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Alex Bentley

Alex Bentley

3 years ago

Why Bill Gates thinks Bitcoin, crypto, and NFTs are foolish

More on Web3 & Crypto

CNET

CNET

3 years ago

How a $300K Bored Ape Yacht Club NFT was accidentally sold for $3K

The Bored Ape Yacht Club is one of the most prestigious NFT collections in the world. A collection of 10,000 NFTs, each depicting an ape with different traits and visual attributes, Jimmy Fallon, Steph Curry and Post Malone are among their star-studded owners. Right now the price of entry is 52 ether, or $210,000.

Which is why it's so painful to see that someone accidentally sold their Bored Ape NFT for $3,066.

Unusual trades are often a sign of funny business, as in the case of the person who spent $530 million to buy an NFT from themselves. In Saturday's case, the cause was a simple, devastating "fat-finger error." That's when people make a trade online for the wrong thing, or for the wrong amount. Here the owner, real name Max or username maxnaut, meant to list his Bored Ape for 75 ether, or around $300,000. Instead he accidentally listed it for 0.75. One hundredth the intended price.

It was bought instantaneously. The buyer paid an extra $34,000 to speed up the transaction, ensuring no one could snap it up before them. The Bored Ape was then promptly listed for $248,000. The transaction appears to have been done by a bot, which can be coded to immediately buy NFTs listed below a certain price on behalf of their owners in order to take advantage of these exact situations.

"How'd it happen? A lapse of concentration I guess," Max told me. "I list a lot of items every day and just wasn't paying attention properly. I instantly saw the error as my finger clicked the mouse but a bot sent a transaction with over 8 eth [$34,000] of gas fees so it was instantly sniped before I could click cancel, and just like that, $250k was gone."

"And here within the beauty of the Blockchain you can see that it is both honest and unforgiving," he added.

Fat finger trades happen sporadically in traditional finance -- like the Japanese trader who almost bought 57% of Toyota's stock in 2014 -- but most financial institutions will stop those transactions if alerted quickly enough. Since cryptocurrency and NFTs are designed to be decentralized, you essentially have to rely on the goodwill of the buyer to reverse the transaction.

Fat finger errors in cryptocurrency trades have made many a headline over the past few years. Back in 2019, the company behind Tether, a cryptocurrency pegged to the US dollar, nearly doubled its own coin supply when it accidentally created $5 billion-worth of new coins. In March, BlockFi meant to send 700 Gemini Dollars to a set of customers, worth roughly $1 each, but mistakenly sent out millions of dollars worth of bitcoin instead. Last month a company erroneously paid a $24 million fee on a $100,000 transaction.

Similar incidents are increasingly being seen in NFTs, now that many collections have accumulated in market value over the past year. Last month someone tried selling a CryptoPunk NFT for $19 million, but accidentally listed it for $19,000 instead. Back in August, someone fat finger listed their Bored Ape for $26,000, an error that someone else immediately capitalized on. The original owner offered $50,000 to the buyer to return the Bored Ape -- but instead the opportunistic buyer sold it for the then-market price of $150,000.

"The industry is so new, bad things are going to happen whether it's your fault or the tech," Max said. "Once you no longer have control of the outcome, forget and move on."

The Bored Ape Yacht Club launched back in April 2021, with 10,000 NFTs being sold for 0.08 ether each -- about $190 at the time. While NFTs are often associated with individual digital art pieces, collections like the Bored Ape Yacht Club, which allow owners to flaunt their NFTs by using them as profile pictures on social media, are becoming increasingly prevalent. The Bored Ape Yacht Club has since become the second biggest NFT collection in the world, second only to CryptoPunks, which launched in 2017 and is considered the "original" NFT collection.

Vitalik

Vitalik

3 years ago

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:

  1. 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
  2. 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

Langston Thomas

3 years ago

A Simple Guide to NFT Blockchains

Ethereum's blockchain rules NFTs. Many consider it the one-stop shop for NFTs, and it's become the most talked-about and trafficked blockchain in existence.

Other blockchains are becoming popular in NFTs. Crypto-artists and NFT enthusiasts have sought new places to mint and trade NFTs due to Ethereum's high transaction costs and environmental impact.

When choosing a blockchain to mint on, there are several factors to consider. Size, creator costs, consumer spending habits, security, and community input are important. We've created a high-level summary of blockchains for NFTs to help clarify the fast-paced world of web3 tech.

Ethereum

Ethereum currently has the most NFTs. It's decentralized and provides financial and legal services without intermediaries. It houses popular NFT marketplaces (OpenSea), projects (CryptoPunks and the Bored Ape Yacht Club), and artists (Pak and Beeple).

