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.

More on Gaming

Chris Moyse

3 years ago

Sony and LEGO raise $2 billion for Epic Games' metaverse

‘Kid-friendly’ project holds $32 billion valuation

Epic Games announced today that it has raised $2 billion USD from Sony Group Corporation and KIRKBI (holding company of The LEGO Group). Both companies contributed $1 billion to Epic Games' upcoming ‘metaverse' project.

“We need partners who share our vision as we reimagine entertainment and play. Our partnership with Sony and KIRKBI has found this,” said Epic Games CEO Tim Sweeney. A new metaverse will be built where players can have fun with friends and brands create creative and immersive experiences, as well as creators thrive.

Last week, LEGO and Epic Games announced their plans to create a family-friendly metaverse where kids can play, interact, and create in digital environments. The service's users' safety and security will be prioritized.

With this new round of funding, Epic Games' project is now valued at $32 billion.

“Epic Games is known for empowering creators large and small,” said KIRKBI CEO Sren Thorup Srensen. “We invest in trends that we believe will impact the world we and our children will live in. We are pleased to invest in Epic Games to support their continued growth journey, with a long-term focus on the future metaverse.”

Epic Games is expected to unveil its metaverse plans later this year, including its name, details, services, and release date.

Ash Parrish

3 years ago

Sonic Prime and indie games on Netflix

Netflix will stream Spiritfarer, Raji: An Ancient Epic, and Lucky Luna.

Netflix's Geeked Week brought a slew of announcements. The flurry of reveals for The Sandman, The Umbrella Academy season 3, One Piece, and more also included game and game-adjacent announcements.

Netflix released a teaser for Cuphead season 2 ahead of its August premiere, featuring more of Grey DeLisle's Ms. Chalice. DOTA: Dragon's Blood season 3 hits Netflix in August. Tekken, the fighting game that throws kids off cliffs, gets an anime, Tekken: Bloodline.

Netflix debuted a clip of Sonic Prime before Sonic Origins in June and Sonic Frontiers in 2022.

Castlevania: Nocturne will follow Richter Belmont.

Netflix is reviving licensed games with titles based on its shows. There's a Queen's Gambit chess game, a Shadow and Bone RPG, a La Casa de Papel heist adventure, and a Too Hot to Handle game where a pregnant woman must choose between stabbing her cheating ex or forgiving him.

Riot's rhythm platformer Hextech Mayhem debuted on Netflix last year, and now Netflix is adding games from Devolver Digital. Reigns: Three Kingdoms is a card game that lets players choose the fate of Three Kingdoms-era China by swiping left or right on cards. Spiritfarer, the "cozy game about death" from 2020, and Raji: An Ancient Epic are coming to Netflix. Poinpy, a vertical climber from the creator of Downwell, is now on Netflix.

Desta: The Memories Between is a turn-based strategy game set in dreams and memories.

Snowman's Lucky Luna will also be added soon.

With these games, Netflix is expanding beyond dinky mobile games — it plans to have 50 by the end of the year — and could be a serious platform for indies that want to expand into mobile. It takes gaming seriously.

Luke Plunkett

3 years ago

Gran Turismo 7 Update Eases Up On The Grind After Fan Outrage

Polyphony Digital has changed the game after apologizing in March.

To make amends for some disastrous downtime, Gran Turismo 7 director Kazunori Yamauchi announced a credits handout and promised to “dramatically change GT7's car economy to help make amends” last month. The first of these has arrived.

The game's 1.11 update includes the following concessions to players frustrated by the economy and its subsequent grind:

The last half of the World Circuits events have increased in-game credit rewards.
Modified Arcade and Custom Race rewards
Clearing all circuit layouts with Gold or Bronze now rewards In-game Credits. Exiting the Sector selection screen with the Exit button will award Credits if an event has already been cleared.
Increased Credits Rewards in Lobby and Daily Races
Increased the free in-game Credits cap from 20,000,000 to 100,000,000.

Additionally, “The Human Comedy” missions are one-hour endurance races that award “up to 1,200,000” credits per event.

