"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.

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SpaceX's Starship.

Launched last week.

Four minutes in:

SpaceX will succeed. When it does, its massiveness will matter.

Its payload will revolutionize space economics.

Civilization will shift.

We don't yet understand how this will affect space and Earth culture. Grab it.

The Cost of Space Transportation Has Decreased Exponentially

Space launches have increased dramatically in recent years.

We mostly send items to LEO, the green area below:

SpaceX's reusable rockets can send these things to LEO. Each may launch dozens of payloads into space.

With all these launches, we're sending more than simply things to space. Volume and mass. Since the 1980s, launching a kilogram of payload to LEO has become cheaper:

One kilogram in a large rocket cost over $75,000 in the 1980s. Carrying one astronaut cost nearly $5M! Falcon Heavy's $1,500/kg price is 50 times lower. SpaceX's larger, reusable rockets are amazing.

SpaceX's Starship rocket will continue. It can carry over 100 tons to LEO, 50% more than the current Falcon heavy. Thousands of launches per year. Elon Musk predicts Falcon Heavy's $1,500/kg cost will plummet to $100 in 23 years.

In context:

People underestimate this.

2. The Benefits of Affordable Transportation

Compare Earth's transportation costs:

It's no surprise that the US and Northern Europe are the wealthiest and have the most navigable interior waterways.

So what? since sea transportation is cheaper than land. Inland waterways are even better than sea transportation since weather is less of an issue, currents can be controlled, and rivers serve two banks instead of one for coastal transportation.

In France, because population density follows river systems, rivers are valuable. Cheap transportation brought people and money to rivers, especially their confluences.

How come? Why were humans surrounding rivers?

Imagine selling meat for $10 per kilogram. Transporting one kg one kilometer costs $1. Your margin decreases $1 each kilometer. You can only ship 10 kilometers. For example, you can only trade with four cities:

If instead, your cost of transportation is half, what happens? It costs you $0.5 per km. You now have higher margins with each city you traded with. More importantly, you can reach 20-km markets.

However, 2x distance 4x surface! You can now trade with sixteen cities instead of four! Metcalfe's law states that a network's value increases with its nodes squared. Since now sixteen cities can connect to yours. Each city now has sixteen connections! They get affluent and can afford more meat.

Rivers lower travel costs, connecting many cities, which can trade more, get wealthy, and buy more.

The right network is worth at least an order of magnitude more than the left! The cheaper the transport, the more trade at a lower cost, the more income generated, the more that wealth can be reinvested in better canals, bridges, and roads, and the wealth grows even more.

Throughout history. Rome was established around cheap Mediterranean transit and preoccupied with cutting overland transportation costs with their famous roadways. Communications restricted their empire.

The Egyptians lived around the Nile, the Vikings around the North Sea, early Japan around the Seto Inland Sea, and China started canals in the 5th century BC.

Transportation costs shaped empires.Starship is lowering new-world transit expenses. What's possible?

3. Change Organizations, Change Companies, Change the World

Starship is a conveyor belt to LEO. A new world of opportunity opens up as transportation prices drop 100x in a decade.

Satellite engineers have spent decades shedding milligrams. Weight influenced every decision: pricing structure, volumes to be sent, material selections, power sources, thermal protection, guiding, navigation, and control software. Weight was everything in the mission. To pack as much science into every millimeter, NASA missions had to be miniaturized. Engineers were indoctrinated against mass.

No way.

Starship is not constrained by any space mission, robotic or crewed.

Starship obliterates the mass constraint and every last vestige of cultural baggage it has gouged into the minds of spacecraft designers. A dollar spent on mass optimization no longer buys a dollar saved on launch cost. It buys nothing. It is time to raise the scope of our ambition and think much bigger. — Casey Handmer, Starship is still not understood

A Tesla Roadster in space makes more sense.

It went beyond bad PR. It told the industry: Did you care about every microgram? No more. My rockets are big enough to send a Tesla without noticing. Industry watchers should have noticed.

Most didn’t. Artemis is a global mission to send astronauts to the Moon and build a base. Artemis uses disposable Space Launch System rockets. Instead of sending two or three dinky 10-ton crew habitats over the next decade, Starship might deliver 100x as much cargo and create a base for 1,000 astronauts in a year or two. Why not? Because Artemis remains in a pre-Starship paradigm where each kilogram costs a million dollars and we must aggressively descope our objective.

Space agencies can deliver 100x more payload to space for the same budget with 100x lower costs and 100x higher transportation volumes. How can space economy saturate this new supply?

