Three things about him stand out:
His vision. He possessed a certain amount of fire.
His vitality. The man had a lot of enthusiasm and spoke quickly and decisively. He takes no chances and pushes the envelope in all he does.
His Rolex.
He didn't do all this in 18 months.
Not really.
He couldn't launch his company without private equity experience.
These accounts disregard entrepreneurs' original knowledge.
Hormozi will tell you how he founded Gym Launch, but he won't tell you how he had a gym first, how he worked at uni to pay for his gym, or how he went to the gym and learnt about fitness, which gave him the idea to open his own.
Nobody knows nothing. If you scale quickly, it's probable because you gained information early.
Lincoln said, "Give me six hours to chop down a tree, and I'll spend four sharpening the axe."
Sharper axes cut trees faster.

Matthew Cluff
3 years ago
GTO Poker 101
"GTO" (Game Theory Optimal) has been used a lot in poker recently. To clarify its meaning and application, the aim of this article is to define what it is, when to use it when playing, what strategies to apply for how to play GTO poker, for beginner and more advanced players!
Poker GTO
In poker, you can choose between two main winning strategies:
Exploitative play maximizes expected value (EV) by countering opponents' sub-optimal plays and weaker tendencies. Yes, playing this way opens you up to being exploited, but the weaker opponents you're targeting won't change their game to counteract this, allowing you to reap maximum profits over the long run.
GTO (Game-Theory Optimal): You try to play perfect poker, which forces your opponents to make mistakes (which is where almost all of your profit will be derived from). It mixes bluffs or semi-bluffs with value bets, clarifies bet sizes, and more.
GTO vs. Exploitative: Which is Better in Poker?
Before diving into GTO poker strategy, it's important to know which of these two play styles is more profitable for beginners and advanced players. The simple answer is probably both, but usually more exploitable.
Most players don't play GTO poker and can be exploited in their gameplay and strategy, allowing for more profits to be made using an exploitative approach. In fact, it’s only in some of the largest games at the highest stakes that GTO concepts are fully utilized and seen in practice, and even then, exploitative plays are still sometimes used.
Knowing, understanding, and applying GTO poker basics will create a solid foundation for your poker game. It's also important to understand GTO so you can deviate from it to maximize profits.
GTO Poker Strategy
According to Ed Miller's book "Poker's 1%," the most fundamental concept that only elite poker players understand is frequency, which could be in relation to cbets, bluffs, folds, calls, raises, etc.
GTO poker solvers (downloadable online software) give solutions for how to play optimally in any given spot and often recommend using mixed strategies based on select frequencies.
In a river situation, a solver may tell you to call 70% of the time and fold 30%. It may also suggest calling 50% of the time, folding 35% of the time, and raising 15% of the time (with a certain range of hands).
Frequencies are a fundamental and often unrecognized part of poker, but they run through these 5 GTO concepts.
1. Preflop ranges
To compensate for positional disadvantage, out-of-position players must open tighter hand ranges.
Premium starting hands aren't enough, though. Considering GTO poker ranges and principles, you want a good, balanced starting hand range from each position with at least some hands that can make a strong poker hand regardless of the flop texture (low, mid, high, disconnected, etc).
Below is a GTO preflop beginner poker chart for online 6-max play, showing which hand ranges one should open-raise with. Table positions are color-coded (see key below).
NOTE: For GTO play, it's advisable to use a mixed strategy for opening in the small blind, combining open-limps and open-raises for various hands. This cannot be illustrated with the color system used for the chart.
Choosing which hands to play is often a math problem, as discussed below.
Other preflop GTO poker charts include which hands to play after a raise, which to 3bet, etc. Solvers can help you decide which preflop hands to play (call, raise, re-raise, etc.).
2. Pot Odds
Always make +EV decisions that profit you as a poker player. Understanding pot odds (and equity) can help.
Postflop Pot Odds
Let’s say that we have JhTh on a board of 9h8h2s4c (open-ended straight-flush draw). We have $40 left and $50 in the pot. He has you covered and goes all-in. As calling or folding are our only options, playing GTO involves calculating whether a call is +EV or –EV. (The hand was empty.)
Any remaining heart, Queen, or 7 wins the hand. This means we can improve 15 of 46 unknown cards, or 32.6% of the time.
What if our opponent has a set? The 4h or 2h could give us a flush, but it could also give the villain a boat. If we reduce outs from 15 to 14.5, our equity would be 31.5%.
We must now calculate pot odds.
(bet/(our bet+pot)) = pot odds
= $50 / ($40 + $90)
= $40 / $130
= 30.7%
To make a profitable call, we need at least 30.7% equity. This is a profitable call as we have 31.5% equity (even if villain has a set). Yes, we will lose most of the time, but we will make a small profit in the long run, making a call correct.
Pot odds aren't just for draws, either. If an opponent bets 50% pot, you get 3 to 1 odds on a call, so you must win 25% of the time to be profitable. If your current hand has more than 25% equity against your opponent's perceived range, call.
