"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.

Non-technical talents can benefit data scientists in addition to statistics and programming.

As our article 5 Most In-Demand Skills for Data Scientists shows, being business-minded is useful. How can you get such a diverse skill set? We've compiled a list of helpful resources.

Data science, data analysis, programming, and business are covered. Even a few of these books will make you a better data scientist.

Ready? Let’s dive in.

Best books for data scientists

1. The Black Swan

Author: Nassim Taleb

First, a less obvious title. Nassim Nicholas Taleb's seminal series examines uncertainty, probability, risk, and decision-making.

Three characteristics define a black swan event:

• It is erratic.

• It has a significant impact.

• Many times, people try to come up with an explanation that makes it seem more predictable than it actually was.

People formerly believed all swans were white because they'd never seen otherwise. A black swan in Australia shattered their belief.

Taleb uses this incident to illustrate how human thinking mistakes affect decision-making. The book teaches readers to be aware of unpredictability in the ever-changing IT business.

Try multiple tactics and models because you may find the answer.

2. High Output Management

Author: Andrew Grove

Intel's former chairman and CEO provides his insights on developing a global firm in this business book. We think Grove would choose “management” to describe the talent needed to start and run a business.

That's a skill for CEOs, techies, and data scientists. Grove writes on developing productive teams, motivation, real-life business scenarios, and revolutionizing work.

Five lessons:

• Every action is a procedure.

• Meetings are a medium of work

• Manage short-term goals in accordance with long-term strategies.

• Mission-oriented teams accelerate while functional teams increase leverage.

• Utilize performance evaluations to enhance output.

So — if the above captures your imagination, it’s well worth getting stuck in.

3. The Hard Thing About Hard Things: Building a Business When There Are No Easy Answers

Author: Ben Horowitz

Few realize how difficult it is to run a business, even though many see it as a tremendous opportunity.

Business schools don't teach managers how to handle the toughest difficulties; they're usually on their own. So Ben Horowitz wrote this book.

It gives tips on creating and maintaining a new firm and analyzes the hurdles CEOs face.

Find suggestions on:

• create software

• Run a business.

• Promote a product

• Obtain resources

• Smart investment

• oversee daily operations

This book will help you cope with tough times.

4. Obviously Awesome: How to Nail Product Positioning

Author: April Dunford

Your job as a data scientist is a product. You should be able to sell what you do to clients. Even if your product is great, you must convince them.

How to? April Dunford's advice: Her book explains how to connect with customers by making your offering seem like a secret sauce.

You'll learn:

• Select the ideal market for your products.

• Connect an audience to the value of your goods right away.

• Take use of three positioning philosophies.

• Utilize market trends to aid purchasers

5. The Mom test

Author: Rob Fitzpatrick

The Mom Test improves communication. Client conversations are rarely predictable. The book emphasizes one of the most important communication rules: enquire about specific prior behaviors.

Both ways work. If a client has suggestions or demands, listen carefully and ensure everyone understands. The book is packed with client-speaking tips.

6. Introduction to Machine Learning with Python: A Guide for Data Scientists

Authors: Andreas C. Müller, Sarah Guido

Now, technical documents.

This book is for Python-savvy data scientists who wish to learn machine learning. Authors explain how to use algorithms instead of math theory.

Their technique is ideal for developers who wish to study machine learning basics and use cases. Sci-kit-learn, NumPy, SciPy, pandas, and Jupyter Notebook are covered beyond Python.

If you know machine learning or artificial neural networks, skip this.

7. Python Data Science Handbook: Essential Tools for Working with Data

Author: Jake VanderPlas

Data work isn't easy. Data manipulation, transformation, cleansing, and visualization must be exact.

Python is a popular tool. The Python Data Science Handbook explains everything. The book describes how to utilize Pandas, Numpy, Matplotlib, Scikit-Learn, and Jupyter for beginners.

The only thing missing is a way to apply your learnings.

8. Python for Data Analysis: Data Wrangling with Pandas, NumPy, and IPython

Author: Wes McKinney

The author leads you through manipulating, processing, cleaning, and analyzing Python datasets using NumPy, Pandas, and IPython.

The book's realistic case studies make it a great resource for Python or scientific computing beginners. Once accomplished, you'll uncover online analytics, finance, social science, and economics solutions.

