Matthew Cluff

3 years ago

GTO Poker 101

"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.

More on Gaming

Ash Parrish

3 years ago

Sonic Prime and indie games on Netflix

Netflix will stream Spiritfarer, Raji: An Ancient Epic, and Lucky Luna.

Netflix's Geeked Week brought a slew of announcements. The flurry of reveals for The Sandman, The Umbrella Academy season 3, One Piece, and more also included game and game-adjacent announcements.

Netflix released a teaser for Cuphead season 2 ahead of its August premiere, featuring more of Grey DeLisle's Ms. Chalice. DOTA: Dragon's Blood season 3 hits Netflix in August. Tekken, the fighting game that throws kids off cliffs, gets an anime, Tekken: Bloodline.

Netflix debuted a clip of Sonic Prime before Sonic Origins in June and Sonic Frontiers in 2022.

Castlevania: Nocturne will follow Richter Belmont.

Netflix is reviving licensed games with titles based on its shows. There's a Queen's Gambit chess game, a Shadow and Bone RPG, a La Casa de Papel heist adventure, and a Too Hot to Handle game where a pregnant woman must choose between stabbing her cheating ex or forgiving him.

Riot's rhythm platformer Hextech Mayhem debuted on Netflix last year, and now Netflix is adding games from Devolver Digital. Reigns: Three Kingdoms is a card game that lets players choose the fate of Three Kingdoms-era China by swiping left or right on cards. Spiritfarer, the "cozy game about death" from 2020, and Raji: An Ancient Epic are coming to Netflix. Poinpy, a vertical climber from the creator of Downwell, is now on Netflix.

Desta: The Memories Between is a turn-based strategy game set in dreams and memories.

Snowman's Lucky Luna will also be added soon.

With these games, Netflix is expanding beyond dinky mobile games — it plans to have 50 by the end of the year — and could be a serious platform for indies that want to expand into mobile. It takes gaming seriously.

Luke Plunkett

3 years ago

Gran Turismo 7 Update Eases Up On The Grind After Fan Outrage

Polyphony Digital has changed the game after apologizing in March.

To make amends for some disastrous downtime, Gran Turismo 7 director Kazunori Yamauchi announced a credits handout and promised to “dramatically change GT7's car economy to help make amends” last month. The first of these has arrived.

The game's 1.11 update includes the following concessions to players frustrated by the economy and its subsequent grind:

The last half of the World Circuits events have increased in-game credit rewards.
Modified Arcade and Custom Race rewards
Clearing all circuit layouts with Gold or Bronze now rewards In-game Credits. Exiting the Sector selection screen with the Exit button will award Credits if an event has already been cleared.
Increased Credits Rewards in Lobby and Daily Races
Increased the free in-game Credits cap from 20,000,000 to 100,000,000.

Additionally, “The Human Comedy” missions are one-hour endurance races that award “up to 1,200,000” credits per event.

This isn't everything Yamauchi promised last month; he said it would take several patches and updates to fully implement the changes. Here's a list of everything he said would happen, some of which have already happened (like the World Cup rewards and credit cap):

Increase rewards in the latter half of the World Circuits by roughly 100%.
Added high rewards for all Gold/Bronze results clearing the Circuit Experience.
Online Races rewards increase.
Add 8 new 1-hour Endurance Race events to Missions. So expect higher rewards.
Increase the non-paid credit limit in player wallets from 20M to 100M.
Expand the number of Used and Legend cars available at any time.
With time, we will increase the payout value of limited time rewards.
New World Circuit events.
Missions now include 24-hour endurance races.
Online Time Trials added, with rewards based on the player's time difference from the leader.
Make cars sellable.

The full list of updates and changes can be found here.

Read the original post.

Chris Moyse

3 years ago

Sony and LEGO raise $2 billion for Epic Games' metaverse

‘Kid-friendly’ project holds $32 billion valuation

Epic Games announced today that it has raised $2 billion USD from Sony Group Corporation and KIRKBI (holding company of The LEGO Group). Both companies contributed $1 billion to Epic Games' upcoming ‘metaverse' project.

“We need partners who share our vision as we reimagine entertainment and play. Our partnership with Sony and KIRKBI has found this,” said Epic Games CEO Tim Sweeney. A new metaverse will be built where players can have fun with friends and brands create creative and immersive experiences, as well as creators thrive.

Last week, LEGO and Epic Games announced their plans to create a family-friendly metaverse where kids can play, interact, and create in digital environments. The service's users' safety and security will be prioritized.

With this new round of funding, Epic Games' project is now valued at $32 billion.

“Epic Games is known for empowering creators large and small,” said KIRKBI CEO Sren Thorup Srensen. “We invest in trends that we believe will impact the world we and our children will live in. We are pleased to invest in Epic Games to support their continued growth journey, with a long-term focus on the future metaverse.”

