"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.

During the dot-com bust, I started my internet career. People used the internet intermittently to check email, plan travel, and do research. The average internet user spent 30 minutes online a day, compared to 7 today. To use the internet, you had to "log on" (most people still used dial-up), unlike today's always-on, high-speed mobile internet. In 2001, Amazon's market cap was $2.2B, 1/500th of what it is today. A study asked Americans if they'd adopt broadband, and most said no. They didn't see a need to speed up email, the most popular internet use. The National Academy of Sciences ranked the internet 13th among the 100 greatest inventions, below radio and phones. The internet was a cool invention, but it had limited uses and wasn't a good place to build a business. 

A small but growing movement of developers and founders believed the internet could be more than a read-only medium, allowing anyone to create and publish. This is web 2. The runner up name was read-write web. (These terms were used in prominent publications and conferences.) 

Web 2 concepts included letting users publish whatever they want ("user generated content" was a buzzword), social graphs, APIs and mashups (what we call composability today), and tagging over hierarchical navigation. Technical innovations occurred. A seemingly simple but important one was dynamically updating web pages without reloading. This is now how people expect web apps to work. Mobile devices that could access the web were niche (I was an avid Sidekick user). 

The contrast between what smart founders and engineers discussed over dinner and on weekends and what the mainstream tech world took seriously during the week was striking. Enterprise security appliances, essentially preloaded servers with security software, were a popular trend. Many of the same people would talk about "serious" products at work, then talk about consumer internet products and web 2. It was tech's biggest news. Web 2 products were seen as toys, not real businesses. They were hobbies, not work-related. 

There's a strong correlation between rich product design spaces and what smart people find interesting, which took me some time to learn and led to blog posts like "The next big thing will start out looking like a toy" Web 2's novel product design possibilities sparked dinner and weekend conversations. Imagine combining these features. What if you used this pattern elsewhere? What new product ideas are next? This excited people. "Serious stuff" like security appliances seemed more limited. 

The small and passionate web 2 community also stood out. I attended the first New York Tech meetup in 2004. Everyone fit in Meetup's small conference room. Late at night, people demoed their software and chatted. I have old friends. Sometimes I get asked how I first met old friends like Fred Wilson and Alexis Ohanian. These topics didn't interest many people, especially on the east coast. We were friends. Real community. Alex Rampell, who now works with me at a16z, is someone I met in 2003 when a friend said, "Hey, I met someone else interested in consumer internet." Rare. People were focused and enthusiastic. Revolution seemed imminent. We knew a secret nobody else did. 

My web 2 startup was called SiteAdvisor. When my co-founders and I started developing the idea in 2003, web security was out of control. Phishing and spyware were common on Internet Explorer PCs. SiteAdvisor was designed to warn users about security threats like phishing and spyware, and then, using web 2 concepts like user-generated reviews, add more subjective judgments (similar to what TrustPilot seems to do today). This staged approach was common at the time; I called it "Come for the tool, stay for the network." We built APIs, encouraged mashups, and did SEO marketing. 

Yahoo's 2005 acquisitions of Flickr and Delicious boosted web 2 in 2005. By today's standards, the amounts were small, around $30M each, but it was a signal. Web 2 was assumed to be a fun hobby, a way to build cool stuff, but not a business. Yahoo was a savvy company that said it would make web 2 a priority. 

As I recall, that's when web 2 started becoming mainstream tech. Early web 2 founders transitioned successfully. Other entrepreneurs built on the early enthusiasts' work. Competition shifted from ideation to execution. You had to decide if you wanted to be an idealistic indie bar band or a pragmatic stadium band. 

Web 2 was booming in 2007 Facebook passed 10M users, Twitter grew and got VC funding, and Google bought YouTube. The 2008 financial crisis tested entrepreneurs' resolve. Smart people predicted another great depression as tech funding dried up. 

Many people struggled during the recession. 2008-2011 was a golden age for startups. By 2009, talented founders were flooding Apple's iPhone app store. Mobile apps were booming. Uber, Venmo, Snap, and Instagram were all founded between 2009 and 2011. Social media (which had replaced web 2), cloud computing (which enabled apps to scale server side), and smartphones converged. Even if social, cloud, and mobile improve linearly, the combination could improve exponentially. 

This chart shows how I view product and financial cycles. Product and financial cycles evolve separately. The Nasdaq index is a proxy for the financial sentiment. Financial sentiment wildly fluctuates. 

