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?

Better technology and lower launch costs revive science-fiction tech.

Airbus engineers showed off sustainable energy's future in Munich last month. They captured sunlight with solar panels, turned it into microwaves, and beamed it into an airplane hangar, where it lighted a city model. The test delivered 2 kW across 36 meters, but it posed a serious question: Should we send enormous satellites to capture solar energy in space? In orbit, free of clouds and nighttime, they could create power 24/7 and send it to Earth.

Airbus engineer Jean-Dominique Coste calls it an engineering problem. “But it’s never been done at [large] scale.”

Proponents of space solar power say the demand for green energy, cheaper space access, and improved technology might change that. Once someone invests commercially, it will grow. Former NASA researcher John Mankins says it might be a trillion-dollar industry.

Myriad uncertainties remain, including whether beaming gigawatts of power to Earth can be done efficiently and without burning birds or people. Concept papers are being replaced with ground and space testing. The European Space Agency (ESA), which supported the Munich demo, will propose ground tests to member nations next month. The U.K. government offered £6 million to evaluate innovations this year. Chinese, Japanese, South Korean, and U.S. agencies are working. NASA policy analyst Nikolai Joseph, author of an upcoming assessment, thinks the conversation's tone has altered. What formerly appeared unattainable may now be a matter of "bringing it all together"

NASA studied space solar power during the mid-1970s fuel crunch. A projected space demonstration trip using 1970s technology would have cost $1 trillion. According to Mankins, the idea is taboo in the agency.

Space and solar power technology have evolved. Photovoltaic (PV) solar cell efficiency has increased 25% over the past decade, Jones claims. Telecoms use microwave transmitters and receivers. Robots designed to repair and refuel spacecraft might create solar panels.

Falling launch costs have boosted the idea. A solar power satellite large enough to replace a nuclear or coal plant would require hundreds of launches. ESA scientist Sanjay Vijendran: "It would require a massive construction complex in orbit."

SpaceX has made the idea more plausible. A SpaceX Falcon 9 rocket costs $2600 per kilogram, less than 5% of what the Space Shuttle did, and the company promised $10 per kilogram for its giant Starship, slated to launch this year. Jones: "It changes the equation." "Economics rules"

Mass production reduces space hardware costs. Satellites are one-offs made with pricey space-rated parts. Mars rover Perseverance cost $2 million per kilogram. SpaceX's Starlink satellites cost less than $1000 per kilogram. This strategy may work for massive space buildings consisting of many identical low-cost components, Mankins has long contended. Low-cost launches and "hypermodularity" make space solar power economical, he claims.

Better engineering can improve economics. Coste says Airbus's Munich trial was 5% efficient, comparing solar input to electricity production. When the Sun shines, ground-based solar arrays perform better. Studies show space solar might compete with existing energy sources on price if it reaches 20% efficiency.

Lighter parts reduce costs. "Sandwich panels" with PV cells on one side, electronics in the middle, and a microwave transmitter on the other could help. Thousands of them build a solar satellite without heavy wiring to move power. In 2020, a team from the U.S. Naval Research Laboratory (NRL) flew on the Air Force's X-37B space plane.

NRL project head Paul Jaffe said the satellite is still providing data. The panel converts solar power into microwaves at 8% efficiency, but not to Earth. The Air Force expects to test a beaming sandwich panel next year. MIT will launch its prototype panel with SpaceX in December.

As a satellite orbits, the PV side of sandwich panels sometimes faces away from the Sun since the microwave side must always face Earth. To maintain 24-hour power, a satellite needs mirrors to keep that side illuminated and focus light on the PV. In a 2012 NASA study by Mankins, a bowl-shaped device with thousands of thin-film mirrors focuses light onto the PV array.