It's also expensive and energy-intensive. This is because Ethereum works using a Proof-of-Work (PoW) mechanism. PoW requires computers to solve puzzles to add blocks and transactions to the blockchain. Solving these puzzles requires a lot of computer power, resulting in astronomical energy loss.

You should consider this blockchain first due to its popularity, security, decentralization, and ease of use.

Solana

Solana is a fast programmable blockchain. Its proof-of-history and proof-of-stake (PoS) consensus mechanisms eliminate complex puzzles. Reduced validation times and fees result.

PoS users stake their cryptocurrency to become a block validator. Validators get SOL. This encourages and rewards users to become stakers. PoH works with PoS to cryptographically verify time between events. Solana blockchain ensures transactions are in order and found by the correct leader (validator).

Solana's PoS and PoH mechanisms keep transaction fees and times low. Solana isn't as popular as Ethereum, so there are fewer NFT marketplaces and blockchain traders.

Tezos

Tezos is a greener blockchain. Tezos rose in 2021. Hic et Nunc was hailed as an economic alternative to Ethereum-centric marketplaces until Nov. 14, 2021.

Similar to Solana, Tezos uses a PoS consensus mechanism and only a PoS mechanism to reduce computational work. This blockchain uses two million times less energy than Ethereum. It's cheaper than Ethereum (but does cost more than Solana).

Tezos is a good place to start minting NFTs in bulk. Objkt is the largest Tezos marketplace.

Flow

Flow is a high-performance blockchain for NFTs, games, and decentralized apps (dApps). Flow is built with scalability in mind, so billions of people could interact with NFTs on the blockchain.

Flow became the NBA's blockchain partner in 2019. Flow, a product of Dapper labs (the team behind CryptoKitties), launched and hosts NBA Top Shot, making the blockchain integral to the popularity of non-fungible tokens.

Flow uses PoS to verify transactions, like Tezos. Developers are working on a model to handle 10,000 transactions per second on the blockchain. Low transaction fees.

Flow NFTs are tradeable on Blocktobay, OpenSea, Rarible, Foundation, and other platforms. NBA, NFL, UFC, and others have launched NFT marketplaces on Flow. Flow isn't as popular as Ethereum, resulting in fewer NFT marketplaces and blockchain traders.

Asset Exchange (WAX)

WAX is king of virtual collectibles. WAX is popular for digitalized versions of legacy collectibles like trading cards, figurines, memorabilia, etc.

Wax uses a PoS mechanism, but also creates carbon offset NFTs and partners with Climate Care. Like Flow, WAX transaction fees are low, and network fees are redistributed to the WAX community as an incentive to collectors.

WAX marketplaces host Topps, NASCAR, Hot Wheels, and cult classic film franchises like Godzilla, The Princess Bride, and Spiderman.

Binance Smart Chain

BSC is another good option for balancing fees and performance. High-speed transactions and low fees hurt decentralization. BSC is most centralized.

Binance Smart Chain uses Proof of Staked Authority (PoSA) to support a short block time and low fees. The 21 validators needed to run the exchange switch every 24 hours. 11 of the 21 validators are directly connected to the Binance Crypto Exchange, according to reports.

While many in the crypto and NFT ecosystems dislike centralization, the BSC NFT market picked up speed in 2021. OpenBiSea, AirNFTs, JuggerWorld, and others are gaining popularity despite not having as robust an ecosystem as Ethereum.

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Katrina Paulson

Katrina Paulson

3 years ago

Dehumanization Against Anthropomorphization

We've fought for humanity's sake. We need equilibrium.

Photo by Bekah Russom on Unsplash

We live in a world of opposites (black/white, up/down, love/hate), thus life is a game of achieving equilibrium. We have a universe of paradoxes within ourselves, not just in physics.

Individually, you balance your intellect and heart, but as a species, we're full of polarities. They might be gentle and compassionate, then ruthless and unsympathetic.

We desire for connection so much that we personify non-human beings and objects while turning to violence and hatred toward others. These contrasts baffle me. Will we find balance?

Anthropomorphization

Assigning human-like features or bonding with objects is common throughout childhood. Cartoons often give non-humans human traits. Adults still anthropomorphize this trait. Researchers agree we start doing it as infants and continue throughout life.

Humans of all ages are good at humanizing stuff. We build emotional attachments to weather events, inanimate objects, animals, plants, and locales. Gods, goddesses, and fictitious figures are anthropomorphized.

Cast Away, starring Tom Hanks, features anthropization. Hanks is left on an island, where he builds an emotional bond with a volleyball he calls Wilson.

We became emotionally invested in Wilson, including myself.

Why do we do it, though?

Our instincts and traits helped us survive and thrive. Our brain is alert to other people's thoughts, feelings, and intentions to assist us to determine who is safe or hazardous. We can think about others and our own mental states, or about thinking. This is the Theory of Mind.

