"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.

Move people with tiny words.

Apple fanboy here.

• Macs are awesome.

• Their iPhones rock.

• $19 cloths are great.

• $999 stands are amazing.

I love Apple's microcopy even more.

It's like the marketing goddess bit into the Apple logo and blessed the world with microcopy.

I took on a 30-day micro-stalking mission.

Every time I caught myself wasting time on YouTube, I had to visit Apple’s website to learn the secrets of the marketing goddess herself.

We've learned. Golden apples are calling.

Cut the friction

Benefit-first, not commitment-first.

Brands lose customers through friction.

Most brands don't think like customers.

• Brands want sales.

• Brands want newsletter signups.

Here's their microcopy:

• “Buy it now.”

• “Sign up for our newsletter.”

Both are difficult. They ask for big commitments.

People are simple creatures. Want pleasure without commitment.

Apple nails this.

So, instead of highlighting the commitment, they highlight the benefit of the commitment.

Saving on the latest iPhone sounds easier than buying it. Everyone saves, but not everyone buys.

A subtle change in framing reduces friction.

Apple eliminates customer objections to reduce friction.

Less customer friction means simpler processes.

Apple's copy expertly reassures customers about shipping fees and not being home. Apple assures customers that returning faulty products is easy.

Apple knows that talking to a real person is the best way to reduce friction and improve their copy.

Always rhyme

Learn about fine rhyme.

Poets make things beautiful with rhyme.

Copywriters use rhyme to stand out.

Apple’s copywriters have mastered the art of corporate rhyme.

Two techniques are used.

1. Perfect rhyme

Here, rhymes are identical.

2. Imperfect rhyme

Here, rhyming sounds vary.

Apple prioritizes meaning over rhyme.

Apple never forces rhymes that don't fit.

It fits so well that the copy seems accidental.

Add alliteration

Alliteration always entertains.

Alliteration repeats initial sounds in nearby words.

Apple's copy uses alliteration like no other brand I've seen to create a rhyming effect or make the text more fun to read.

For example, in the sentence "Sam saw seven swans swimming," the initial "s" sound is repeated five times. This creates a pleasing rhythm.

Microcopy overuse is like pouring ketchup on a Michelin-star meal.

Alliteration creates a memorable phrase in copywriting. It's subtler than rhyme, and most people wouldn't notice; it simply resonates.

I love how Apple uses alliteration and contrast between "wonders" and "ease".

Assonance, or repeating vowels, isn't Apple's thing.

You ≠ Hero, Customer = Hero

Your brand shouldn't be the hero.

Because they'll be using your product or service, your customer should be the hero of your copywriting. With your help, they should feel like they can achieve their goals.

I love how Apple emphasizes what you can do with the machine in this microcopy.

It's divine how they position their tools as sidekicks to help below.

This one takes the cake:

Dialogue-style writing

Conversational copy engages.

Excellent copy Like sharing gum with a friend.

This helps build audience trust.

Apple does this by using natural connecting words like "so" and phrases like "But that's not all."

Snowclone-proof

The mother of all microcopy techniques.

A snowclone uses an existing phrase or sentence to create a new one. The new phrase or sentence uses the same structure but different words.

It’s usually a well know saying like:

To be or not to be.

This becomes a formula:

To _ or not to _.

Copywriters fill in the blanks with cause-related words. Example:

To click or not to click.

Apple turns "survival of the fittest" into "arrival of the fittest."

It's unexpected and surprises the reader.

So this was fun.

But my fun has just begun.

Microcopy is 21st-century poetry.

I came as an Apple fanboy.

I leave as an Apple fanatic.

Now I’m off to find an apple tree.

Cause you know how it goes.

(Apples, trees, etc.)

This post is a summary. Original post available here.

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.

Startup entrepreneurs assume what risks when pitching?

Last week I signed four NDAs.

Four!

NDA stands for non-disclosure agreement. A legal document given to someone receiving confidential information. By signing, the person pledges not to share the information for a certain time. If they do, they may be in breach of contract and face legal action.

Companies use NDAs to protect trade secrets and confidential internal information from employees and contractors. Appropriate. If you manage a huge, successful firm, you don't want your employees selling their information to your competitors. To be true, business NDAs don't always prevent corporate espionage, but they usually make employees and contractors think twice before sharing.

I understand employee and contractor NDAs, but I wasn't asked to sign one. I counsel entrepreneurs, thus the NDAs I signed last week were from startups that wanted my feedback on their concepts.

I’m not a startup investor. I give startup guidance online. Despite that, four entrepreneurs thought their company ideas were so important they wanted me to sign a generically written legal form they probably acquired from a shady, spam-filled legal templates website before we could chat.

False. One company tried to get me to sign their NDA a few days after our conversation. I gently rejected, but their tenacity encouraged me. I considered sending retroactive NDAs to everyone I've ever talked to about one of my startups in case they establish a successful company based on something I said.

Two of the other three NDAs were from nearly identical companies. Good thing I didn't sign an NDA for the first one, else they may have sued me for talking to the second one as though I control the firms people pitch me.

I wasn't talking to the fourth NDA company. Instead, I received an unsolicited email from someone who wanted comments on their fundraising pitch deck but required me to sign an NDA before sending it.

That's right, before I could read a random Internet stranger's unsolicited pitch deck, I had to sign his NDA, potentially limiting my ability to discuss what was in it.

You should understand. Advisors, mentors, investors, etc. talk to hundreds of businesses each year. They cannot manage all the companies they deal with, thus they cannot risk legal trouble by talking to someone. Well, if I signed NDAs for all the startups I spoke with, half of the 300+ articles I've written on Medium over the past several years could get me sued into the next century because I've undoubtedly addressed topics in my articles that I discussed with them.

The four NDAs I received last week are part of a recent trend of entrepreneurs sending out NDAs before meetings, despite the practical and legal issues. They act like asking someone to sign away their right to talk about all they see and hear in a day is as straightforward as asking for a glass of water.

Given this inflow of NDAs, I wanted to briefly remind entrepreneurs reading this blog about the merits and cons of requesting investors (or others in the startup ecosystem) to sign your NDA.

Benefits of having investors sign your NDA include:

None. Zero. Nothing.

Disadvantages of requesting investor NDAs:

• You'll come off as an amateur who has no idea what it takes to launch a successful firm.

• Investors won't trust you with their money since you appear to be a complete amateur.

• Printing NDAs will be a waste of paper because no genuine entrepreneur will ever sign one.

I apologize for missing any cons. Please leave your remarks.