"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.

I was entering tens of millions of records per hour when I first published Slonik PostgreSQL client for Node.js. The data being entered was usually flat, making it straightforward to use INSERT INTO ... SELECT * FROM unnset() pattern. I advocated the unnest approach for inserting rows in groups (that was part I).

However, today I’ve found a better way: jsonb_to_recordset.

jsonb_to_recordset expands the top-level JSON array of objects to a set of rows having the composite type defined by an AS clause.

jsonb_to_recordset allows us to query and insert records from arbitrary JSON, like unnest. Since we're giving JSON to PostgreSQL instead of unnest, the final format is more expressive and powerful.

SELECT *
FROM json_to_recordset('[{"name":"John","tags":["foo","bar"]},{"name":"Jane","tags":["baz"]}]')
AS t1(name text, tags text[]);
 name |   tags
------+-----------
 John | {foo,bar}
 Jane | {baz}
(2 rows)

Let’s demonstrate how you would use it to insert data.

Inserting data using json_to_recordset

Say you need to insert a list of people with attributes into the database.

const persons = [
  {
    name: 'John',
    tags: ['foo', 'bar']
  },
  {
    name: 'Jane',
    tags: ['baz']
  }
];

You may be tempted to traverse through the array and insert each record separately, e.g.

for (const person of persons) {
  await pool.query(sql`
    INSERT INTO person (name, tags)
    VALUES (
      ${person.name},
      ${sql.array(person.tags, 'text[]')}
    )
  `);
}

It's easier to read and grasp when working with a few records. If you're like me and troubleshoot a 2M+ insert query per day, batching inserts may be beneficial.

What prompted the search for better alternatives.

Inserting using unnest pattern might look like this:

await pool.query(sql`
  INSERT INTO public.person (name, tags)
  SELECT t1.name, t1.tags::text[]
  FROM unnest(
    ${sql.array(['John', 'Jane'], 'text')},
    ${sql.array(['{foo,bar}', '{baz}'], 'text')}
  ) AS t1.(name, tags);
`);

You must convert arrays into PostgreSQL array strings and provide them as text arguments, which is unsightly. Iterating the array to create slices for each column is likewise unattractive.

However, with jsonb_to_recordset, we can:

await pool.query(sql`
  INSERT INTO person (name, tags)
  SELECT *
  FROM jsonb_to_recordset(${sql.jsonb(persons)}) AS t(name text, tags text[])
`);

In contrast to the unnest approach, using jsonb_to_recordset we can easily insert complex nested data structures, and we can pass the original JSON document to the query without needing to manipulate it.

In terms of performance they are also exactly the same. As such, my current recommendation is to prefer jsonb_to_recordset whenever inserting lots of rows or nested data structures.

It's cheaper, faster charging, longer lasting, safer, and better for the environment.

Batteries are the future. Next-gen and planet-saving technology, including solar power and EVs, require batteries. As these smart technologies become more popular, we find that our batteries can't keep up. Lithium-ion batteries are expensive, slow to charge, big, fast to decay, flammable, and not environmentally friendly. MIT just created a new battery that eliminates all of these problems.  So, is this the battery of the future? Or is there a catch?

When I say entirely new, I mean it. This battery employs no currently available materials. Its electrodes are constructed of aluminium and pure sulfur instead of lithium-complicated ion's metals and graphite. Its electrolyte is formed of molten chloro-aluminate salts, not an organic solution with lithium salts like lithium-ion batteries.

How does this change in materials help?

Aluminum, sulfur, and chloro-aluminate salts are abundant, easy to acquire, and cheap. This battery might be six times cheaper than a lithium-ion battery and use less hazardous mining. The world and our wallets will benefit.

But don’t go thinking this means it lacks performance.

This battery charged in under a minute in tests. At 25 degrees Celsius, the battery will charge 25 times slower than at 110 degrees Celsius. This is because the salt, which has a very low melting point, is in an ideal state at 110 degrees and can carry a charge incredibly quickly. Unlike lithium-ion, this battery self-heats when charging and discharging, therefore no external heating is needed.

Anyone who's seen a lithium-ion battery burst might be surprised. Unlike lithium-ion batteries, none of the components in this new battery can catch fire. Thus, high-temperature charging and discharging speeds pose no concern.

These batteries are long-lasting. Lithium-ion batteries don't last long, as any iPhone owner can attest. During charging, metal forms a dendrite on the electrode. This metal spike will keep growing until it reaches the other end of the battery, short-circuiting it. This is why phone batteries only last a few years and why electric car range decreases over time. This new battery's molten salt slows deposition, extending its life. This helps the environment and our wallets.

These batteries are also energy dense. Some lithium-ion batteries have 270 Wh/kg energy density (volume and mass). Aluminum-sulfur batteries could have 1392 Wh/kg, according to calculations. They'd be 5x more energy dense. Tesla's Model 3 battery would weigh 96 kg instead of 480 kg if this battery were used. This would improve the car's efficiency and handling.

These calculations were for batteries without molten salt electrolyte. Because they don't reflect the exact battery chemistry, they aren't a surefire prediction.

This battery seems great. It will take years, maybe decades, before it reaches the market and makes a difference. Right?

Nope. The project's scientists founded Avanti to develop and market this technology.

