For some people, the glass is half empty. For others, it’s half full. And for some, the question is, How do I get this glass totally full again?

Problem-solvers are the last group. They're neutral. Pragmatists.

Problems surround them. They fix things instead of judging them. Problem-solvers improve the world wherever they go.

Some fail. Sometimes their good intentions have terrible results. Like when they try to help a grandma cross the road because she can't do it alone but discover she never wanted to.

Most programmers, software engineers, and data scientists solve problems. They use computer code to fix problems they see.

Coding is best done by understanding and solving the problem.

Despite your best intentions, building the wrong solution may have negative consequences. Helping an unwilling grandma cross the road.

How can you improve problem-solving?

1. Examine your presumptions.

Don’t think There’s a grandma, and she’s unable to cross the road. Therefore I must help her over the road. Instead think This grandma looks unable to cross the road. Let’s ask her whether she needs my help to cross it.

Maybe the grandma can’t cross the road alone, but maybe she can. You can’t tell for sure just by looking at her. It’s better to ask.

Maybe the grandma wants to cross the road. But maybe she doesn’t. It’s better to ask!

Building software is similar. Do only I find this website ugly? Who can I consult?

We all have biases, mental shortcuts, and worldviews. They simplify life.

Problem-solving requires questioning all assumptions. They might be wrong!

Think less. Ask more.

Secondly, fully comprehend the issue.

Grandma wants to cross the road? Does she want flowers from the shop across the street?

Understanding the problem advances us two steps. Instead of just watching people and their challenges, try to read their intentions.

Don't ask, How can I help grandma cross the road? Why would this grandma cross the road? What's her goal?

Understand what people want before proposing solutions.

3. Request more information. This is not a scam!

People think great problem solvers solve problems immediately. False!

Problem-solvers study problems. Understanding the problem makes solving it easy.

When you see a grandma struggling to cross the road, you want to grab her elbow and pull her over. However, a good problem solver would ask grandma what she wants. So:

Problem solver: Excuse me, ma’am? Do you wish to get over the road? Grandma: Yes indeed, young man! Thanks for asking. Problem solver: What do you want to do on the other side? Grandma: I want to buy a bouquet of flowers for my dear husband. He loves flowers! I wish the shop wasn’t across this busy road… Problem solver: Which flowers does your husband like best? Grandma: He loves red dahlia. I usually buy about 20 of them. They look so pretty in his vase at the window! Problem solver: I can get those dahlia for you quickly. Go sit on the bench over here while you’re waiting; I’ll be back in five minutes. Grandma: You would do that for me? What a generous young man you are!

A mediocre problem solver would have helped the grandma cross the road, but he might have forgotten that she needs to cross again. She must watch out for cars and protect her flowers on the way back.

A good problem solver realizes that grandma's husband wants 20 red dahlias and completes the task.

4- Rapid and intense brainstorming

Understanding a problem makes solutions easy. However, you may not have all the information needed to solve the problem.

Additionally, retrieving crucial information can be difficult.

You could start a blog. You don't know your readers' interests. You can't ask readers because you don't know who they are.

Brainstorming works here. Set a stopwatch (most smartphones have one) to ring after five minutes. In the remaining time, write down as many topics as possible.

No answer is wrong. Note everything.

Sort these topics later. Programming or data science? What might readers scroll past—are these your socks this morning?

Rank your ideas intuitively and logically. Write Medium stories using the top 35 ideas.

5 - Google it.

Doctor Google may answer this seemingly insignificant question. If you understand your problem, try googling or binging.

Someone has probably had your problem before. The problem-solver may have posted their solution online.

Use others' experiences. If you're social, ask a friend or coworker for help.

6 - Consider it later

Rest your brain.

Reread. Your brain needs rest to function.

Hustle culture encourages working 24/7. It doesn't take a neuroscientist to see that this is mental torture.

Leave an unsolvable problem. Visit friends, take a hot shower, or do whatever you enjoy outside of problem-solving.

Nap.

I get my best ideas in the morning after working on a problem. I couldn't have had these ideas last night.

Sleeping subconsciously. Leave it alone and you may be surprised by the genius it produces.

7 - Learn to live with frustration

There are problems that you’ll never solve.

Mathematicians are world-class problem-solvers. The brightest minds in history have failed to solve many mathematical problems.

A Gordian knot problem can frustrate you. You're smart!

Frustration-haters don't solve problems well. They choose simple problems to avoid frustration.

No. Great problem solvers want to solve a problem but know when to give up.

Frustration initially hurts. You adapt.

Famous last words

If you read this article, you probably solve problems. We've covered many ways to improve, so here's a summary:

1. Test your presumptions. Is the issue the same for everyone else when you see one? Or are your prejudices and self-judgments misguiding you?