International Electric Company's Ian Cash has a new strategy. His proposed satellite uses enormous, fixed mirrors to redirect light onto a PV and microwave array while the structure spins (see graphic, above). 1 billion minuscule perpendicular antennas act as a "phased array" to electronically guide the beam toward Earth, regardless of the satellite's orientation. This design, argues Cash, is "the most competitive economically"

If a space-based power plant ever flies, its power must be delivered securely and efficiently. Jaffe's team at NRL just beamed 1.6 kW over 1 km, and teams in Japan, China, and South Korea have comparable attempts. Transmitters and receivers lose half their input power. Vijendran says space solar beaming needs 75% efficiency, "preferably 90%."

Beaming gigawatts through the atmosphere demands testing. Most designs aim to produce a beam kilometers wide so every ship, plane, human, or bird that strays into it only receives a tiny—hopefully harmless—portion of the 2-gigawatt transmission. Receiving antennas are cheap to build but require a lot of land, adds Jones. You could grow crops under them or place them offshore.

Europe's public agencies currently prioritize space solar power. Jones: "There's a devotion you don't see in the U.S." ESA commissioned two solar cost/benefit studies last year. Vijendran claims it might match ground-based renewables' cost. Even at a higher price, equivalent to nuclear, its 24/7 availability would make it competitive.

ESA will urge member states in November to fund a technical assessment. If the news is good, the agency will plan for 2025. With €15 billion to €20 billion, ESA may launch a megawatt-scale demonstration facility by 2030 and a gigawatt-scale facility by 2040. "Moonshot"

Monkeypox was rare until recently. In 2005, a research called a cluster of six monkeypox cases in the Republic of Congo "the longest reported chain to date."

That's changed. This year, over 25,000 monkeypox cases have been reported in 83 countries, indicating widespread human-to-human transmission.

What spreads monkeypox? Monkeypox transmission research is ongoing; findings may change. But science says...

Most cases were formerly animal-related.

According to the WHO, monkeypox was first diagnosed in an infant in the DRC in 1970. After that, instances were infrequent and often tied to animals. In 2003, 47 Americans contracted rabies from pet prairie dogs.

In 2017, Nigeria saw a significant outbreak. NPR reported that doctors diagnosed young guys without animal exposure who had genital sores. Nigerian researchers highlighted the idea of sexual transmission in a 2019 study, but the theory didn't catch on. “People tend to cling on to tradition, and the idea is that monkeypox is transmitted from animals to humans,” explains research co-author Dr. Dimie Ogoina.

Most monkeypox cases are sex-related.

Human-to-human transmission of monkeypox occurs, and sexual activity plays a role.

Joseph Osmundson, a clinical assistant professor of biology at NYU, says most transmission occurs in queer and gay sexual networks through sexual or personal contact.

Monkeypox spreads by skin-to-skin contact, especially with its blister-like rash, explains Ogoina. Researchers are exploring whether people can be asymptomatically contagious, but they are infectious until their rash heals and fresh skin forms, according to the CDC.

A July research in the New England Journal of Medicine reported that of more than 500 monkeypox cases in 16 countries as of June, 95% were linked to sexual activity and 98% were among males who have sex with men. WHO Director-General Tedros Adhanom Ghebreyesus encouraged males to temporarily restrict their number of male partners in July.

Is monkeypox a sexually transmitted infection (STI)?

Skin-to-skin contact can spread monkeypox, not simply sexual activities. Dr. Roy Gulick, infectious disease chief at Weill Cornell Medicine and NewYork-Presbyterian, said monkeypox is not a "typical" STI. Monkeypox isn't a STI, claims the CDC.

Most cases in the current outbreak are tied to male sexual behavior, but Osmundson thinks the virus might also spread on sports teams, in spas, or in college dorms.

Can you get monkeypox from surfaces?

Monkeypox can be spread by touching infected clothing or bedding. According to a study, a U.K. health care worker caught monkeypox in 2018 after handling ill patient's bedding.

Angela Rasmussen, a virologist at the University of Saskatchewan in Canada, believes "incidental" contact seldom distributes the virus. “You need enough virus exposure to get infected,” she says. It's conceivable after sharing a bed or towel with an infectious person, but less likely after touching a doorknob, she says.