Before Starship, NASA supplied heavy equipment for Moon base construction. After Starship, Caterpillar and Deere may space-qualify their products with little alterations. Instead than waiting decades for NASA engineers to catch up, we could send people to build a space outpost with John Deere equipment in a few years.

History is littered with the wreckage of former industrial titans that underestimated the impact of new technology and overestimated their ability to adapt: Blockbuster, Motorola, Kodak, Nokia, RIM, Xerox, Yahoo, IBM, Atari, Sears, Hitachi, Polaroid, Toshiba, HP, Palm, Sony, PanAm, Sega, Netscape, Compaq, GM… — Casey Handmer, Starship is still not understood

Everyone saw it coming, but senior management failed to realize that adaption would involve moving beyond their established business practice. Others will if they don't.

4. The Starship Possibilities

It's Starlink.

SpaceX invented affordable cargo space and grasped its implications first. How can we use all this inexpensive cargo nobody knows how to use?

Satellite communications seemed like the best way to capitalize on it. They tried. Starlink, designed by SpaceX, provides fast, dependable Internet worldwide. Beaming information down is often cheaper than cable. Already profitable.

Starlink is one use for all this cheap cargo space. Many more. The longer firms ignore the opportunity, the more SpaceX will acquire.

What are these chances?

Satellite imagery is outdated and lacks detail. We can improve greatly. Synthetic aperture radar can take beautiful shots like this:

Have you ever used Google Maps and thought, "I want to see this in more detail"? What if I could view Earth live? What if we could livestream an infrared image of Earth?

We could launch hundreds of satellites with such mind-blowing visual precision of the Earth that we would dramatically improve the accuracy of our meteorological models; our agriculture; where crime is happening; where poachers are operating in the savannah; climate change; and who is moving military personnel where. Is that useful?

What if we could see Earth in real time? That affects businesses? That changes society?

Crypto and blockchain have rebranded as web3. They probably thought it sounded better and didn't want the baggage of scam ICOs, STOs, and skirted securities laws.

It was like Facebook becoming Meta. Crypto's biggest players wanted to change public (and regulator) perception away from pump-and-dump schemes.

After the 2018 ICO gold rush, it's understandable. Every project that raised millions (or billions) never shipped a meaningful product.

Like many crazes, charlatans took the money and ran.

Despite its grifter past, web3 is THE hot topic today as more founders, venture firms, and larger institutions look to build the future decentralized internet.

Supposedly.

How often have you heard: This will change the world, fix the internet, and give people power?

Why are most of web3's biggest proponents (and beneficiaries) the same rich, powerful players who built and invested in the modern internet? It's like they want to remake and own the internet.

Something seems off about that.

Why are insiders getting preferential presale terms before the public, allowing early investors and proponents to flip dirt cheap tokens and advisors shares almost immediately after the public sale?

It's a good gig with guaranteed markups, no risk or progress.

If it sounds like insider trading, it is, at least practically. This is clear when people talk about blockchain/web3 launches and tokens.

Fast money, quick flips, and guaranteed markups/returns are common.

Incentives-wise, it's hard to blame them. Who can blame someone for following the rules to win? Is it their fault or regulators' for not leveling the playing field?

It's similar to oil companies polluting for profit, Instagram depressing you into buying a new dress, or pharma pushing an unnecessary pill.

All of that is fair game, at least until we change the playbook, because people (and corporations) change for pain or love. Who doesn't love money?

belief based on money gain

Sinclair:

“It is difficult to get a man to understand something when his salary depends upon his not understanding it.”

Bitcoin, blockchain, and web3 analogies?

Most blockchain and web3 proponents are true believers, not cynical capitalists. They believe blockchain's inherent transparency and permissionless trust allow humanity to evolve beyond our reptilian ways and build a better decentralized and democratic world.

They highlight issues with the modern internet and monopoly players like Google, Facebook, and Apple. Decentralization fixes everything

If we could give power back to the people and get governments/corporations/individuals out of the way, we'd fix everything.

Blockchain solves supply chain and child labor issues in China.

To meet Paris climate goals, reduce emissions. Create a carbon token.

Fixing online hatred and polarization Web3 Twitter and Facebook replacement.

Web3 must just be the answer for everything… your “perfect” silver bullet.

Nothing fits everyone. Blockchain has pros and cons like everything else.

Blockchain's viral, ponzi-like nature has an MLM (mid level marketing) feel. If you bought Taylor Swift's NFT, your investment is tied to her popularity.

Probably makes you promote Swift more. Play music loudly.

