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

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.

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.

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.

Cody Collins

3 years ago

The direction of the economy is as follows.

What quarterly bank earnings reveal

Big banks know the economy best. Unless we’re talking about a housing crisis in 2007…

Banks are crucial to the U.S. economy. The Fed, communities, and investments exchange money.

An economy depends on money flow. Banks' views on the economy can affect their decision-making.

Most large banks released quarterly earnings and forward guidance last week. Others were pessimistic about the future.

What Makes Banks Confident

Bank of America's profit decreased 30% year-over-year, but they're optimistic about the economy. Comparatively, they're bullish.

Who banks serve affects what they see. Bank of America supports customers.

They think consumers' future is bright. They believe this for many reasons.

The average customer has decent credit, unless the system is flawed. Bank of America's new credit card and mortgage borrowers averaged 771. New-car loan and home equity borrower averages were 791 and 797.

2008's housing crisis affected people with scores below 620.

Bank of America and the economy benefit from a robust consumer. Major problems can be avoided if individuals maintain spending.

Reasons Other Banks Are Less Confident

Spending requires income. Many companies, mostly in the computer industry, have announced they will slow or freeze hiring. Layoffs are frequently an indication of poor times ahead.

BOA is positive, but investment banks are bearish.

Jamie Dimon, CEO of JPMorgan, outlined various difficulties our economy could confront.

But geopolitical tension, high inflation, waning consumer confidence, the uncertainty about how high rates have to go and the never-before-seen quantitative tightening and their effects on global liquidity, combined with the war in Ukraine and its harmful effect on global energy and food prices are very likely to have negative consequences on the global economy sometime down the road.

That's more headwinds than tailwinds.

JPMorgan, which helps with mergers and IPOs, is less enthusiastic due to these concerns. Incoming headwinds signal drying liquidity, they say. Less business will be done.

Final Reflections

I don't think we're done. Yes, stocks are up 10% from a month ago. It's a long way from old highs.

I don't think the stock market is a strong economic indicator.

Many executives foresee a 2023 recession. According to the traditional definition, we may be in a recession when Q2 GDP statistics are released next week.

Regardless of criteria, I predict the economy will have a terrible year.

Weekly layoffs are announced. Inflation persists. Will prices return to 2020 levels if inflation cools? Perhaps. Still expensive energy. Ukraine's war has global repercussions.

I predict BOA's next quarter earnings won't be as bullish about the consumer's strength.

Evgenii Nelepko

3 years ago

My 3 biggest errors as a co-founder and CEO

Reflections on the closed company Hola! Dating app

I'll discuss my fuckups as an entrepreneur and CEO. All of them refer to the dating app Hola!, which I co-founded and starred in.

Spring 2021 was when we started. Two techies and two non-techies created a dating app. Pokemon Go and Tinder were combined.

Online dating is a business, and it takes two weeks from a like to a date. We questioned online dating app users if they met anyone offline last year.

75% replied yes, 50% sometimes, 25% usually.

Offline dating is popular, yet people have concerns.

Men are reluctant to make mistakes in front of others.
Women are curious about the background of everyone who approaches them.

We designed unique mechanics that let people date after a match. No endless chitchat. Women would be safe while men felt like cowboys.

I wish to emphasize three faults that lead to founders' estrangement.

This detachment ultimately led to us shutting down the company.

The wrong technology stack

Situation

Instead of generating a faster MVP and designing an app in a universal stack for iOS and Android, I argued we should pilot the app separately for iOS and Android. Technical founders' expertise made this possible.

Self-reflection

Mistaken strategy. We lost time and resources developing two apps at once. We chose iOS since it's more profitable. Apple took us out after the release, citing Guideline 4.3 Spam. After 4 months, we had nothing. We had a long way to go to get the app on Android and the Store.

I suggested creating a uniform platform for the company's growth. This makes parallel product development easier. The strategist's lack of experience and knowledge made it a piece of crap.

What would I have changed if I could?

We should have designed an Android universal stack. I expected Apple to have issues with a dating app.

Our approach should have been to launch something and subsequently improve it, but prejudice won.

The lesson

Discuss the IT stack with your CTO. It saves time and money. Choose the easiest MVP method.

2. A tardy search for investments

Situation

Though the universe and other founders encouraged me to locate investors first, I started pitching when we almost had an app.

When angels arrived, it was time to close. The app was banned, war broke out, I left the country, and the other co-founders stayed. We had no savings.