2. Recognize the issue completely. On the surface, a problem may seem straightforward, but what's really going on? Try to see what the current situation might be building up to by thinking two steps ahead of the current situation.

3. Request more information. You are no longer a high school student. A two-sentence problem statement is not sufficient to provide a solution. Ask away if you need more details!

4. Think quickly and thoroughly. In a constrained amount of time, try to write down all your thoughts. All concepts are worthwhile! Later, you can order them.

5. Google it. There is a purpose for the internet. Use it.

6. Consider it later at night. A rested mind is more creative. It might seem counterintuitive to leave a problem unresolved. But while you're sleeping, your subconscious will handle the laborious tasks.

7. Accept annoyance as a normal part of life. Don't give up if you're feeling frustrated. It's a step in the procedure. It's also perfectly acceptable to give up on a problem because there are other, more pressing issues that need to be addressed.

You might feel stupid sometimes, but that just shows that you’re human. You care about the world and you want to make it better.

At the end of the day, that’s all there is to problem solving — making the world a little bit better.

I read 53 novels last year and hope to do so again.

Books are best if you love learning. You get a range of perspectives, unlike podcasts and YouTube channels where you get the same ones.

Book quality varies. I've read useless books. Most books teach me something.

These 9 novels have changed my outlook in recent years. They've made me rethink what I believed or introduced me to a fresh perspective that changed my worldview.

You can order these books yourself. Or, read my summaries to learn what I've synthesized.

Enjoy!

Fooled By Randomness

Nassim Taleb worked as a Wall Street analyst. He used options trading to bet on unlikely events like stock market crashes.

Using financial models, investors predict stock prices. The models assume constant, predictable company growth.

These models base their assumptions on historical data, so they assume the future will be like the past.

Fooled By Randomness argues that the future won't be like the past. We often see impossible market crashes like 2008's housing market collapse. The world changes too quickly to use historical data: by the time we understand how it works, it's changed.

Most people don't live to see history unfold. We think our childhood world will last forever. That goes double for stable societies like the U.S., which hasn't seen major turbulence in anyone's lifetime.

Fooled By Randomness taught me to expect the unexpected. The world is deceptive and rarely works as we expect. You can't always trust your past successes or what you've learned.

Antifragile

More Taleb. Some things, like the restaurant industry and the human body, improve under conditions of volatility and turbulence.

We didn't have a word for this counterintuitive concept until Taleb wrote Antifragile. The human body (which responds to some stressors, like exercise, by getting stronger) and the restaurant industry both benefit long-term from disorder (when economic turbulence happens, bad restaurants go out of business, improving the industry as a whole).

Many human systems are designed to minimize short-term variance because humans don't understand it. By eliminating short-term variation, we increase the likelihood of a major disaster.

Once, we put out every forest fire we found. Then, dead wood piled up in forests, causing catastrophic fires.

We don't like price changes, so politicians prop up markets with stimulus packages and printing money. This leads to a bigger crash later. Two years ago, we printed a ton of money for stimulus checks, and now we have double-digit inflation.

Antifragile taught me how important Plan B is. A system with one or two major weaknesses will fail. Make large systems redundant, foolproof, and change-responsive.

Reality is broken

We dread work. Work is tedious. Right?

Wrong. Work gives many people purpose. People are happiest when working. (That's why some are workaholics.)

Factory work saps your soul, office work is boring, and working for a large company you don't believe in and that operates unethically isn't satisfying.

Jane McGonigal says in Reality Is Broken that meaningful work makes us happy. People love games because they simulate good work. McGonigal says work should be more fun.

Some think they'd be happy on a private island sipping cocktails all day. That's not true. Without anything to do, most people would be bored. Unemployed people are miserable. Many retirees die within 2 years, much more than expected.

Instead of complaining, find meaningful work. If you don't like your job, it's because you're in the wrong environment. Find the right setting.

The Lean Startup

Before the airplane was invented, Harvard scientists researched flying machines. Who knew two North Carolina weirdos would beat them?

The Wright Brothers' plane design was key. Harvard researchers were mostly theoretical, designing an airplane on paper and trying to make it fly in theory. They'd build it, test it, and it wouldn't fly.

The Wright Brothers were different. They'd build a cheap plane, test it, and it'd crash. Then they'd learn from their mistakes, build another plane, and it'd crash.

They repeated this until they fixed all the problems and one of their planes stayed aloft.

Mistakes are considered bad. On the African savannah, one mistake meant death. Even today, if you make a costly mistake at work, you'll be fired as a scapegoat. Most people avoid failing.

In reality, making mistakes is the best way to learn.

Eric Reis offers an unintuitive recipe in The Lean Startup: come up with a hypothesis, test it, and fail. Then, try again with a new hypothesis. Keep trying, learning from each failure.

