"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.

Who founded bitcoin is the biggest mystery in technology today, not how it works.

On October 31, 2008, Satoshi Nakamoto posted a whitepaper to a cryptography email list. Still confused by the mastermind who changed monetary history.

Journalists and bloggers have tried in vain to uncover bitcoin's creator. Some candidates self-nominated. We're still looking for the mystery's perpetrator because none of them have provided proof.

One person. I'm confident he invented bitcoin. Let's assess Satoshi Nakamoto before I reveal my pick. Or what he wants us to know.

Satoshi's P2P Foundation biography says he was born in 1975. He doesn't sound or look Japanese. First, he wrote the whitepaper and subsequent articles in flawless English. His sleeping habits are unusual for a Japanese person.

Stefan Thomas, a Bitcoin Forum member, displayed Satoshi's posting timestamps. Satoshi Nakamoto didn't publish between 2 and 8 p.m., Japanese time. Satoshi's identity may not be real.

Why would he disguise himself?

There is a legitimate explanation for this

Phil Zimmermann created PGP to give dissidents an open channel of communication, like Pretty Good Privacy. US government seized this technology after realizing its potential. Police investigate PGP and Zimmermann.

This technology let only two people speak privately. Bitcoin technology makes it possible to send money for free without a bank or other intermediary, removing it from government control.

How much do we know about the person who invented bitcoin?

Here's what we know about Satoshi Nakamoto now that I've covered my doubts about his personality.

Satoshi Nakamoto first appeared with a whitepaper on metzdowd.com. On Halloween 2008, he presented a nine-page paper on a new peer-to-peer electronic monetary system.

Using the nickname satoshi, he created the bitcointalk forum. He kept developing bitcoin and created bitcoin.org. Satoshi mined the genesis block on January 3, 2009.

Satoshi Nakamoto worked with programmers in 2010 to change bitcoin's protocol. He engaged with the bitcoin community. Then he gave Gavin Andresen the keys and codes and transferred community domains. By 2010, he'd abandoned the project.

The bitcoin creator posted his goodbye on April 23, 2011. Mike Hearn asked Satoshi if he planned to rejoin the group.

“I’ve moved on to other things. It’s in good hands with Gavin and everyone.”

Nakamoto Satoshi

The man who broke the banking system vanished. Why?

Satoshi's wallets held 1,000,000 BTC. In December 2017, when the price peaked, he had over US$19 billion. Nakamoto had the 44th-highest net worth then. He's never cashed a bitcoin.

This data suggests something happened to bitcoin's creator. I think Hal Finney is Satoshi Nakamoto .

Hal Finney had ALS and died in 2014. I suppose he created the future of money, then he died, leaving us with only rumors about his identity.

Hal Finney, who was he?

Hal Finney graduated from Caltech in 1979. Student peers voted him the smartest. He took a doctoral-level gravitational field theory course as a freshman. Finney's intelligence meets the first requirement for becoming Satoshi Nakamoto.

Students remember Finney holding an Ayn Rand book. If he'd read this, he may have developed libertarian views.

His beliefs led him to a small group of freethinking programmers. In the 1990s, he joined Cypherpunks. This action promoted the use of strong cryptography and privacy-enhancing technologies for social and political change. Finney helped them achieve a crypto-anarchist perspective as self-proclaimed privacy defenders.

Zimmermann knew Finney well.

Hal replied to a Cypherpunk message about Phil Zimmermann and PGP. He contacted Phil and became PGP Corporation's first member, retiring in 2011. Satoshi Nakamoto quit bitcoin in 2011.

Finney improved the new PGP protocol, but he had to do so secretly. He knew about Phil's PGP issues. I understand why he wanted to hide his identity while creating bitcoin.

Why did he pretend to be from Japan?

His envisioned persona was spot-on. He resided near scientist Dorian Prentice Satoshi Nakamoto. Finney could've assumed Nakamoto's identity to hide his. Temple City has 36,000 people, so what are the chances they both lived there? A cryptographic genius with the same name as Bitcoin's creator: coincidence?

Things went differently, I think.

I think Hal Finney sent himself Satoshis messages. I know it's odd. If you want to conceal your involvement, do as follows. He faked messages and transferred the first bitcoins to himself to test the transaction mechanism, so he never returned their money.

Hal Finney created the first reusable proof-of-work system. The bitcoin protocol. In the 1990s, Finney was intrigued by digital money. He invented CRypto cASH in 1993.

Legacy

Hal Finney's contributions should not be forgotten. Even if I'm wrong and he's not Satoshi Nakamoto, we shouldn't forget his bitcoin contribution. He helped us achieve a better future.

German stellarator revamped to run longer, hotter, compete with tokamaks

Tokamaks have dominated the search for fusion energy for decades. Just as ITER, the world's largest and most expensive tokamak, nears completion in southern France, a smaller, twistier testbed will start up in Germany.