This isn't everything Yamauchi promised last month; he said it would take several patches and updates to fully implement the changes. Here's a list of everything he said would happen, some of which have already happened (like the World Cup rewards and credit cap):

Increase rewards in the latter half of the World Circuits by roughly 100%.
Added high rewards for all Gold/Bronze results clearing the Circuit Experience.
Online Races rewards increase.
Add 8 new 1-hour Endurance Race events to Missions. So expect higher rewards.
Increase the non-paid credit limit in player wallets from 20M to 100M.
Expand the number of Used and Legend cars available at any time.
With time, we will increase the payout value of limited time rewards.
New World Circuit events.
Missions now include 24-hour endurance races.
Online Time Trials added, with rewards based on the player's time difference from the leader.
Make cars sellable.

The full list of updates and changes can be found here.

Read the original post.

Jari Roomer

3 years ago

After 240 articles and 2.5M views on Medium, 9 Raw Writing Tips

Late in 2018, I published my first Medium article, but I didn't start writing seriously until 2019. Since then, I've written more than 240 articles, earned over $50,000 through Medium's Partner Program, and had over 2.5 million page views.

Write A Lot

Most people don't have the patience and persistence for this simple writing secret:

Write + Write + Write = possible success

Writing more improves your skills.

The more articles you publish, the more likely one will go viral.

If you only publish once a month, you have no views. If you publish 10 or 20 articles a month, your success odds increase 10- or 20-fold.

Tim Denning, Ayodeji Awosika, Megan Holstein, and Zulie Rane. Medium is their jam. How are these authors alike? They're productive and consistent. They're prolific.

80% is publishable

Many writers battle perfectionism.

To succeed as a writer, you must publish often. You'll never publish if you aim for perfection.

Adopt the 80 percent-is-good-enough mindset to publish more. It sounds terrible, but it'll boost your writing success.

Your work won't be perfect. Always improve. Waiting for perfection before publishing will take a long time.

Second, readers are your true critics, not you. What you consider "not perfect" may be life-changing for the reader. Don't let perfectionism hinder the reader.

Don't let perfectionism hinder the reader. ou don't want to publish mediocre articles. When the article is 80% done, publish it. Don't spend hours editing. Realize it. Get feedback. Only this will work.

Make Your Headline Irresistible

We all judge books by their covers, despite the saying. And headlines. Readers, including yourself, judge articles by their titles. We use it to decide if an article is worth reading.

Make your headlines irresistible. Want more article views? Then, whether you like it or not, write an attractive article title.

Many high-quality articles are collecting dust because of dull, vague headlines. It didn't make the reader click.

As a writer, you must do more than produce quality content. You must also make people click on your article. This is a writer's job. How to create irresistible headlines:

Curiosity makes readers click. Here's a tempting example...

Example: What Women Actually Look For in a Guy, According to a Huge Study by Luba Sigaud

Use Numbers: Click-bait lists. I mean, which article would you click first? ‘Some ways to improve your productivity’ or ’17 ways to improve your productivity.’ Which would I click?

Example: 9 Uncomfortable Truths You Should Accept Early in Life by Sinem Günel

Most headlines are dull. If you want clicks, get 'sexy'. Buzzword-ify. Invoke emotion. Trendy words.

Example: 20 Realistic Micro-Habits To Live Better Every Day by Amardeep Parmar

Concise paragraphs

Our culture lacks focus. If your headline gets a click, keep paragraphs short to keep readers' attention.

Some writers use 6–8 lines per paragraph, but I prefer 3–4. Longer paragraphs lose readers' interest.

A writer should help the reader finish an article, in my opinion. I consider it a job requirement. You can't force readers to finish an article, but you can make it 'snackable'

Help readers finish an article with concise paragraphs, interesting subheadings, exciting images, clever formatting, or bold attention grabbers.

Work And Move On

I've learned over the years not to get too attached to my articles. Many writers report a strange phenomenon:

The articles you're most excited about usually bomb, while the ones you're not tend to do well.

This isn't always true, but I've noticed it in my own writing. My hopes for an article usually make it worse. The more objective I am, the better an article does.

Let go of a finished article. 40 or 40,000 views, whatever. Now let the article do its job. Onward. Next story. Start another project.

Disregard Haters

Online content creators will encounter haters, whether on YouTube, Instagram, or Medium. More views equal more haters. Fun, right?

As a web content creator, I learned:

Don't debate haters. Never.

