"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.

Would you abandon your bank for Apple?

Banks are struggling.

• not as a result of inflation

• not due to the economic downturn.

• not due to the conflict in Ukraine.

But because they’re underestimating Apple.

Slowly but surely, Apple is looking more like a bank.

An easy new savings account like Apple

Apple has a new savings account.

Apple says Apple Card users may set up and manage savings straight in Wallet.

• No more charges

• Colorfully high yields

• With no minimum balance

• No minimal down payments

Most consumer-facing banks will have to match Apple's offer or suffer disruption.

Users may set it up from their iPhones without traveling to a bank or filling out paperwork.

It’s built into the iPhone in your pocket.

So now more waiting for slow approval processes.

Once the savings account is set up, Apple will automatically transfer all future Daily Cash into it. Users may also add these cash to an Apple Cash card in their Apple Wallet app and adjust where Daily Cash is paid at any time.

Apple Pay and Apple Wallet VP Jennifer Bailey:

Savings enables Apple Card users to grow their Daily Cash rewards over time, while also saving for the future.

Bailey says Savings adds value to Apple Card's Daily Cash benefit and offers another easy-to-use tool to help people lead healthier financial lives.

Transfer money from a linked bank account or Apple Cash to a Savings account. Users can withdraw monies to a connected bank account or Apple Cash card without costs.

Once set up, Apple Card customers can track their earnings via Wallet's Savings dashboard. This dashboard shows their account balance and interest.

This product targets younger people as the easiest way to start a savings account on the iPhone.

Why would a Gen Z account holder travel to the bank if their iPhone could be their bank?

Using this concept, Apple will transform the way we think about banking by 2030.

Two other nightmares keep bankers awake at night

Apple revealed two new features in early 2022 that banks and payment gateways hated.

• Tap to Pay with Apple

• Late Apple Pay

They startled the industry.

Tap To Pay converts iPhones into mobile POS card readers. Apple Pay Later is pushing the BNPL business in a consumer-friendly direction, hopefully ending dodgy lending practices.

Tap to Pay with Apple

iPhone POS

Millions of US merchants, from tiny shops to huge establishments, will be able to accept Apple Pay, contactless credit and debit cards, and other digital wallets with a tap.

No hardware or payment terminal is needed.

Revolutionary!

Stripe has previously launched this feature.

Tap to Pay on iPhone will provide companies with a secure, private, and quick option to take contactless payments and unleash new checkout experiences, said Bailey.

Apple's solution is ingenious. Brilliant!

Bailey says that payment platforms, app developers, and payment networks are making it easier than ever for businesses of all sizes to accept contactless payments and thrive.

I admire that Apple is offering this up to third-party services instead of closing off other functionalities.

Slow POS terminals, farewell.

Late Apple Pay

Pay Apple later.

Apple Pay Later enables US consumers split Apple Pay purchases into four equal payments over six weeks with no interest or fees.

The Apple ecosystem integration makes this BNPL scheme unique. Nonstick. No dumb forms.

Frictionless.

Just double-tap the button.

Apple Pay Later was designed with users' financial well-being in mind. Apple makes it easy to use, track, and pay back Apple Pay Later from Wallet.

Apple Pay Later can be signed up in Wallet or when using Apple Pay. Apple Pay Later can be used online or in an app that takes Apple Pay and leverages the Mastercard network.

Apple Pay Order Tracking helps consumers access detailed receipts and order tracking in Wallet for Apple Pay purchases at participating stores.

Bad BNPL suppliers, goodbye.

Most bankers will be caught in Apple's eye playing mini golf in high-rise offices.

The big problem:

• Banks still think about features and big numbers just like other smartphone makers did not too long ago.

• Apple thinks about effortlessness, seamlessness, and frictionlessness that just work through integrated hardware and software.

Let me know what you think Apple’s next power moves in the banking industry could be.

Most crypto is probably too.

The goals of Web 3 and the metaverse are admirable and attractive. Who doesn't want an internet owned by users? Who wouldn't want a digital realm where anything is possible? A better way to collaborate and visit pals.

Companies pursue profits endlessly. Infinite growth and revenue are expected, and if a corporation needs to sacrifice profits to safeguard users, the CEO, board of directors, and any executives will lose to the system of incentives that (1) retains workers with shares and (2) makes a company answerable to all of its shareholders. Only the government can guarantee user protections, but we know how successful that is. This is nothing new, just a problem with modern capitalism and tech platforms that a user-owned internet might remedy. Moxie, the founder of Signal, has a good articulation of some of these current Web 2 tech platform problems (but I forget the timestamp); thoughts on JRE aside, this episode is worth listening to (it’s about a bunch of other stuff too).

Moxie Marlinspike, founder of Signal, on the Joe Rogan Experience podcast.