If the 16-meter-wide stellarator can match or outperform similar-size tokamaks, fusion experts may rethink their future. Stellarators can keep their superhot gases stable enough to fuse nuclei and produce energy. They can theoretically run forever, but tokamaks must pause to reset their magnet coils.

The €1 billion German machine, Wendelstein 7-X (W7-X), is already getting "tokamak-like performance" in short runs, claims plasma physicist David Gates, preventing particles and heat from escaping the superhot gas. If W7-X can go long, "it will be ahead," he says. "Stellarators excel" Eindhoven University of Technology theorist Josefine Proll says, "Stellarators are back in the game." A few of startup companies, including one that Gates is leaving Princeton Plasma Physics Laboratory, are developing their own stellarators.

W7-X has been running at the Max Planck Institute for Plasma Physics (IPP) in Greifswald, Germany, since 2015, albeit only at low power and for brief runs. W7-X's developers took it down and replaced all inner walls and fittings with water-cooled equivalents, allowing for longer, hotter runs. The team reported at a W7-X board meeting last week that the revised plasma vessel has no leaks. It's expected to restart later this month to show if it can get plasma to fusion-igniting conditions.

Wendelstein 7-X's water-cooled inner surface allows for longer runs.

HOSAN/IPP

Both stellarators and tokamaks create magnetic gas cages hot enough to melt metal. Microwaves or particle beams heat. Extreme temperatures create a plasma, a seething mix of separated nuclei and electrons, and cause the nuclei to fuse, releasing energy. A fusion power plant would use deuterium and tritium, which react quickly. Non-energy-generating research machines like W7-X avoid tritium and use hydrogen or deuterium instead.

Tokamaks and stellarators use electromagnetic coils to create plasma-confining magnetic fields. A greater field near the hole causes plasma to drift to the reactor's wall.

Tokamaks control drift by circulating plasma around a ring. Streaming creates a magnetic field that twists and stabilizes ionized plasma. Stellarators employ magnetic coils to twist, not plasma. Once plasma physicists got powerful enough supercomputers, they could optimize stellarator magnets to improve plasma confinement.

W7-X is the first large, optimized stellarator with 50 6- ton superconducting coils. Its construction began in the mid-1990s and cost roughly twice the €550 million originally budgeted.

The wait hasn't disappointed researchers. W7-X director Thomas Klinger: "The machine operated immediately." "It's a friendly machine." It did everything we asked." Tokamaks are prone to "instabilities" (plasma bulging or wobbling) or strong "disruptions," sometimes associated to halted plasma flow. IPP theorist Sophia Henneberg believes stellarators don't employ plasma current, which "removes an entire branch" of instabilities.

In early stellarators, the magnetic field geometry drove slower particles to follow banana-shaped orbits until they collided with other particles and leaked energy. Gates believes W7-X's ability to suppress this effect implies its optimization works.

W7-X loses heat through different forms of turbulence, which push particles toward the wall. Theorists have only lately mastered simulating turbulence. W7-X's forthcoming campaign will test simulations and turbulence-fighting techniques.

A stellarator can run constantly, unlike a tokamak, which pulses. W7-X has run 100 seconds—long by tokamak standards—at low power. The device's uncooled microwave and particle heating systems only produced 11.5 megawatts. The update doubles heating power. High temperature, high plasma density, and extensive runs will test stellarators' fusion power potential. Klinger wants to heat ions to 50 million degrees Celsius for 100 seconds. That would make W7-X "a world-class machine," he argues. The team will push for 30 minutes. "We'll move step-by-step," he says.

W7-X's success has inspired VCs to finance entrepreneurs creating commercial stellarators. Startups must simplify magnet production.

Princeton Stellarators, created by Gates and colleagues this year, has $3 million to build a prototype reactor without W7-X's twisted magnet coils. Instead, it will use a mosaic of 1000 HTS square coils on the plasma vessel's outside. By adjusting each coil's magnetic field, operators can change the applied field's form. Gates: "It moves coil complexity to the control system." The company intends to construct a reactor that can fuse cheap, abundant deuterium to produce neutrons for radioisotopes. If successful, the company will build a reactor.

Renaissance Fusion, situated in Grenoble, France, raised €16 million and wants to coat plasma vessel segments in HTS. Using a laser, engineers will burn off superconductor tracks to carve magnet coils. They want to build a meter-long test segment in 2 years and a full prototype by 2027.

Type One Energy in Madison, Wisconsin, won DOE money to bend HTS cables for stellarator magnets. The business carved twisting grooves in metal with computer-controlled etching equipment to coil cables. David Anderson of the University of Wisconsin, Madison, claims advanced manufacturing technology enables the stellarator.

Anderson said W7-X's next phase will boost stellarator work. “Half-hour discharges are steady-state,” he says. “This is a big deal.”