Dr. Müge evik, a clinical lecturer in infectious diseases at the University of St. Andrews in Scotland, says there is a "spectrum" of risk connected with monkeypox. "Every exposure isn't equal," she explains. "People must know where to be cautious. Reducing [sexual] partners may be more useful than cleaning coffee shop seats.

Is monkeypox airborne?

Exposure to an infectious person's respiratory fluids can cause monkeypox, but the WHO says it needs close, continuous face-to-face contact. CDC researchers are still examining how often this happens.

Under precise laboratory conditions, scientists have shown that monkeypox can spread via aerosols, or tiny airborne particles. But there's no clear evidence that this is happening in the real world, Rasmussen adds. “This is expanding predominantly in communities of males who have sex with men, which suggests skin-to-skin contact,” she explains. If airborne transmission were frequent, she argues, we'd find more occurrences in other demographics.

In the shadow of COVID-19, people are worried about aerosolized monkeypox. Rasmussen believes the epidemiology is different. Different viruses.

Can kids get monkeypox?

More than 80 youngsters have contracted the virus thus far, mainly through household transmission. CDC says pregnant women can spread the illness to their fetus.

Among the 1970s, monkeypox predominantly affected children, but by the 2010s, it was more common in adults, according to a February study. The study's authors say routine smallpox immunization (which protects against monkeypox) halted when smallpox was eradicated. Only toddlers were born after smallpox vaccination halted decades ago. More people are vulnerable now.

Schools and daycares could become monkeypox hotspots, according to pediatric instances. Ogoina adds this hasn't happened in Nigeria's outbreaks, which is encouraging. He says, "I'm not sure if we should worry." We must be careful and seek evidence.

I pitched 10 brands per workday for a total of 200.

How did I do?

It was difficult.

I've never pitched so much.

What did this challenge teach me?

• the superiority of quality over quantity

• When you need help, outsource

• Don't disregard burnout in order to complete a challenge because it exists.

First, pitching brands for brand deals requires quality. Find firms that align with your brand to expose to your audience.

If you associate with any company, you'll lose audience loyalty. I didn't lose sight of that, but I couldn't resist finishing the task.

Outsourcing.

Delegating work to teammates is effective.

I wish I'd done it.

Three people can pitch 200 companies a month significantly faster than one.

One person does research, one to two do outreach, and one to two do follow-up and negotiating.

Simple.

In 2022, I'll outsource everything.

Burnout.

I felt this, so I slowed down at the end of the month.

Thanksgiving week in November was slow.

I was buying and decorating for Christmas. First time putting up outdoor holiday lights was fun.

Much was happening.

I'm not perfect.

I'm being honest.

The Outcomes

Less than 50 brands pitched.

Result: A deal with 3 brands.

I hoped for 4 brands with reaching out to 200 companies, so three with under 50 is wonderful.

That’s a 6% conversion rate!

Whoo-hoo!

I needed 2%.

Here's a screenshot from one of the deals I booked.

These companies fit my company well. Each campaign is different, but I've booked $2,450 in brand work with a couple of pending transactions for December and January.

$2,450 in brand work booked!

How did I do? You tell me.

Is this something you’d try yourself?

"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.

Using math to write efficient code in any language

Programmers design, build, test, and maintain software. Employ cases and personal preferences determine the programming languages we use throughout development. Mobile app developers use JavaScript or Dart. Some programmers design performance-first software in C/C++.

A generic source code includes language-specific grammar, pre-implemented function calls, mathematical operators, and control statements. Some mathematical principles assist us enhance our programming and problem-solving skills.

We all use basic mathematical concepts like formulas and relational operators (aka comparison operators) in programming in our daily lives. Beyond these mathematical syntaxes, we'll see discrete math topics. This narrative explains key math topics programmers must know. Master these ideas to produce clean and efficient software code.