Source: https://open.spotify.com/episode/2uVHiMqqJxy8iR2YB63aeP?si=4962b5ecb1854288

Web 3 champions are premature. There was so much spectacular growth during Web 2 that the next wave of founders want to make an even bigger impact, while investors old and new want a chance to get a piece of the moonshot action. Worse, crypto enthusiasts believe — and financially need — the fact of its success to be true, whether or not it is.

I’m doubtful that it will play out like current proponents say. Crypto has been the white-hot focus of SV’s best and brightest for a long time yet still struggles to come up any mainstream use case other than ‘buy, HODL, and believe’: a store of value for your financial goals and wishes. Some kind of the metaverse is likely, but will it be decentralized, mostly in VR, or will Meta (previously FB) play a big role? Unlikely.

METAVERSE

The metaverse exists already. Our digital lives span apps, platforms, and games. I can design a 3D house, invite people, use Discord, and hang around in an artificial environment. Millions of gamers do this in Rust, Minecraft, Valheim, and Animal Crossing, among other games. Discord's voice chat and Slack-like servers/channels are the present social anchor, but the interface, integrations, and data portability will improve. Soon you can stream YouTube videos on digital house walls. You can doodle, create art, play Jackbox, and walk through a door to play Apex Legends, Fortnite, etc. Not just gaming. Digital whiteboards and screen sharing enable real-time collaboration. They’ll review code and operate enterprises. Music is played and made. In digital living rooms, they'll watch movies, sports, comedy, and Twitch. They'll tweet, laugh, learn, and shittalk.

The metaverse is the evolution of our digital life at home, the third place. The closest analog would be Discord and the integration of Facebook, Slack, YouTube, etc. into a single, 3D, customizable hangout space.

I'm not certain this experience can be hugely decentralized and smoothly choreographed, managed, and run, or that VR — a luxury, cumbersome, and questionably relevant technology — must be part of it. Eventually, VR will be pragmatic, achievable, and superior to real life in many ways. A total sensory experience like the Matrix or Sword Art Online, where we're physically hooked into the Internet yet in our imaginations we're jumping, flying, and achieving athletic feats we never could in reality; exploring realms far grander than our own (as grand as it is). That VR is different from today's.

https://podcasts.google.com/feed/aHR0cHM6Ly9leHBvbmVudC5mbS9mZWVkLw/episode/aHR0cHM6Ly9leHBvbmVudC5mbS8_cD00MzM?hl=en&ved=2ahUKEwjH5u6r4rv2AhUjc98KHeybAP8QjrkEegQIChAF&ep=6

Ben Thompson released an episode of Exponent after Facebook changed its name to Meta. Ben was suspicious about many metaverse champion claims, but he made a good analogy between Oculus and the PC. The PC was initially far too pricey for the ordinary family to afford. It began as a business tool. It got so powerful and pervasive that it affected our personal life. Price continues to plummet and so much consumer software was produced that it's impossible to envision life without a home computer (or in our pockets). If Facebook shows product market fit with VR in business, through use cases like remote work and collaboration, maybe VR will become practical in our personal lives at home.

Before PCs, we relied on Blockbuster, the Yellow Pages, cabs to get to the airport, handwritten taxes, landline phones to schedule social events, and other archaic methods. It is impossible for me to conceive what VR, in the form of headsets and hand controllers, stands to give both professional and especially personal digital experiences that is an order of magnitude better than what we have today. Is looking around better than using a mouse to examine a 3D landscape? Do the hand controls make x10 or x100 work or gaming more fun or efficient? Will VR replace scalable Web 2 methods and applications like Web 1 and Web 2 did for analog? I don't know.

My guess is that the metaverse will arrive slowly, initially on displays we presently use, with more app interoperability. I doubt that it will be controlled by the people or by Facebook, a corporation that struggles to properly innovate internally, as practically every large digital company does. Large tech organizations are lousy at hiring product-savvy employees, and if they do, they rarely let them explore new things.

These companies act like business schools when they seek founders' results, with bureaucracy and dependency. Which company launched the last popular consumer software product that wasn't a clone or acquisition? Recent examples are scarce.

Web 3

Investors and entrepreneurs of Web 3 firms are declaring victory: 'Web 3 is here!' Web 3 is the future! Many profitable Web 2 enterprises existed when Web 2 was defined. The word was created to explain user behavior shifts, not a personal pipe dream.

Origins of Web 2: http://www.oreilly.com/pub/a/web2/archive/what-is-web-20.html

One of these Web 3 startups may provide the connecting tissue to link all these experiences or become one of the major new digital locations. Even so, successful players will likely use centralized power arrangements, as Web 2 businesses do now. Some Web 2 startups integrated our digital lives. Rockmelt (2010–2013) was a customizable browser with bespoke connectors to every program a user wanted; imagine seeing Facebook, Twitter, Discord, Netflix, YouTube, etc. all in one location. Failure. Who knows what Opera's doing?