9. Data Science from Scratch

Author: Joel Grus

Here's a title for data scientists with Python, stats, maths, and algebra skills (alongside a grasp of algorithms and machine learning). You'll learn data science's essential libraries, frameworks, modules, and toolkits.

The author works through all the key principles, providing you with the practical abilities to develop simple code. The book is appropriate for intermediate programmers interested in data science and machine learning.

Not that prior knowledge is required. The writing style matches all experience levels, but understanding will help you absorb more.

10. Machine Learning Yearning

Author: Andrew Ng

Andrew Ng is a machine learning expert. Co-founded and teaches at Stanford. This free book shows you how to structure an ML project, including recognizing mistakes and building in complex contexts.

The book delivers knowledge and teaches how to apply it, so you'll know how to:

• Determine the optimal course of action for your ML project.

• Create software that is more effective than people.

• Recognize when to use end-to-end, transfer, and multi-task learning, and how to do so.

• Identifying machine learning system flaws

Ng writes easy-to-read books. No rigorous math theory; just a terrific approach to understanding how to make technical machine learning decisions.

11. Deep Learning with PyTorch Step-by-Step

Author: Daniel Voigt Godoy

The last title is also the most recent. The book was revised on 23 January 2022 to discuss Deep Learning and PyTorch, a Python coding tool.

It comprises four parts:

1. Fundamentals (gradient descent, training linear and logistic regressions in PyTorch)

2. Machine Learning (deeper models and activation functions, convolutions, transfer learning, initialization schemes)

3. Sequences (RNN, GRU, LSTM, seq2seq models, attention, self-attention, transformers)

4. Automatic Language Recognition (tokenization, embeddings, contextual word embeddings, ELMo, BERT, GPT-2)

We admire the book's readability. The author avoids difficult mathematical concepts, making the material feel like a conversation.

Is every data scientist a humanist?

Even as a technological professional, you can't escape human interaction, especially with clients.

We hope these books will help you develop interpersonal skills.

Alex Mashinsky, CEO of Celsius, speaks at Web Summit 2021 in Lisbon. 

Celsius Network filed for Chapter 11 bankruptcy a month after freezing customer withdrawals, joining other crypto casualties.

Celsius took the step to stabilize its business and restructure for all stakeholders. The filing was done in the Southern District of New York.

The company, which amassed more than $20 billion by offering 18% interest on cryptocurrency deposits, paused withdrawals and other functions in mid-June, citing "extreme market conditions."

As the Fed raises interest rates aggressively, it hurts risk sentiment and squeezes funding costs. Voyager Digital Ltd. filed for Chapter 11 bankruptcy this month, and Three Arrows Capital has called in liquidators.

Celsius called the pause "difficult but necessary." Without the halt, "the acceleration of withdrawals would have allowed certain customers to be paid in full while leaving others to wait for Celsius to harvest value from illiquid or longer-term asset deployment activities," it said.

Celsius declined to comment. CEO Alex Mashinsky said the move will strengthen the company's future.

The company wants to keep operating. It's not requesting permission to allow customer withdrawals right now; Chapter 11 will handle customer claims. The filing estimates assets and liabilities between $1 billion and $10 billion.

Celsius is advised by Kirkland & Ellis, Centerview Partners, and Alvarez & Marsal.

Yield-promises

Celsius promised 18% returns on crypto loans. It lent those coins to institutional investors and participated in decentralized-finance apps.

When TerraUSD (UST) and Luna collapsed in May, Celsius pulled its funds from Terra's Anchor Protocol, which offered 20% returns on UST deposits. Recently, another large holding, staked ETH, or stETH, which is tied to Ether, became illiquid and discounted to Ether.

The lender is one of many crypto companies hurt by risky bets in the bear market. Also, Babel halted withdrawals. Voyager Digital filed for bankruptcy, and crypto hedge fund Three Arrows Capital filed for Chapter 15 bankruptcy.

According to blockchain data and tracker Zapper, Celsius repaid all of its debt in Aave, Compound, and MakerDAO last month.

Celsius charged Symbolic Capital Partners Ltd. 2,000 Ether as collateral for a cash loan on June 13. According to company filings, Symbolic was charged 2,545.25 Ether on June 11.

In July 6 filings, it said it reshuffled its board, appointing two new members and firing others.