This is a great startup strategy. Startups are new businesses. Startups face uncertainty. Run lots of low-cost experiments to fail, learn, and succeed.

Don't fear failing. Low-cost failure is good because you learn more from it than you lose. As long as your worst-case scenario is acceptable, risk-taking is good.

The Sovereign Individual

Today, nation-states rule the world. The UN recognizes 195 countries, and they claim almost all land outside of Antarctica.

We agree. For the past 2,000 years, much of the world's territory was ungoverned.

Why today? Because technology has created incentives for nation-states for most of the past 500 years. The logic of violence favors nation-states, according to James Dale Davidson, author of the Sovereign Individual. Governments have a lot to gain by conquering as much territory as possible, so they do.

Not always. During the Dark Ages, Europe was fragmented and had few central governments. Partly because of armor. With armor, a sword, and a horse, you couldn't be stopped. Large states were hard to form because they rely on the threat of violence.

When gunpowder became popular in Europe, violence changed. In a world with guns, assembling large armies and conquest are cheaper.

James Dale Davidson says the internet will make nation-states obsolete. Most of the world's wealth will be online and in people's heads, making capital mobile.

Nation-states rely on predatory taxation of the rich to fund large militaries and welfare programs.

When capital is mobile, people can live anywhere in the world, Davidson says, making predatory taxation impossible. They're not bound by their job, land, or factory location. Wherever they're treated best.

Davidson says that over the next century, nation-states will collapse because they won't have enough money to operate as they do now. He imagines a world of small city-states, like Italy before 1900. (or Singapore today).

We've already seen some movement toward a more Sovereign Individual-like world. The pandemic proved large-scale remote work is possible, freeing workers from their location. Many cities and countries offer remote workers incentives to relocate.

Many Western businesspeople live in tax havens, and more people are renouncing their US citizenship due to high taxes. Increasing globalization has led to poor economic conditions and resentment among average people in the West, which is why politicians like Trump and Sanders rose to popularity with angry rhetoric, even though Obama rose to popularity with a more hopeful message.

The Sovereign Individual convinced me that the future will be different than Nassim Taleb's. Large countries like the U.S. will likely lose influence in the coming decades, while Portugal, Singapore, and Turkey will rise. If the trend toward less freedom continues, people may flee the West en masse.

So a traditional life of college, a big firm job, hard work, and corporate advancement may not be wise. Young people should learn as much as possible and develop flexible skills to adapt to the future.

Sapiens

Sapiens is a history of humanity, from proto-humans in Ethiopia to our internet society today, with some future speculation.

Sapiens views humans (and Homo sapiens) as a unique species on Earth. We were animals 100,000 years ago. We're slowly becoming gods, able to affect the climate, travel to every corner of the Earth (and the Moon), build weapons that can kill us all, and wipe out thousands of species.

Sapiens examines what makes Homo sapiens unique. Humans can believe in myths like religion, money, and human-made entities like countries and LLCs.

These myths facilitate large-scale cooperation. Ants from the same colony can cooperate. Any two humans can trade, though. Even if they're not genetically related, large groups can bond over religion and nationality.

Combine that with intelligence, and you have a species capable of amazing feats.

Sapiens may make your head explode because it looks at the world without presupposing values, unlike most books. It questions things that aren't usually questioned and says provocative things.

It also shows how human history works. It may help you understand and predict the world. Maybe.

The 4-hour Workweek

Things can be done better.

Tradition, laziness, bad bosses, or incentive structures cause complacency. If you're willing to make changes and not settle for the status quo, you can do whatever you do better and achieve more in less time.

The Four-Hour Work Week advocates this. Tim Ferriss explains how he made more sales in 2 hours than his 8-hour-a-day colleagues.

By firing 2 of his most annoying customers and empowering his customer service reps to make more decisions, he was able to leave his business and travel to Europe.

Ferriss shows how to escape your 9-to-5, outsource your life, develop a business that feeds you with little time, and go on mini-retirement adventures abroad.

Don't accept the status quo. Instead, level up. Find a way to improve your results. And try new things.

Why Nations Fail

Nogales, Arizona and Mexico were once one town. The US/Mexico border was arbitrarily drawn.

Both towns have similar cultures and populations. Nogales, Arizona is well-developed and has a high standard of living. Nogales, Mexico is underdeveloped and has a low standard of living. Whoa!

Why Nations Fail explains how government-created institutions affect country development. Strong property rights, capitalism, and non-corrupt governments promote development. Countries without capitalism, strong property rights, or corrupt governments don't develop.

Successful countries must also embrace creative destruction. They must offer ordinary citizens a way to improve their lot by creating value for others, not reducing them to slaves, serfs, or peasants. Authors say that ordinary people could get rich on trading expeditions in 11th-century Venice.