It's a mistake I've made several times. It's tempting to prove haters wrong, but they'll always find a way to be 'right'. Your response is their fuel.

I smile and ignore hateful comments. I'm indifferent. I won't enter a negative environment. I have goals, money, and a life to build. "I'm not paid to argue," Drake once said.

Use Grammarly

Grammarly saves me as a non-native English speaker. You know Grammarly. It shows writing errors and makes article suggestions.

As a writer, you need Grammarly. I have a paid plan, but their free version works. It improved my writing greatly.

Put The Reader First, Not Yourself

Many writers write for themselves. They focus on themselves rather than the reader.

Ask yourself:

This article teaches what? How can they be entertained or educated?

Personal examples and experiences improve writing quality. Don't focus on yourself.

It's not about you, the content creator. Reader-focused. Putting the reader first will change things.

Extreme ownership: Stop blaming others

I remember writing a lot on Medium but not getting many views. I blamed Medium first. Poor algorithm. Poor publishing. All sucked.

Instead of looking at what I could do better, I blamed others.

When you blame others, you lose power. Owning your results gives you power.

As a content creator, you must take full responsibility. Extreme ownership means 100% responsibility for work and results.

You don’t blame others. You don't blame the economy, president, platform, founders, or audience. Instead, you look for ways to improve. Few people can do this.

Blaming is useless. Zero. Taking ownership of your work and results will help you progress. It makes you smarter, better, and stronger.

Instead of blaming others, you'll learn writing, marketing, copywriting, content creation, productivity, and other skills. Game-changer.

Ajay Shrestha

2 years ago

Bitcoin's technical innovation: addressing the issue of the Byzantine generals

The 2008 Bitcoin white paper solves the classic computer science consensus problem.

Figure 1: Illustration of the Byzantine Generals problem by Lord Belbury, CC BY-SA 4.0 / Source

Issue Statement

The Byzantine Generals Problem (BGP) is called after an allegory in which several generals must collaborate and attack a city at the same time to win (figure 1-left). Any general who retreats at the last minute loses the fight (figure 1-right). Thus, precise messengers and no rogue generals are essential. This is difficult without a trusted central authority.

In their 1982 publication, Leslie Lamport, Robert Shostak, and Marshall Please termed this topic the Byzantine Generals Problem to simplify distributed computer systems.

Consensus in a distributed computer network is the issue. Reaching a consensus on which systems work (and stay in the network) and which don't makes maintaining a network tough (i.e., needs to be removed from network). Challenges include unreliable communication routes between systems and mis-reporting systems.

Solving BGP can let us construct machine learning solutions without single points of failure or trusted central entities. One server hosts model parameters while numerous workers train the model. This study describes fault-tolerant Distributed Byzantine Machine Learning.

Bitcoin invented a mechanism for a distributed network of nodes to agree on which transactions should go into the distributed ledger (blockchain) without a trusted central body. It solved BGP implementation. Satoshi Nakamoto, the pseudonymous bitcoin creator, solved the challenge by cleverly combining cryptography and consensus mechanisms.

Disclaimer

This is not financial advice. It discusses a unique computer science solution.

Bitcoin

Bitcoin's white paper begins:

“A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.” Source: https://www.ussc.gov/sites/default/files/pdf/training/annual-national-training-seminar/2018/Emerging_Tech_Bitcoin_Crypto.pdf

Bitcoin's main parts:

The open-source and versioned bitcoin software that governs how nodes, miners, and the bitcoin token operate.
The native kind of token, known as a bitcoin token, may be created by mining (up to 21 million can be created), and it can be transferred between wallet addresses in the bitcoin network.
Distributed Ledger, which contains exact copies of the database (or "blockchain") containing each transaction since the first one in January 2009.
distributed network of nodes (computers) running the distributed ledger replica together with the bitcoin software. They broadcast the transactions to other peer nodes after validating and accepting them.
Proof of work (PoW) is a cryptographic requirement that must be met in order for a miner to be granted permission to add a new block of transactions to the blockchain of the cryptocurrency bitcoin. It takes the form of a valid hash digest. In order to produce new blocks on average every 10 minutes, Bitcoin features a built-in difficulty adjustment function that modifies the valid hash requirement (length of nonce). PoW requires a lot of energy since it must continually generate new hashes at random until it satisfies the criteria.
The competing parties known as miners carry out continuous computing processing to address recurrent cryptography issues. Transaction fees and some freshly minted (mined) bitcoin are the rewards they receive. The amount of hashes produced each second—or hash rate—is a measure of mining capacity.