So we'll soon be driving cheap, durable, eco-friendly, lightweight, and ultra-safe EVs? Nope.

This battery must be kept hot to keep the salt molten; otherwise, it won't work and will expand and contract, causing damage. This issue could be solved by packs that can rapidly pre-heat, but that project is far off.

Rapid and constant charge-discharge cycles make these batteries ideal for solar farms, homes, and EV charging stations. The battery is constantly being charged or discharged, allowing it to self-heat and maintain an ideal temperature.

These batteries aren't as sexy as those making EVs faster, more efficient, and cheaper. Grid batteries are crucial to our net-zero transition because they allow us to use more low-carbon energy. As we move away from fossil fuels, we'll need millions of these batteries, so the fact that they're cheap, safe, long-lasting, and environmentally friendly will be huge. Who knows, maybe EVs will use this technology one day. MIT has created another world-changing technology.

The Lex Fridman podcast host has interviewed Elon Musk.

Lex is a minimalist YouTuber. His videos are sloppy. Suits are his trademark.

In a video, he shares a typical day. I've smashed my 6-month goals using its ideas.

Here's his schedule.

Morning Mantra

Not woo-woo. Lex's mantra reflects his practicality.

Four parts.

Rulebook

"I remember the game's rules," he says.

Among them:

• Sleeping 6–8 hours nightly

• 1–3 times a day, he checks social media.

• Every day, despite pain, he exercises. "I exercise uninjured body parts."

Visualize

He imagines his day. "Like Sims..."

He says three things he's grateful for and contemplates death.

"Today may be my last"

Objectives

Then he visualizes his goals. He starts big. Five-year goals.

Short-term goals follow. Lex says they're year-end goals.

Near but out of reach.

Principles

He lists his principles. Assertions. His goals.

He acknowledges his cliche beliefs. Compassion, empathy, and strength are key.

Here's my mantra routine:

Four-Hour Deep Work

Lex begins a four-hour deep work session after his mantra routine. Today's toughest.

AI is Lex's specialty. His video doesn't explain what he does.

Clearly, he works hard.

Before starting, he has water, coffee, and a bathroom break.

"During deep work sessions, I minimize breaks."

He's distraction-free. Phoneless. Silence. Nothing. Any loose ideas are typed into a Google doc for later. He wants to work.

"Just get the job done. Don’t think about it too much and feel good once it’s complete." — Lex Fridman

30-Minute Social Media & Music

After his first deep work session, Lex rewards himself.

10 minutes on social media, 20 on music. Upload content and respond to comments in 10 minutes. 20 minutes for guitar or piano.

"In the real world, I’m currently single, but in the music world, I’m in an open relationship with this beautiful guitar. Open relationship because sometimes I cheat on her with the acoustic." — Lex Fridman

Two-hour exercise

Then exercise for two hours.

Daily runs six miles. Then he chooses how far to go. Run time is an hour.

He does bodyweight exercises. Every minute for 15 minutes, do five pull-ups and ten push-ups. It's David Goggins-inspired. He aims for an hour a day.

He's hungry. Before running, he takes a salt pill for electrolytes.

He'll then take a one-minute cold shower while listening to cheesy songs. Afterward, he might eat.

Four-Hour Deep Work

Lex's second work session.

He works 8 hours a day.

Again, zero distractions.

Eating

The video's meal doesn't look appetizing, but it's healthy.

It's ground beef with vegetables. Cauliflower is his "ground-floor" veggie. "Carrots are my go-to party food."

Lex's keto diet includes 1800–2000 calories.

He drinks a "nutrient-packed" Atheltic Greens shake and takes tablets. It's:

• One daily tablet of sodium.

• Magnesium glycinate tablets stopped his keto headaches.

• Potassium — "For electrolytes"

• Fish oil: healthy joints

“So much of nutrition science is barely a science… I like to listen to my own body and do a one-person, one-subject scientific experiment to feel good.” — Lex Fridman

Four-hour shallow session

This work isn't as mentally taxing.

Lex planned to:

• Finish last session's deep work (about an hour)

• Adobe Premiere podcasting (about two hours).

• Email-check (about an hour). Three times a day max. First, check for emergencies.

If he's sick, he may watch Netflix or YouTube documentaries or visit friends.

“The possibilities of chaos are wide open, so I can do whatever the hell I want.” — Lex Fridman

Two-hour evening reading

Nonstop work.

Lex ends the day reading academic papers for an hour. "Today I'm skimming two machine learning and neuroscience papers"

This helps him "think beyond the paper."

He reads for an hour.

“When I have a lot of energy, I just chill on the bed and read… When I’m feeling tired, I jump to the desk…” — Lex Fridman

Takeaways

Lex's day-in-the-life video is inspiring.

He has positive energy and works hard every day.

Schedule:

• Mantra Routine includes rules, visualizing, goals, and principles.

• Deep Work Session #1: Four hours of focus.

• 10 minutes social media, 20 minutes guitar or piano. "Music brings me joy"

• Six-mile run, then bodyweight workout. Two hours total.

• Deep Work #2: Four hours with no distractions. Google Docs stores random thoughts.

• Lex supplements his keto diet.

• This four-hour session is "open to chaos."

• Evening reading: academic papers followed by fiction.

"I value some things in life. Work is one. The other is loving others. With those two things, life is great." — Lex Fridman