East and West Germany and North and South Korea have different economies because their citizens are motivated differently. It explains why Chile, China, and Singapore grow so quickly after becoming market economies.

People have spent a lot of money on third-world poverty. According to Why Nations Fail, education and infrastructure aren't the answer. Developing nations must adopt free-market economic policies.

Elon Musk

Elon Musk is the world's richest man, but that’s not a good way to describe him. Elon Musk is the world's richest man, which is like calling Steve Jobs a turtleneck-wearer or Benjamin Franklin a printer.

Elon Musk does cool sci-fi stuff to help humanity avoid existential threats.

Oil will run out. We've delayed this by developing better extraction methods. We only have so much nonrenewable oil.

Our society is doomed if it depends on oil. Elon Musk invested heavily in Tesla and SolarCity to speed the shift to renewable energy.

Musk worries about AI: we'll build machines smarter than us. We won't be able to stop these machines if something goes wrong, just like cows can't fight humans. Neuralink: we need to be smarter to compete with AI when the time comes.

If Earth becomes uninhabitable, we need a backup plan. Asteroid or nuclear war could strike Earth at any moment. We may not have much time to react if it happens in a few days. We must build a new civilization while times are good and resources are plentiful.

Short-term problems dominate our politics, but long-term issues are more important. Long-term problems can cause mass casualties and homelessness. Musk demonstrates how to think long-term.

The main reason people are impressed by Elon Musk, and why Ashlee Vances' biography influenced me so much, is that he does impossible things.

Electric cars were once considered unprofitable, but Tesla has made them mainstream. SpaceX is the world's largest private space company.

People lack imagination and dismiss ununderstood ideas as impossible. Humanity is about pushing limits. Don't worry if your dreams seem impossible. Try it.

Thanks for reading.

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.

One great idea might make you rich.

Imagine having a million-dollar concept in college that made a million.

2005 precisely.

Alex Tew, 21, from Wiltshire, England, created The Million Dollar Homepage in August 2005. The idea is basic but beyond the ordinary, which is why it worked.

Alex built a 1,000,000-pixel webpage.

Each website pixel would cost $1. Since pixels are hard to discern, he sold 10x10 squares for $100.

He'd make a million if all the spots sold.

He may have thought about NFTs and the Metaverse decades ago.

MillionDollarHomepage.com launched in 2005.

Businesses and individuals could buy a website spot and add their logo, website link, and tagline. You bought an ad, but nobody visited the website.

If a few thousand people visited the website, it could drive traffic to your business's site.

Alex promised buyers the website would be up for 5 years, so it was a safe bet.

Alex's friend with a music website was the first to buy real estate on the site. Within two weeks, 4,700 pixels sold, and a tracker showed how many were sold and available.

Word-of-mouth marketing got the press's attention quickly. Everyone loves reading about new ways to make money, so it was a good news story.

By September, over 250,000 pixels had been sold, according to a BBC press release.

Alex and the website gained more media and public attention, so traffic skyrocketed. Two months after the site launched, 1,400 customers bought more than 500,000 pixels.

Businesses bought online real estate. They heard thousands visited the site, so they could get attention cheaply.

Unless you bought a few squares, I'm not sure how many people would notice your ad or click your link.

A sponge website owner emailed Alex:

“We tried Million Dollar Homepage because we were impressed at the level of ingenuity and the sheer simplicity of it. If we’re honest, we didn’t expect too much from it. Now, as a direct result, we are pitching for £18,000 GBP worth of new clients and have seen our site traffic increase over a hundred-fold. We’re even going to have to upgrade our hosting facility! It’s been exceptional.”

Web.archive.org screenshots show how the website changed.

“The idea is to create something of an internet time capsule: a homepage that is unique and permanent. Everything on the internet keeps changing so fast, it will be nice to have something that stays solid and permanent for many years. You can be a part of that!” Alex Tew, 2005

The last 1,000 pixels were sold on January 1, 2006.

By then, the homepage had hundreds of thousands of monthly visitors. Alex put the last space on eBay due to high demand.

MillionDollarWeightLoss.com won the last pixels for $38,100, bringing revenue to $1,037,100 in 4 months.

Many have tried to replicate this website's success. They've all failed.

This idea only worked because no one had seen this website before.

This winner won't be repeated, but it should inspire you to try something new and creative.

Still popular, you could buy one of the linked domains. You can't buy pixels, but you can buy an expired domain.

One link I clicked costs $59,888.

You'd own a piece of internet history if you spent that much on a domain.

Someone bought stablesgallery.co.uk after the domain expired and restored it.

Many of the linked websites have expired or been redirected, but some still link to the original. I couldn't find sponge's website. Can you?

This is a great example of how a simple creative idea can go viral.

Comment on this amazing success story.

"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.