Cryptography, decentralization, and the proof-of-work consensus method are Bitcoin's most unique features.

Bitcoin uses encryption

Bitcoin employs this established cryptography.

Hashing
digital signatures based on asymmetric encryption

Hashing (SHA-256) (SHA-256)

Figure 2: SHA-256 Hash operation on Block Header’s Hash + nonce

Hashing converts unique plaintext data into a digest. Creating the plaintext from the digest is impossible. Bitcoin miners generate new hashes using SHA-256 to win block rewards.

A new hash is created from the current block header and a variable value called nonce. To achieve the required hash, mining involves altering the nonce and re-hashing.

The block header contains the previous block hash and a Merkle root, which contains hashes of all transactions in the block. Thus, a chain of blocks with increasing hashes links back to the first block. Hashing protects new transactions and makes the bitcoin blockchain immutable. After a transaction block is mined, it becomes hard to fabricate even a little entry.

Asymmetric Cryptography Digital Signatures

Figure 3: Transaction signing and verifying process with asymmetric encryption and hashing operations

Asymmetric cryptography (public-key encryption) requires each side to have a secret and public key. Public keys (wallet addresses) can be shared with the transaction party, but private keys should not. A message (e.g., bitcoin payment record) can only be signed by the owner (sender) with the private key, but any node or anybody with access to the public key (visible in the blockchain) can verify it. Alex will submit a digitally signed transaction with a desired amount of bitcoin addressed to Bob's wallet to a node to send bitcoin to Bob. Alex alone has the secret keys to authorize that amount. Alex's blockchain public key allows anyone to verify the transaction.

Solution

Now, apply bitcoin to BGP. BGP generals resemble bitcoin nodes. The generals' consensus is like bitcoin nodes' blockchain block selection. Bitcoin software on all nodes can:

Check transactions (i.e., validate digital signatures)

2. Accept and propagate just the first miner to receive the valid hash and verify it accomplished the task. The only way to guess the proper hash is to brute force it by repeatedly producing one with the fixed/current block header and a fresh nonce value.

Thus, PoW and a dispersed network of nodes that accept blocks from miners that solve the unfalsifiable cryptographic challenge solve consensus.

Suppose:

Unreliable nodes
Unreliable miners

Bitcoin accepts the longest chain if rogue nodes cause divergence in accepted blocks. Thus, rogue nodes must outnumber honest nodes in accepting/forming the longer chain for invalid transactions to reach the blockchain. As of November 2022, 7000 coordinated rogue nodes are needed to takeover the bitcoin network.

Dishonest miners could also try to insert blocks with falsified transactions (double spend, reverse, censor, etc.) into the chain. This requires over 50% (51% attack) of miners (total computational power) to outguess the hash and attack the network. Mining hash rate exceeds 200 million (source). Rewards and transaction fees encourage miners to cooperate rather than attack. Quantum computers may become a threat.

Visit my Quantum Computing post.

Quantum computers—what are they? Quantum computers will have a big influence. towardsdatascience.com

Nodes have more power than miners since they can validate transactions and reject fake blocks. Thus, the network is secure if honest nodes are the majority.

Summary

Table 1 compares three Byzantine Generals Problem implementations.

Table 1: Comparison of Byzantine Generals Problem implementations

Bitcoin white paper and implementation solved the consensus challenge of distributed systems without central governance. It solved the illusive Byzantine Generals Problem.