Preflop Pot Odds
Preflop, you raise to 3bb and the button 3bets to 9bb. You must decide how to act. In situations like these, we can actually use pot odds to assist our decision-making.
This pot is:
(our open+3bet size+small blind+big blind)
(3bb+9bb+0.5bb+1bb)
= 13.5
This means we must call 6bb to win a pot of 13.5bb, which requires 30.7% equity against the 3bettor's range.
Three additional factors must be considered:
Being out of position on our opponent makes it harder to realize our hand's equity, as he can use his position to put us in tough spots. To profitably continue against villain's hand range, we should add 7% to our equity.
Implied Odds / Reverse Implied Odds: The ability to win or lose significantly more post-flop (than pre-flop) based on our remaining stack.
While statistics on 3bet stats can be gained with a large enough sample size (i.e. 8% 3bet stat from button), the numbers don't tell us which 8% of hands villain could be 3betting with. Both polarized and depolarized charts below show 8% of possible hands.
7.4% of hands are depolarized.
Polarized Hand range (7.54%):
Each hand range has different contents. We don't know if he 3bets some hands and calls or folds others.
Using an exploitable strategy can help you play a hand range correctly. The next GTO concept will make things easier.
3. Minimum Defense Frequency:
This concept refers to the % of our range we must continue with (by calling or raising) to avoid being exploited by our opponents. This concept is most often used off-table and is difficult to apply in-game.
These beginner GTO concepts will help your decision-making during a hand, especially against aggressive opponents.
MDF formula:
MDF = POT SIZE/(POT SIZE+BET SIZE)
Here's a poker GTO chart of common bet sizes and minimum defense frequency.
Take the number of hand combos in your starting hand range and use the MDF to determine which hands to continue with. Choose hands with the most playability and equity against your opponent's betting range.
Say you open-raise HJ and BB calls. Qh9h6c flop. Your opponent leads you for a half-pot bet. MDF suggests keeping 67% of our range.
Using the above starting hand chart, we can determine that the HJ opens 254 combos:
We must defend 67% of these hands, or 170 combos, according to MDF. Hands we should keep include:
Flush draws
Open-Ended Straight Draws
Gut-Shot Straight Draws
Overcards
Any Pair or better
So, our flop continuing range could be:
Some highlights:
Fours and fives have little chance of improving on the turn or river.
We only continue with AX hearts (with a flush draw) without a pair or better.
We'll also include 4 AJo combos, all of which have the Ace of hearts, and AcJh, which can block a backdoor nut flush combo.
Let's assume all these hands are called and the turn is blank (2 of spades). Opponent bets full-pot. MDF says we must defend 50% of our flop continuing range, or 85 of 170 combos, to be unexploitable. This strategy includes our best flush draws, straight draws, and made hands.
Here, we keep combining:
Nut flush draws
Pair + flush draws
GS + flush draws
Second Pair, Top Kicker+
One combo of JJ that doesn’t block the flush draw or backdoor flush draw.
On the river, we can fold our missed draws and keep our best made hands. When calling with weaker hands, consider blocker effects and card removal to avoid overcalling and decide which combos to continue.
4. Poker GTO Bet Sizing
To avoid being exploited, balance your bluffs and value bets. Your betting range depends on how much you bet (in relation to the pot). This concept only applies on the river, as draws (bluffs) on the flop and turn still have equity (and are therefore total bluffs).
On the flop, you want a 2:1 bluff-to-value-bet ratio. On the flop, there won't be as many made hands as on the river, and your bluffs will usually contain equity. The turn should have a "bluffing" ratio of 1:1. Use the chart below to determine GTO river bluff frequencies (relative to your bet size):
This chart relates to your opponent's pot odds. If you bet 50% pot, your opponent gets 3:1 odds and must win 25% of the time to call. Poker GTO theory suggests including 25% bluff combinations in your betting range so you're indifferent to your opponent calling or folding.
Best river bluffs don't block hands you want your opponent to have (or not have). For example, betting with missed Ace-high flush draws is often a mistake because you block a missed flush draw you want your opponent to have when bluffing on the river (meaning that it would subsequently be less likely he would have it, if you held two of the flush draw cards). Ace-high usually has some river showdown value.
If you had a 3-flush on the river and wanted to raise, you could bluff raise with AX combos holding the bluff suit Ace. Blocking the nut flush prevents your opponent from using that combo.
5. Bet Sizes and Frequency
GTO beginner strategies aren't just bluffs and value bets. They show how often and how much to bet in certain spots. Top players have benefited greatly from poker solvers, which we'll discuss next.
GTO Poker Software
In recent years, various poker GTO solvers have been released to help beginner, intermediate, and advanced players play balanced/GTO poker in various situations.
PokerSnowie and PioSolver are popular GTO and poker study programs.
While you can't compute players' hand ranges and what hands to bet or check with in real time, studying GTO play strategies with these programs will pay off. It will improve your poker thinking and understanding.