Epic Games is expected to unveil its metaverse plans later this year, including its name, details, services, and release date.

Marcus Lu

3 years ago

The Brand Structure of U.S. Electric Vehicle Production

Will Tesla be able to maintain its lead in the EV market for very long?

This is one of the most pressing issues in the American auto sector today. One positive aspect of Tesla is the company's devoted customer base and recognizable name recognition (similar to Apple). It also invests more in research and development per vehicle than its rivals and has a head start in EV production.

Conversely, established automakers like Volkswagen are actively plotting their strategy to surpass Tesla. As the current market leaders, they have decades of experience in the auto industry and are spending billions to catch up.

We've visualized data from the EPA's 2022 Automotive Trends Report to bring you up to speed on this developing story.

Info for the Model Year of 2021

The full production data used in this infographic is for the 2021 model year, but it comes from a report for 2022.

Combined EV and PHEV output is shown in the table below (plug-in hybrid electric vehicle).

It is important to note that Toyota and Stellantis, the two largest legacy automakers in this dataset, only produced PHEVs. Toyota's first electric vehicle, the bZ4X, won't hit the market until 2023.

Stellantis seems to be falling even further behind, despite having enormous unrealized potential in its Jeep and Ram brands. Stellantis CEO Carlos Tavares said in a recent interview that the firm has budgeted $36 billion for electrification and software.

Legacy Brands with the Most Momentum

In the race to develop electric vehicles, some long-standing manufacturers have gotten the jump on their rivals.

Volkswagen, one of these storied manufacturers, has made a significant investment in electric vehicles (EVs) in the wake of the Dieselgate scandal. The company plans to roll out multiple EV models, including the ID.3 hatchback, ID.4 SUV, and ID. Buzz, with the goal of producing 22 million EVs by 2028. (an electric revival of the classic Microbus).

Even Ford is keeping up, having just announced an EV investment of $22 billion between 2021 and 2025. In November of 2022, the company manufactured their 150,000th Mustang Mach-E, and by the end of 2023, they hoped to have 270,000 of them in circulation.

Additionally, over 200,000 F-150 Lightnings have been reserved since Ford announced the truck. The Lightning is scheduled to have a production run of 15,000 in 2022, 55,000 in 2023, and 80,000 in 2024. Ford's main competitor in the electric pickup truck segment, Rivian, is on track to sell 25,000 vehicles by 2022.

Stephen Moore

3 years ago

Web 2 + Web 3 = Web 5.

Monkey jpegs and shitcoins have tarnished Web3's reputation. Let’s move on.

Web3 was called "the internet's future."

Well, 'crypto bros' shouted about it loudly.

As quickly as it arrived to be the next internet, it appears to be dead. It's had scandals, turbulence, and crashes galore:

Web 3.0's cryptocurrencies have crashed. Bitcoin's all-time high was $66,935. This month, Ethereum fell from $2130 to $1117. Six months ago, the cryptocurrency market peaked at $3 trillion. Worst is likely ahead.
Gas fees make even the simplest Web3 blockchain transactions unsustainable.
Terra, Luna, and other dollar pegs collapsed, hurting crypto markets. Celsius, a crypto lender backed by VCs and Canada's second-largest pension fund, and Binance, a crypto marketplace, have withheld money and coins. They're near collapse.
NFT sales are falling rapidly and losing public interest.

Web3 has few real-world uses, like most crypto/blockchain technologies. Web3's image has been tarnished by monkey profile pictures and shitcoins while failing to become decentralized (the whole concept is controlled by VCs).

The damage seems irreparable, leaving Web3 in the gutter.

Step forward our new saviour — Web5

Fear not though, as hero awaits to drag us out of the Web3 hellscape. Jack Dorsey revealed his plan to save the internet quickly.

Dorsey has long criticized Web3, believing that VC capital and silicon valley insiders have created a centralized platform. In a tweet that upset believers and VCs (he was promptly blocked by Marc Andreessen), Dorsey argued, "You don't own "Web3." VCs and LPs do. Their incentives prevent it. It's a centralized organization with a new name.

Dorsey announced Web5 on June 10 in a very Elon-like manner. Block's TBD unit will work on the project (formerly Square).

Web5's pitch is that users will control their own data and identity. Bitcoin-based. Sound familiar? The presentation pack's official definition emphasizes decentralization. Web5 is a decentralized web platform that enables developers to write decentralized web apps using decentralized identifiers, verifiable credentials, and decentralized web nodes, returning ownership and control over identity and data to individuals.

Web5 would be permission-less, open, and token-less. What that means for Earth is anyone's guess. Identity. Ownership. Blockchains. Bitcoin. Different.

Web4 appears to have been skipped, forever destined to wish it could have shown the world what it could have been. (It was probably crap.) As this iteration combines Web2 and Web3, simple math and common sense add up to 5. Or something.