Neurologically, specialists believe the Theory of Mind has to do with our mirror neurons, which exhibit the same activity while executing or witnessing an action.

Mirror neurons may contribute to anthropization, but they're not the only ones. In 2021, Harvard Medical School researchers at MGH and MIT colleagues published a study on the brain's notion of mind.

“Our study provides evidence to support theory of mind by individual neurons. Until now, it wasn’t clear whether or how neurons were able to perform these social cognitive computations.”

Neurons have particular functions, researchers found. Others encode information that differentiates one person's beliefs from another's. Some neurons reflect tale pieces, whereas others aren't directly involved in social reasoning but may multitask contributing factors.

Combining neuronal data gives a precise portrait of another's beliefs and comprehension. The theory of mind describes how we judge and understand each other in our species, and it likely led to anthropomorphism. Neuroscience indicates identical brain regions react to human or non-human behavior, like mirror neurons.

Some academics believe we're wired for connection, which explains why we anthropomorphize. When we're alone, we may anthropomorphize non-humans.

Humanizing non-human entities may make them deserving of moral care, according to another theory. Animamorphizing something makes it responsible for its actions and deserves punishments or rewards. This mental shift is typically apparent in our connections with pets and leads to deanthropomorphization.

Dehumanization

Dehumanizing involves denying someone or anything ethical regard, the opposite of anthropomorphizing.

Dehumanization occurs throughout history. We do it to everything in nature, including ourselves. We experiment on and torture animals. We enslave, hate, and harm other groups of people.

Race, immigrant status, dress choices, sexual orientation, social class, religion, gender, politics, need I go on? Our degrading behavior is promoting fascism and division everywhere.

Dehumanizing someone or anything reduces their agency and value. Many assume they're immune to this feature, but tests disagree.

It's inevitable. Humans are wired to have knee-jerk reactions to differences. We are programmed to dehumanize others, and it's easier than we'd like to admit.

Why do we do it, though?

Dehumanizing others is simpler than humanizing things for several reasons. First, we consider everything unusual as harmful, which has helped our species survive for hundreds of millions of years. Our propensity to be distrustful of others, like our fear of the unknown, promotes an us-vs.-them mentality.

Since WWII, various studies have been done to explain how or why the holocaust happened. How did so many individuals become radicalized to commit such awful actions and feel morally justified? Researchers quickly showed how easily the mind can turn gloomy.

Stanley Milgram's 1960s electroshock experiment highlighted how quickly people bow to authority to injure others. Philip Zimbardo's 1971 Stanford Prison Experiment revealed how power may be abused.

The us-versus-them attitude is natural and even young toddlers act on it. Without a relationship, empathy is more difficult.

It's terrifying how quickly dehumanizing behavior becomes commonplace. The current pandemic is an example. Most countries no longer count deaths. Long Covid is a major issue, with predictions of a handicapped tsunami in the future years. Mostly, we shrug.

In 2020, we panicked. Remember everyone's caution? Now Long Covid is ruining more lives, threatening to disable an insane amount of our population for months or their entire lives.

There's little research. Experts can't even classify or cure it. The people should be outraged, but most have ceased caring. They're over covid.

We're encouraged to find a method to live with a terrible pandemic that will cause years of damage. People aren't worried about infection anymore. They shrug and say, "We'll all get it eventually," then hope they're not one of the 30% who develops Long Covid.

We can correct course before further damage. Because we can recognize our urges and biases, we're not captives to them. We can think critically about our thoughts and behaviors, then attempt to improve. We can recognize our deficiencies and work to attain balance.

Changing perspectives

We're currently attempting to find equilibrium between opposites. It's superficial to defend extremes by stating we're only human or wired this way because both imply we have no control.

Being human involves having self-awareness, and by being careful of our thoughts and acts, we can find balance and recognize opposites' purpose.

Extreme anthropomorphizing and dehumanizing isolate and imperil us. We anthropomorphize because we desire connection and dehumanize because we're terrified, frequently of the connection we crave. Will we find balance?

Katrina Paulson ponders humanity, unanswered questions, and discoveries. Please check out her newsletters, Curious Adventure and Curious Life.

Daniel Clery

3 years ago

Twisted device investigates fusion alternatives

German stellarator revamped to run longer, hotter, compete with tokamaks

Wendelstein 7-X’s complex geometry was a nightmare to build but, when fired up, worked from the start.

Tokamaks have dominated the search for fusion energy for decades. Just as ITER, the world's largest and most expensive tokamak, nears completion in southern France, a smaller, twistier testbed will start up in Germany.

If the 16-meter-wide stellarator can match or outperform similar-size tokamaks, fusion experts may rethink their future. Stellarators can keep their superhot gases stable enough to fuse nuclei and produce energy. They can theoretically run forever, but tokamaks must pause to reset their magnet coils.