Solvers can help you balance ranges, choose optimal bet sizes, and master cbet frequencies.
GTO Poker Tournament
Late-stage tournaments have shorter stacks than cash games. In order to follow GTO poker guidelines, Nash charts have been created, tweaked, and used for many years (and also when to call, depending on what number of big blinds you have when you find yourself shortstacked).
The charts are for heads-up push/fold. In a multi-player game, the "pusher" chart can only be used if play is folded to you in the small blind. The "caller" chart can only be used if you're in the big blind and assumes a small blind "pusher" (with a much wider range than if a player in another position was open-shoving).
Divide the pusher chart's numbers by 2 to see which hand to use from the Button. Divide the original chart numbers by 4 to find the CO's pushing range. Some of the figures will be impossible to calculate accurately for the CO or positions to the right of the blinds because the chart's highest figure is "20+" big blinds, which is also used for a wide range of hands in the push chart.
Both of the GTO charts below are ideal for heads-up play, but exploitable HU shortstack strategies can lead to more +EV decisions against certain opponents. Following the charts will make your play GTO and unexploitable.
Poker pro Max Silver created the GTO push/fold software SnapShove. (It's accessible online at www.snapshove.com or as iOS or Android apps.)
Players can access GTO shove range examples in the full version. (You can customize the number of big blinds you have, your position, the size of the ante, and many other options.)
In Conclusion
Due to the constantly changing poker landscape, players are always improving their skills. Exploitable strategies often yield higher profit margins than GTO-based approaches, but knowing GTO beginner and advanced concepts can give you an edge for a few reasons.
It creates a solid gameplay base.
Having a baseline makes it easier to exploit certain villains.
You can avoid leveling wars with your opponents by making sound poker decisions based on GTO strategy.
It doesn't require assuming opponents' play styles.
Not results-oriented.
This is just the beginning of GTO and poker theory. Consider investing in the GTO poker solver software listed above to improve your game.

Pat Vieljeux
3 years ago
Your entrepreneurial experience can either be a beautiful adventure or a living hell with just one decision.
Choose.
DNA makes us distinct.
We act alike. Most people follow the same road, ignoring differences. We remain quiet about our uniqueness for fear of exclusion (family, social background, religion). We live a more or less imposed life.
Off the beaten path, we stand out from the others. We obey without realizing we're sewing a shroud. We're told to do as everyone else and spend 40 years dreaming of a golden retirement and regretting not living.
“One of the greatest regrets in life is being what others would want you to be, rather than being yourself.” - Shannon L. Alder
Others dare. Again, few are creative; most follow the example of those who establish a business for the sake of entrepreneurship. To live.
They pick a potential market and model their MVP on an existing solution. Most mimic others, alter a few things, appear to be original, and end up with bland products, adding to an already crowded market.
SaaS, PaaS, etc. followed suit. It's reduced pricing, profitability, and product lifespan.
As competitors become more aggressive, their profitability diminishes, making life horrible for them and their employees. They fail to innovate, cut costs, and close their company.
Few of them look happy and fulfilled.
How did they do it?
The answer is unsettlingly simple.
They are themselves.
They start their company, propelled at first by a passion or maybe a calling.
Then, at their own pace, they create it with the intention of resolving a dilemma.
They assess what others are doing and consider how they might improve it.
In contrast to them, they respond to it in their own way by adding a unique personal touch. Therefore, it is obvious.
Originals, like their DNA, can't be copied. Or if they are, they're poorly printed. Originals are unmatched. Artist-like. True collectors only buy Picasso paintings by the master, not forgeries, no matter how good.
Imaginative people are constantly ahead. Copycats fall behind unless they innovate. They watch their competition continuously. Their solution or product isn't sexy. They hope to cash in on their copied product by flooding the market.
They're mostly pirates. They're short-sighted, unlike creators.
Creators see further ahead and have no rivals. They use copiers to confirm a necessity. To maintain their individuality, creators avoid copying others. They find copying boring. It's boring. They oppose plagiarism.
It's thrilling and inspiring.
It will also make them more able to withstand their opponents' tension. Not to mention roadblocks. For creators, impediments are games.
Others fear it. They race against the clock and fear threats that could interrupt their momentum since they lack inventiveness and their product has a short life cycle.
Creators have time on their side. They're dedicated. Clearly. Passionate booksellers will have their own bookstore. Their passion shows in their book choices. Only the ones they love.
The copier wants to display as many as possible, including mediocre authors, and will cut costs. All this to dominate the market. They're digging their own grave.
The bookseller is just one example. I could give you tons of them.
Closing remarks
Entrepreneurs might follow others or be themselves. They risk exhaustion trying to predict what their followers will do.
It's true.
Life offers choices.
Being oneself or doing as others do, with the possibility of regretting not expressing our uniqueness and not having lived.
“Be yourself; everyone else is already taken”. Oscar Wilde
The choice is yours.