Next row shows iconic startup or product years. Bottom-row product cycles dictate timing. Product cycles are more predictable than financial cycles because they follow internal logic. In the incubation phase, enthusiasts build products for other enthusiasts on nights and weekends. When the right mix of technology, talent, and community knowledge arrives, products go mainstream. (I show the biggest tech cycles in the chart, but smaller ones happen, like web 2 in the 2000s and fintech and SaaS in the 2010s.) 

Tech has changed since the 2000s. Few tech giants dominate the internet, exerting economic and cultural influence. In the 2000s, web 2 was ignored or dismissed as trivial. Entrenched interests respond aggressively to new movements that could threaten them. Creative patterns from the 2000s continue today, driven by enthusiasts who see possibilities where others don't. Know where to look. Crypto and web 3 are where I'd start. 

Today's negative financial sentiment reminds me of 2008. If we face a prolonged downturn, we can learn from 2008 by preserving capital and focusing on the long term. Keep an eye on the product cycle. Smart people are interested in things with product potential. This becomes true. Toys become necessities. Hobbies become mainstream. Optimists build the future, not cynics.

Full article is available here

Bear markets don't last forever, but that's hard to remember. Jamie Cullen's illustration

A bear market is a 20% decline from peak to trough in stock prices.

The S&P 500 was down 24% from its January highs at its low point this year. Bear market.

The U.S. stock market has had 13 bear markets since WWII (including the current one). Previous 12 bear markets averaged –32.7% losses. From peak to trough, the stock market averaged 12 months. The average time from bottom to peak was 21 months.

In the past seven decades, a bear market roundtrip to breakeven has averaged less than three years.

Long-term averages can vary widely, as with all historical market data. Investors can learn from past market crashes.

Historical bear markets offer lessons.

Bear market duration

A bear market can cost investors money and time. Most of the pain comes from stock market declines, but bear markets can be long.

Here are the longest U.S. stock bear markets since World war 2:

Stock market crashes can make it difficult to break even. After the 2008 financial crisis, the stock market took 4.5 years to recover. After the dotcom bubble burst, it took seven years to break even.

The longer you're underwater in the market, the more suffering you'll experience, according to research. Suffering can lead to selling at the wrong time.

Bear markets require patience because stocks can take a long time to recover.

Stock crash recovery

Bear markets can end quickly. The Corona Crash in early 2020 is an example.

The S&P 500 fell 34% in 23 trading sessions, the fastest bear market from a high in 90 years. The entire crash lasted one month. Stocks broke even six months after bottoming. Stocks rose 100% from those lows in 15 months.

Seven bear markets have lasted two years or less since 1945.

The 2020 recovery was an outlier, but four other bear markets have made investors whole within 18 months.

During a bear market, you don't know if it will end quickly or feel like death by a thousand cuts.

Recessions vs. bear markets

Many people believe the U.S. economy is in or heading for a recession.

I agree. Four-decade high inflation. Since 1945, inflation has exceeded 5% nine times. Each inflationary spike caused a recession. Only slowing economic demand seems to stop price spikes.

This could happen again. Stocks seem to be pricing in a recession.

Recessions almost always cause a bear market, but a bear market doesn't always equal a recession. In 1946, the stock market fell 27% without a recession in sight. Without an economic slowdown, the stock market fell 22% in 1966. Black Monday in 1987 was the most famous stock market crash without a recession. Stocks fell 30% in less than a week. Many believed the stock market signaled a depression. The crash caused no slowdown.

Economic cycles are hard to predict. Even Wall Street makes mistakes.

Bears vs. bulls

Bear markets for U.S. stocks always end. Every stock market crash in U.S. history has been followed by new all-time highs.

How should investors view the recession? Investing risk is subjective.

You don't have as long to wait out a bear market if you're retired or nearing retirement. Diversification and liquidity help investors with limited time or income. Cash and short-term bonds drag down long-term returns but can ensure short-term spending.

Young people with years or decades ahead of them should view this bear market as an opportunity. Stock market crashes are good for net savers in the future. They let you buy cheap stocks with high dividend yields.

You need discipline, patience, and planning to buy stocks when it doesn't feel right.

Bear markets aren't fun because no one likes seeing their portfolio fall. But stock market downturns are a feature, not a bug. If stocks never crashed, they wouldn't offer such great long-term returns.