The €1 billion German machine, Wendelstein 7-X (W7-X), is already getting "tokamak-like performance" in short runs, claims plasma physicist David Gates, preventing particles and heat from escaping the superhot gas. If W7-X can go long, "it will be ahead," he says. "Stellarators excel" Eindhoven University of Technology theorist Josefine Proll says, "Stellarators are back in the game." A few of startup companies, including one that Gates is leaving Princeton Plasma Physics Laboratory, are developing their own stellarators.

W7-X has been running at the Max Planck Institute for Plasma Physics (IPP) in Greifswald, Germany, since 2015, albeit only at low power and for brief runs. W7-X's developers took it down and replaced all inner walls and fittings with water-cooled equivalents, allowing for longer, hotter runs. The team reported at a W7-X board meeting last week that the revised plasma vessel has no leaks. It's expected to restart later this month to show if it can get plasma to fusion-igniting conditions.

Wendelstein 7-X’s twisting inner surface is now water cooled, enabling longer runs

Wendelstein 7-X's water-cooled inner surface allows for longer runs.

HOSAN/IPP

Both stellarators and tokamaks create magnetic gas cages hot enough to melt metal. Microwaves or particle beams heat. Extreme temperatures create a plasma, a seething mix of separated nuclei and electrons, and cause the nuclei to fuse, releasing energy. A fusion power plant would use deuterium and tritium, which react quickly. Non-energy-generating research machines like W7-X avoid tritium and use hydrogen or deuterium instead.

Tokamaks and stellarators use electromagnetic coils to create plasma-confining magnetic fields. A greater field near the hole causes plasma to drift to the reactor's wall.

Tokamaks control drift by circulating plasma around a ring. Streaming creates a magnetic field that twists and stabilizes ionized plasma. Stellarators employ magnetic coils to twist, not plasma. Once plasma physicists got powerful enough supercomputers, they could optimize stellarator magnets to improve plasma confinement.

W7-X is the first large, optimized stellarator with 50 6- ton superconducting coils. Its construction began in the mid-1990s and cost roughly twice the €550 million originally budgeted.

The wait hasn't disappointed researchers. W7-X director Thomas Klinger: "The machine operated immediately." "It's a friendly machine." It did everything we asked." Tokamaks are prone to "instabilities" (plasma bulging or wobbling) or strong "disruptions," sometimes associated to halted plasma flow. IPP theorist Sophia Henneberg believes stellarators don't employ plasma current, which "removes an entire branch" of instabilities.

In early stellarators, the magnetic field geometry drove slower particles to follow banana-shaped orbits until they collided with other particles and leaked energy. Gates believes W7-X's ability to suppress this effect implies its optimization works.

W7-X loses heat through different forms of turbulence, which push particles toward the wall. Theorists have only lately mastered simulating turbulence. W7-X's forthcoming campaign will test simulations and turbulence-fighting techniques.

A stellarator can run constantly, unlike a tokamak, which pulses. W7-X has run 100 seconds—long by tokamak standards—at low power. The device's uncooled microwave and particle heating systems only produced 11.5 megawatts. The update doubles heating power. High temperature, high plasma density, and extensive runs will test stellarators' fusion power potential. Klinger wants to heat ions to 50 million degrees Celsius for 100 seconds. That would make W7-X "a world-class machine," he argues. The team will push for 30 minutes. "We'll move step-by-step," he says.

W7-X's success has inspired VCs to finance entrepreneurs creating commercial stellarators. Startups must simplify magnet production.

Princeton Stellarators, created by Gates and colleagues this year, has $3 million to build a prototype reactor without W7-X's twisted magnet coils. Instead, it will use a mosaic of 1000 HTS square coils on the plasma vessel's outside. By adjusting each coil's magnetic field, operators can change the applied field's form. Gates: "It moves coil complexity to the control system." The company intends to construct a reactor that can fuse cheap, abundant deuterium to produce neutrons for radioisotopes. If successful, the company will build a reactor.

Renaissance Fusion, situated in Grenoble, France, raised €16 million and wants to coat plasma vessel segments in HTS. Using a laser, engineers will burn off superconductor tracks to carve magnet coils. They want to build a meter-long test segment in 2 years and a full prototype by 2027.

Type One Energy in Madison, Wisconsin, won DOE money to bend HTS cables for stellarator magnets. The business carved twisting grooves in metal with computer-controlled etching equipment to coil cables. David Anderson of the University of Wisconsin, Madison, claims advanced manufacturing technology enables the stellarator.

Anderson said W7-X's next phase will boost stellarator work. “Half-hour discharges are steady-state,” he says. “This is a big deal.”

Matthew Cluff

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.