Silicon Valley and tech Twitter in general have a history of jumping on dumb bandwagons that go nowhere. Dot-com crash in 2000? The huge deployment of capital into bad ideas and businesses is well-documented. And live video. It was the future until it became a niche sector for gamers. Live audio will play out a similar reality as CEOs with little comprehension of audio and no awareness of lasting new user behavior deceive each other into making more and bigger investments on fool's gold. Twitter trying to buy Clubhouse for $4B, Spotify buying Greenroom, Facebook exploring live audio and 'Tiktok for audio,' and now Amazon developing a live audio platform. This live audio frenzy won't be worth their time or energy. Blind guides blind. Instead of learning from prior failures like Twitter buying Periscope for $100M pre-launch and pre-product market fit, they're betting on unproven and uncompelling experiences.

NFTs

NFTs are also nonsense. Take Loot, a time-limited bag drop of "things" (text on the blockchain) for a game that didn't exist, bought by rich techies too busy to play video games and foolish enough to think they're getting in early on something with a big reward. What gaming studio is incentivized to use these items? Who's encouraged to join? No one cares besides Loot owners who don't have NFTs. Skill, merit, and effort should be rewarded with rare things for gamers. Even if a small minority of gamers can make a living playing, the average game's major appeal has never been to make actual money - that's a profession.

No game stays popular forever, so how is this objective sustainable? Once popularity and usage drop, exclusive crypto or NFTs will fall. And if NFTs are designed to have cross-game appeal, incentives apart, 30 years from now any new game will need millions of pre-existing objects to build around before they start. It doesn’t work.

Many games already feature item economies based on real in-game scarcity, generally for cosmetic things to avoid pay-to-win, which undermines scaled gaming incentives for huge player bases. Counter-Strike, Rust, etc. may be bought and sold on Steam with real money. Since the 1990s, unofficial cross-game marketplaces have sold in-game objects and currencies. NFTs aren't needed. Making a popular, enjoyable, durable game is already difficult.

With NFTs, certain JPEGs on the internet went from useless to selling for $69 million. Why? Crypto, Web 3, early Internet collectibles. NFTs are digital Beanie Babies (unlike NFTs, Beanie Babies were a popular children's toy; their destinies are the same). NFTs are worthless and scarce. They appeal to crypto enthusiasts seeking for a practical use case to support their theory and boost their own fortune. They also attract to SV insiders desperate not to miss the next big thing, not knowing what it will be. NFTs aren't about paying artists and creators who don't get credit for their work.

South Park's Underpants Gnomes

NFTs are a benign, foolish plan to earn money on par with South Park's underpants gnomes. At worst, they're the world of hucksterism and poor performers. Or those with money and enormous followings who, like everyone, don't completely grasp cryptocurrencies but are motivated by greed and status and believe Gary Vee's claim that CryptoPunks are the next Facebook. Gary's watertight logic: if NFT prices dip, they're on the same path as the most successful corporation in human history; buy the dip! NFTs aren't businesses or museum-worthy art. They're bs.

Gary Vee compares NFTs to Amazon.com. vm.tiktok.com/TTPdA9TyH2

We grew up collecting: Magic: The Gathering (MTG) cards printed in the 90s are now worth over $30,000. Imagine buying a digital Magic card with no underlying foundation. No one plays the game because it doesn't exist. An NFT is a contextless image someone conned you into buying a certificate for, but anyone may copy, paste, and use. Replace MTG with Pokemon for younger readers.

When Gary Vee strongarms 30 tech billionaires and YouTube influencers into buying CryptoPunks, they'll talk about it on Twitch, YouTube, podcasts, Twitter, etc. That will convince average folks that the product has value. These guys are smart and/or rich, so I'll get in early like them. Cryptography is similar. No solid, scaled, mainstream use case exists, and no one knows where it's headed, but since the global crypto financial bubble hasn't burst and many people have made insane fortunes, regular people are putting real money into something that is highly speculative and could be nothing because they want a piece of the action. Who doesn’t want free money? Rich techies and influencers won't be affected; normal folks will.

Imagine removing every $1 invested in Bitcoin instantly. What would happen? How far would Bitcoin fall? Over 90%, maybe even 95%, and Bitcoin would be dead. Bitcoin as an investment is the only scalable widespread use case: it's confidence that a better use case will arise and that being early pays handsomely. It's like pouring a trillion dollars into a company with no business strategy or users and a CEO who makes vague future references.

New tech and efforts may provoke a 'get off my lawn' mentality as you approach 40, but I've always prided myself on having a decent bullshit detector, and it's flying off the handle at this foolishness. If we can accomplish a functional, responsible, equitable, and ethical user-owned internet, I'm for it.

Postscript:

I wanted to summarize my opinions because I've been angry about this for a while but just sporadically tweeted about it. A friend handed me a Dan Olson YouTube video just before publication. He's more knowledgeable, articulate, and convincing about crypto. It's worth seeing:

This post is a summary. See the original one here.