Here's another example:

Imagine if Jehovah’s Witnesses (or evangelical preachers…) got paid for every single person they converted to their cause.

It becomes a self-fulfilling prophecy as their faith and wealth grow.

Which breeds extremism? Ultra-Orthodox Jews are an example. maximalists

Bitcoin and blockchain are causes, religions. It's a money-making movement and ideal.

We're good at convincing ourselves of things we want to believe, hence filter bubbles.

I ignore anything that doesn't fit my worldview and seek out like-minded people, which algorithms amplify.

Then what?

Is web3 merely a new scam?

No, never!

Blockchain has many crucial uses.

Sending money home/abroad without bank fees;

Like fleeing a war-torn country and converting savings to Bitcoin;

Like preventing Twitter from silencing dissidents.

Permissionless, trustless databases could benefit society and humanity. There are, however, many limitations.

Lost password?

What if you're cheated?

What if Trump/Putin/your favorite dictator incites a coup d'état?

What-ifs abound. Decentralization's openness brings good and bad.

No gatekeepers or firefighters to rescue you.

ISIS's fundraising is also frictionless.

Community-owned apps with bad interfaces and service.

Trade-offs rule.

So what compromises does web3 make?

What are your trade-offs? Decentralization has many strengths and flaws. Like Bitcoin's wasteful proof-of-work or Ethereum's political/wealth-based proof-of-stake.

To ensure the survival and veracity of the network/blockchain and to safeguard its nodes, extreme measures have been designed/put in place to prevent hostile takeovers aimed at altering the blockchain, i.e., adding money to your own wallet (account), etc.

These protective measures require significant resources and pose challenges. Reduced speed and throughput, high gas fees (cost to submit/write a transaction to the blockchain), and delayed development times, not to mention forked blockchain chains oops, web3 projects.

Protecting dissidents or rogue regimes makes sense. You need safety, privacy, and calm.

First-world life?

What if you assumed EVERYONE you saw was out to rob/attack you? You'd never travel, trust anyone, accomplish much, or live fully. The economy would collapse.

It's like an ant colony where half the ants do nothing but wait to be attacked.

Waste of time and money.

11% of the US budget goes to the military. Imagine what we could do with the $766B+ we spend on what-ifs annually.

Is so much hypothetical security needed?

Blockchain and web3 are similar.

Does your app need permissionless decentralization? Does your scooter-sharing company really need a proof-of-stake system and 1000s of nodes to avoid Russian hackers? Why?

Worst-case scenario? It's not life or death, unless you overstate the what-ifs. Web3 proponents find improbable scenarios to justify decentralization and tokenization.

Do I need a token to prove ownership of my painting? Unless I'm a master thief, I probably bought it.

despite losing the receipt.

I do, however, love Web 3.

Enough Web3 bashing for now. Understand? Decentralization isn't perfect, but it has huge potential when applied to the right problems.

I see many of the right problems as disrupting big tech's ruthless monopolies. I wrote several years ago about how tokenized blockchains could be used to break big tech's stranglehold on platforms, marketplaces, and social media.

Tokenomics schemes can be used for good and are powerful. Here’s how.

Before the ICO boom, I made a series of predictions about blockchain/crypto's future. It's still true.

Here's where I was then and where I see web3 going:

My 11 Big & Bold Predictions for Blockchain

In the near future, people may wear crypto cash rings or bracelets.

1. While some governments repress cryptocurrency, others will start to embrace it.

2. Blockchain will fundamentally alter voting and governance, resulting in a more open election process.

3. Money freedom will lead to a more geographically open world where people will be more able to leave when there is unrest.

4. Blockchain will make record keeping significantly easier, eliminating the need for a significant portion of government workers whose sole responsibility is paperwork.

5. Overrated are smart contracts.

6. Tokens will replace company stocks.

7. Blockchain increases real estate's liquidity, value, and volatility.

8. Healthcare may be most affected.

9. Crypto could end privacy and lead to Minority Report.

10. New companies with network effects will displace incumbents.

11. Soon, people will wear rings or bracelets with crypto cash.

Some have already happened, while others are still possible.

Time will tell if they happen.

And finally:

What will web3 be?

Who will be in charge?

Closing remarks

Hope you enjoyed this web3 dive. There's much more to say, but that's for another day.

We're writing history as we go.

Tech regulation, mergers, Bitcoin surge How will history remember us?

What about web3 and blockchain?

Is this a revolution or a tulip craze?

Remember, actions speak louder than words (share them in the comments).

Your turn.