Dorsey and his team have had this idea simmering for a while. Daniel Buchner, a member of Block's Decentralized Identity team, said, "We're finishing up Web5's technical components."

Web5 could be the project that decentralizes the internet. It must be useful to users and convince everyone to drop the countless Web3 projects, products, services, coins, blockchains, and websites being developed as I write this.

Web5 may be too late for Dorsey and the incoming flood of creators.

Web6 is planned!

The next months and years will be hectic and less stable than the transition from Web 1.0 to Web 2.0.

Web1 was around 1991-2004.
Web2 ran from 2004 to 2021. (though the Web3 term was first used in 2014, it only really gained traction years later.)
Web3 lasted a year.
Web4 is dead.

Silicon Valley billionaires are turning it into a startup-style race, each disrupting the next iteration until they crack it. Or destroy it completely.

Web5 won't last either.

Thomas Tcheudjio

3 years ago

If you don't crush these 3 metrics, skip the Series A.

I recently wrote about getting VCs excited about Marketplace start-ups. SaaS founders became envious!

Understanding how people wire tens of millions is the only Series A hack I recommend.

Few people understand the intellectual process behind investing.

VC is risk management.

Series A-focused VCs must cover two risks.

1. Market risk

You need a large market to cross a threshold beyond which you can build defensibilities. Series A VCs underwrite market risk.

They must see you have reached product-market fit (PMF) in a large total addressable market (TAM).

2. Execution risk

When evaluating your growth engine's blitzscaling ability, execution risk arises.

When investors remove operational uncertainty, they profit.

Series A VCs like businesses with derisked revenue streams. Don't raise unless you have a predictable model, pipeline, and growth.

Please beat these 3 metrics before Series A:

Achieve $1.5m ARR in 12-24 months (Market risk)
Above 100% Net Dollar Retention. (Market danger)
Lead Velocity Rate supporting $10m ARR in 2–4 years (Execution risk)

Hit the 3 and you'll raise $10M in 4 months. Discussing 2/3 may take 6–7 months.

If none, don't bother raising and focus on becoming a capital-efficient business (Topics for other posts).

Let's examine these 3 metrics for the brave ones.

1. Lead Velocity Rate supporting €$10m ARR in 2 to 4 years

Last because it's the least discussed. LVR is the most reliable data when evaluating a growth engine, in my opinion.

SaaS allows you to see the future.

Monthly Sales and Sales Pipelines, two predictive KPIs, have poor data quality. Both are lagging indicators, and minor changes can cause huge modeling differences.

Analysts and Associates will trash your forecasts if they're based only on Monthly Sales and Sales Pipeline.

LVR, defined as month-over-month growth in qualified leads, is rock-solid. There's no lag. You can See The Future if you use Qualified Leads and a consistent formula and process to qualify them.

With this metric in your hand, scaling your company turns into an execution play on which VCs are able to perform calculations risk.

2. Above-100% Net Dollar Retention.

Net Dollar Retention is a better-known SaaS health metric than LVR.

Net Dollar Retention measures a SaaS company's ability to retain and upsell customers. Ask what $1 of net new customer spend will be worth in years n+1, n+2, etc.

Depending on the business model, SaaS businesses can increase their share of customers' wallets by increasing users, selling them more products in SaaS-enabled marketplaces, other add-ons, and renewing them at higher price tiers.

If a SaaS company's annualized Net Dollar Retention is less than 75%, there's a problem with the business.

Slack's ARR chart (below) shows how powerful Net Retention is. Layer chart shows how existing customer revenue grows. Slack's S1 shows 171% Net Dollar Retention for 2017–2019.

Slack S-1

3. $1.5m ARR in the last 12-24 months.

According to Point 9, $0.5m-4m in ARR is needed to raise a $5–12m Series A round.

Target at least what you raised in Pre-Seed/Seed. If you've raised $1.5m since launch, don't raise before $1.5m ARR.

Capital efficiency has returned since Covid19. After raising $2m since inception, it's harder to raise $1m in ARR.

P9's 2016-2021 SaaS Funding Napkin

In summary, less than 1% of companies VCs meet get funded. These metrics can help you win.

If there’s demand for it, I’ll do one on direct-to-consumer.

Cheers!

GTO Poker 101

More on Gaming

Sonic Prime and indie games on Netflix

Gran Turismo 7 Update Eases Up On The Grind After Fan Outrage

Sony and LEGO raise $2 billion for Epic Games' metaverse

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The Brand Structure of U.S. Electric Vehicle Production

Info for the Model Year of 2021

Legacy Brands with the Most Momentum

Web 2 + Web 3 = Web 5.

Step forward our new saviour — Web5

If you don't crush these 3 metrics, skip the Series A.

1. Market risk

2. Execution risk

1. Lead Velocity Rate supporting €$10m ARR in 2 to 4 years

2. Above-100% Net Dollar Retention.

3. $1.5m ARR in the last 12-24 months.