"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.

James Howells lost 8,000 bitcoins. He has $11 million to get them back.

His life altered when he threw out an iPhone-sized hard drive.

Howells, from the city of Newport in southern Wales, had two identical laptop hard drives squirreled away in a drawer in 2013. One was blank; the other had 8,000 bitcoins, currently worth around $181 million.

He wanted to toss out the blank one, but the drive containing the Bitcoin went to the dump.

He's determined to reclaim his 2009 stash.

Howells, 36, wants to arrange a high-tech treasure hunt for bitcoins. He can't enter the landfill.

Newport's city council has rebuffed Howells' requests to dig for his hard drive for almost a decade, stating it would be expensive and environmentally destructive.

I got an early look at his $11 million idea to search 110,000 tons of trash. He expects submitting it to the council would convince it to let him recover the hard disk.

110,000 tons of trash, 1 hard drive

Finding a hard disk among heaps of trash may seem Herculean.

Former IT worker Howells claims it's possible with human sorters, robot dogs, and an AI-powered computer taught to find hard drives on a conveyor belt.

His idea has two versions, depending on how much of the landfill he can search.

His most elaborate solution would take three years and cost $11 million to sort 100,000 metric tons of waste. Scaled-down version costs $6 million and takes 18 months.

He's created a team of eight professionals in AI-powered sorting, landfill excavation, garbage management, and data extraction, including one who recovered Columbia's black box data.

The specialists and their companies would be paid a bonus if they successfully recovered the bitcoin stash.

Howells: "We're trying to commercialize this project."

Howells claimed rubbish would be dug up by machines and sorted near the landfill.

Human pickers and a Max-AI machine would sort it. The machine resembles a scanner on a conveyor belt.

Remi Le Grand of Max-AI told us it will train AI to recognize Howells-like hard drives. A robot arm would select candidates.

Howells has added security charges to his scheme because he fears people would steal the hard drive.

He's budgeted for 24-hour CCTV cameras and two robotic "Spot" canines from Boston Dynamics that would patrol at night and look for his hard drive by day.

Howells said his crew met in May at the Celtic Manor Resort outside Newport for a pitch rehearsal.

Richard Hammond's narrative swings from banal to epic.

Richard Hammond filmed the meeting and created a YouTube documentary on Howells.

Hammond said of Howells' squad, "They're committed and believe in him and the idea."

Hammond: "It goes from banal to gigantic." "If I were in his position, I wouldn't have the strength to answer the door."

Howells said trash would be cleaned and repurposed after excavation. Reburying the rest.

"We won't pollute," he declared. "We aim to make everything better."

After the project is finished, he hopes to develop a solar or wind farm on the dump site. The council is unlikely to accept his vision soon.

A council representative told us, "Mr. Howells can't convince us of anything." "His suggestions constitute a significant ecological danger, which we can't tolerate and are forbidden by our permit."

Will the recovered hard drive work?

The "platter" is a glass or metal disc that holds the hard drive's data. Howells estimates 80% to 90% of the data will be recoverable if the platter isn't damaged.

Phil Bridge, a data-recovery expert who consulted Howells, confirmed these numbers.

If the platter is broken, Bridge adds, data recovery is unlikely.

Bridge says he was intrigued by the proposal. "It's an intriguing case," he added. Helping him get it back and proving everyone incorrect would be a great success story.

Who'd pay?

Swiss and German venture investors Hanspeter Jaberg and Karl Wendeborn told us they would fund the project if Howells received council permission.

Jaberg: "It's a needle in a haystack and a high-risk investment."

Howells said he had no contract with potential backers but had discussed the proposal in Zoom meetings. "Until Newport City Council gives me something in writing, I can't commit," he added.

Suppose he finds the bitcoins.

Howells said he would keep 30% of the data, worth $54 million, if he could retrieve it.

A third would go to the recovery team, 30% to investors, and the remainder to local purposes, including gifting £50 ($61) in bitcoin to each of Newport's 150,000 citizens.

Howells said he opted to spend extra money on "professional firms" to help convince the council.

What if the council doesn't approve?

If Howells can't win the council's support, he'll sue, claiming its actions constitute a "illegal embargo" on the hard drive. "I've avoided that path because I didn't want to cause complications," he stated. I wanted to cooperate with Newport's council.

Howells never met with the council face-to-face. He mentioned he had a 20-minute Zoom meeting in May 2021 but thought his new business strategy would help.

He met with Jessica Morden on June 24. Morden's office confirmed meeting.

After telling the council about his proposal, he can only wait. "I've never been happier," he said. This is our most professional operation, with the best employees.

The "crypto proponent" buys bitcoin every month and sells it for cash.

Howells tries not to think about what he'd do with his part of the money if the hard disk is found functional. "Otherwise, you'll go mad," he added.

This post is a summary. Read the full article here.

And why we must keep arming Ukraine

Russian expatriates write about horrific news from home.

Read this from Nadin Brzezinski. She's not a native English speaker, so there are grammar errors, but her tale smells true.

Terrible truth.

There's much more that reveals Russia's grim reality.

Non-leadership. Millions of missing supplies are presumably sold for profit, leaving untrained troops without food or gear. Missile attacks pause because they run out. Fake schemes to hold talks as a way of stalling while they scramble for solutions.

Street men were mobilized. Millions will be ground up to please a crazed despot. Fear, wrath, and hunger pull apart civilization.

It's the most dystopian story, but Ukraine is worse. Destruction of a society, country, and civilization. Only the invaders' corruption and incompetence save the Ukrainians.

Rochester, NY. My suburb had many Soviet-era Ukrainian refugees. Their kids were my classmates. Fifty years later, many are still my friends. I loved their food and culture. My town has 20,000 Ukrainians.

Grieving but determined. They don't quit. They won't quit. Russians are eternal enemies.

It's the Russian people's willingness to tolerate corruption, abuse, and stupidity by their leaders. They are paying. 65000 dead. Ruined economy. No freedom to speak. Americans do not appreciate that freedom as we should.

It lets me write/publish.

Russian friends are shocked. Many are here because their parents escaped Russian anti-semitism and authoritarian oppression. A Russian cultural legacy says a strongman's methods are admirable.

A legacy of a slavery history disguised as serfdom. Peasants and Princes.

Read Tolstoy. Then Anna Karenina. The main characters are princes and counts, whose leaders are incompetent idiots with wealth and power.

Peasants who die in their wars due to incompetence are nameless ciphers.

Sound familiar?