Resources

https://en.wikipedia.org/wiki/Byzantine_fault
Source-code for Bitcoin Core Software — https://github.com/bitcoin/bitcoin
Bitcoin white paper — https://bitcoin.org/bitcoin.pdf
https://en.wikipedia.org/wiki/Bitcoin
https://www.microsoft.com/en-us/research/publication/byzantine-generals-problem/
https://www.microsoft.com/en-us/research/uploads/prod/2016/12/The-Byzantine-Generals-Problem.pdf
https://en.wikipedia.org/wiki/Hash_function
https://en.wikipedia.org/wiki/Merkle_tree
https://en.wikipedia.org/wiki/SHA-2
https://en.wikipedia.org/wiki/Public-key_cryptography
https://en.wikipedia.org/wiki/Digital_signature
https://en.wikipedia.org/wiki/Proof_of_work
https://en.wikipedia.org/wiki/Quantum_cryptography
https://dci.mit.edu/bitcoin-security-initiative
https://dci.mit.edu/51-attacks
Genuinely Distributed Byzantine Machine Learning, El-Mahdi El-Mhamdi et al., 2020. ACM, New York, NY, https://doi.org/10.1145/3382734.3405695

JEFF JOHN ROBERTS

3 years ago

What just happened in cryptocurrency? A plain-English Q&A about Binance's FTX takedown.

Crypto people have witnessed things. They've seen big hacks, mind-boggling swindles, and amazing successes. They've never seen a day like Tuesday, when the world's largest crypto exchange murdered its closest competition.

Here's a primer on Binance and FTX's lunacy and why it matters if you're new to crypto.

What happened?

CZ, a shrewd Chinese-Canadian billionaire, runs Binance. FTX, a newcomer, has challenged Binance in recent years. SBF (Sam Bankman-Fried)—a young American with wild hair—founded FTX (initials are a thing in crypto).

Last weekend, CZ complained about SBF's lobbying and then exploited Binance's market power to attack his competition.

How did CZ do that?

CZ invested in SBF's new cryptocurrency exchange when they were friends. CZ sold his investment in FTX for FTT when he no longer wanted it. FTX clients utilize those tokens to get trade discounts, although they are less liquid than Bitcoin.

SBF made a mistake by providing CZ just too many FTT tokens, giving him control over FTX. It's like Pepsi handing Coca-Cola a lot of stock it could sell at any time. CZ got upset with SBF and flooded the market with FTT tokens.

SBF owns a trading fund with many FTT tokens, therefore this was catastrophic. SBF sought to defend FTT's worth by selling other assets to buy up the FTT tokens flooding the market, but it didn't succeed, and as FTT's value plummeted, his liabilities exceeded his assets. By Tuesday, his companies were insolvent, so he sold them to his competition.

Crazy. How could CZ do that?

CZ likely did this to crush a rising competition. It was also personal. In recent months, regulators have been tough toward the crypto business, and Binance and FTX have been trying to stay on their good side. CZ believed SBF was poisoning U.S. authorities by saying CZ was linked to China, so CZ took retribution.

“We supported previously, but we won't pretend to make love after divorce. We're neutral. But we won't assist people that push against other industry players behind their backs," CZ stated in a tragic tweet on Sunday. He crushed his rival's company two days later.

So does Binance now own FTX?

No. Not yet. CZ has only stated that Binance signed a "letter of intent" to acquire FTX. CZ and SBF say Binance will protect FTX consumers' funds.

Who’s to blame?

You could blame CZ for using his control over FTX to destroy it. SBF is also being criticized for not disclosing the full overlap between FTX and his trading company, which controlled plenty of FTT. If he had been upfront, someone might have warned FTX about this vulnerability earlier, preventing this mess.

Others have alleged that SBF utilized customer monies to patch flaws in his enterprises' balance accounts. That happened to multiple crypto startups that collapsed this spring, which is unfortunate. These are allegations, not proof.

Why does this matter? Isn't this common in crypto?

Crypto is notorious for shady executives and pranks. FTX is the second-largest crypto business, and SBF was largely considered as the industry's golden boy who would help it get on authorities' good side. Thus far.

Does this affect cryptocurrency prices?

Short-term, it's bad. Prices fell on suspicions that FTX was in peril, then rallied when Binance rescued it, only to fall again later on Tuesday.

These occurrences have hurt FTT and SBF's Solana token. It appears like a huge token selloff is affecting the rest of the market. Bitcoin fell 10% and Ethereum 15%, which is bad but not catastrophic for the two largest coins by market cap.

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Issue Statement

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What just happened in cryptocurrency? A plain-English Q&A about Binance's FTX takedown.

What happened?

How did CZ do that?

Crazy. How could CZ do that?

So does Binance now own FTX?

Who’s to blame?

Why does this matter? Isn't this common in crypto?

Does this affect cryptocurrency prices?