Self-reflection

I loved interviewing users. I'm proud of having done 1,000 interviews. I wanted to understand people's pain points and improve the product.

Interview results no longer affected the product. I was terrified to start pitching. I filled out accelerator applications and redid my presentation. You must go through that so you won't be terrified later.

What would I have changed if I could?

Get an external or internal mentor to help me with my first pitch as soon as possible. I'd be supported if criticized. He'd cheer with me if there was enthusiasm.

In 99% of cases, I'm comfortable jumping into the unknown, but there are exceptions. The mentor's encouragement would have prompted me to act sooner.

The lesson

Begin fundraising immediately. Months may pass. Show investors your pre-MVP project. Draw inferences from feedback.

3. Role ambiguity

Situation

My technical co-founders were also part-time lead developers, which produced communication issues. As co-founders, we communicated well and recognized the problems. Stakes, vesting, target markets, and approach were agreed upon.

We were behind schedule. Technical debt and strategic gap grew.

Bi-daily and weekly reviews didn't help. Each time, there were explanations. Inside, I was freaking out.

Self-reflection

I am a fairly easy person to talk to. I always try to stick to agreements; otherwise, my head gets stuffed with unnecessary information, interpretations, and emotions.

Sit down -> talk -> decide -> do -> evaluate the results. Repeat it.

If I don't get detailed comments, I start ruining everyone's mood. If there's a systematic violation of agreements without a good justification, I won't join the project or I'll end the collaboration.

What would I have done otherwise?

This is where it’s scariest to draw conclusions. Probably the most logical thing would have been not to start the project as we started it. But that was already a completely different project. So I would not have done anything differently and would have failed again.

But I drew conclusions for the future.

The lesson

First-time founders should find an adviser or team coach for a strategic session. It helps split the roles and responsibilities.

Shan Vernekar

3 years ago

How the Ethereum blockchain's transactions are carried out

Overview

Ethereum blockchain is a network of nodes that validate transactions. Any network node can be queried for blockchain data for free. To write data as a transition requires processing and writing to each network node's storage. Fee is paid in ether and is also called as gas.

We'll examine how user-initiated transactions flow across the network and into the blockchain.

Flow of transactions

A user wishes to move some ether from one external account to another. He utilizes a cryptocurrency wallet for this (like Metamask), which is a browser extension.
The user enters the desired transfer amount and the external account's address. He has the option to choose the transaction cost he is ready to pay.
Wallet makes use of this data, signs it with the user's private key, and writes it to an Ethereum node. Services such as Infura offer APIs that enable writing data to nodes. One of these services is used by Metamask. An example transaction is shown below. Notice the “to” address and value fields.

var rawTxn = {
    nonce: web3.toHex(txnCount),
    gasPrice: web3.toHex(100000000000),
    gasLimit: web3.toHex(140000),
    to: '0x633296baebc20f33ac2e1c1b105d7cd1f6a0718b',
    value: web3.toHex(0),
    data: '0xcc9ab24952616d6100000000000000000000000000000000000000000000000000000000'
};

The transaction is written to the target Ethereum node's local TRANSACTION POOL. It informed surrounding nodes of the new transaction, and those nodes reciprocated. Eventually, this transaction is received by and written to each node's local TRANSACTION pool.
The miner who finds the following block first adds pending transactions (with a higher gas cost) from the nearby TRANSACTION POOL to the block.
The transactions written to the new block are verified by other network nodes.
A block is added to the main blockchain after there is consensus and it is determined to be genuine. The local blockchain is updated with the new node by additional nodes as well.
Block mining begins again next.

The image above shows how transactions go via the network and what's needed to submit them to the main block chain.

References

ethereum.org/transactions How Ethereum transactions function, their data structure, and how to send them via app. ethereum.org

GTO Poker 101

More on Gaming

Sonic Prime and indie games on Netflix

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

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

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The direction of the economy is as follows.

What Makes Banks Confident

Reasons Other Banks Are Less Confident

Final Reflections

My 3 biggest errors as a co-founder and CEO

The wrong technology stack

Situation

Self-reflection

What would I have changed if I could?

The lesson

2. A tardy search for investments

Situation

Self-reflection

What would I have changed if I could?

The lesson

3. Role ambiguity

Situation

Self-reflection

What would I have done otherwise?

The lesson

How the Ethereum blockchain's transactions are carried out

Overview

Flow of transactions

References