Expressions in mathematics and built-in mathematical functions

A source code can only contain a mathematical algorithm or prebuilt API functions. We develop source code between these two ends. If you create code to fetch JSON data from a RESTful service, you'll invoke an HTTP client and won't conduct any math. If you write a function to compute the circle's area, you conduct the math there.

When your source code gets more mathematical, you'll need to use mathematical functions. Every programming language has a math module and syntactical operators. Good programmers always consider code readability, so we should learn to write readable mathematical expressions.

Linux utilizes clear math expressions.

Inbuilt max and min functions can minimize verbose if statements.

How can we compute the number of pages needed to display known data? In such instances, the ceil function is often utilized.

import math as m
results = 102
items_per_page = 10 
pages = m.ceil(results / items_per_page)
print(pages)

Learn to write clear, concise math expressions.

Combinatorics in Algorithm Design

Combinatorics theory counts, selects, and arranges numbers or objects. First, consider these programming-related questions. Four-digit PIN security? what options exist? What if the PIN has a prefix? How to locate all decimal number pairs?

Combinatorics questions. Software engineering jobs often require counting items. Combinatorics counts elements without counting them one by one or through other verbose approaches, therefore it enables us to offer minimum and efficient solutions to real-world situations. Combinatorics helps us make reliable decision tests without missing edge cases. Write a program to see if three inputs form a triangle. This is a question I commonly ask in software engineering interviews.

Graph theory is a subfield of combinatorics. Graph theory is used in computerized road maps and social media apps.

Logarithms and Geometry Understanding

Geometry studies shapes, angles, and sizes. Cartesian geometry involves representing geometric objects in multidimensional planes. Geometry is useful for programming. Cartesian geometry is useful for vector graphics, game development, and low-level computer graphics. We can simply work with 2D and 3D arrays as plane axes.

GetWindowRect is a Windows GUI SDK geometric object.

High-level GUI SDKs and libraries use geometric notions like coordinates, dimensions, and forms, therefore knowing geometry speeds up work with computer graphics APIs.

How does exponentiation's inverse function work? Logarithm is exponentiation's inverse function. Logarithm helps programmers find efficient algorithms and solve calculations. Writing efficient code involves finding algorithms with logarithmic temporal complexity. Programmers prefer binary search (O(log n)) over linear search (O(n)). Git source specifies O(log n):

Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.

Employing Mathematical Data Structures

Programmers must know data structures to develop clean, efficient code. Stack, queue, and hashmap are computer science basics. Sets and graphs are discrete arithmetic data structures. Most computer languages include a set structure to hold distinct data entries. In most computer languages, graphs can be represented using neighboring lists or objects.

Using sets as deduped lists is powerful because set implementations allow iterators. Instead of a list (or array), store WebSocket connections in a set.

Most interviewers ask graph theory questions, yet current software engineers don't practice algorithms. Graph theory challenges become obligatory in IT firm interviews.

Recognizing Applications of Recursion

A function in programming isolates input(s) and output(s) (s). Programming functions may have originated from mathematical function theories. Programming and math functions are different but similar. Both function types accept input and return value.

Recursion involves calling the same function inside another function. In its implementation, you'll call the Fibonacci sequence. Recursion solves divide-and-conquer software engineering difficulties and avoids code repetition. I recently built the following recursive Dart code to render a Flutter multi-depth expanding list UI:

Recursion is not the natural linear way to solve problems, hence thinking recursively is difficult. Everything becomes clear when a mathematical function definition includes a base case and recursive call.

Conclusion

Every codebase uses arithmetic operators, relational operators, and expressions. To build mathematical expressions, we typically employ log, ceil, floor, min, max, etc. Combinatorics, geometry, data structures, and recursion help implement algorithms. Unless you operate in a pure mathematical domain, you may not use calculus, limits, and other complex math in daily programming (i.e., a game engine). These principles are fundamental for daily programming activities.

Master the above math fundamentals to build clean, efficient code.