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Katharine Valentino

Katharine Valentino

3 years ago

A Gun-toting Teacher Is Like a Cook With Rat Poison

Pink or blue AR-15s?

A teacher teaches; a gun kills. Killing isn't teaching. Killing is opposite of teaching.

Without 27 school shootings this year, we wouldn't be talking about arming teachers. Gun makers, distributors, and the NRA cause most school shootings. Gun makers, distributors, and the NRA wouldn't be huge business if weapons weren't profitable.

Guns, ammo, body armor, holsters, concealed carriers, bore sights, cleaner kits, spare magazines and speed loaders, gun safes, and ear protection are sold. And more guns.

And lots more profit.

Guns aren't bread. You eat a loaf of bread in a week or so and then must buy more. Bread makers will make money. Winchester 94.30–30 1899 Lever Action Rifle from 1894 still kills. (For safety, I won't link to the ad.) Gun makers don't object if you collect antique weapons, but they need you to buy the latest, in-style killing machine. The youngster who killed 19 students and 2 teachers at Robb Elementary School in Uvalde, Texas, used an AR-15. Better yet, two.

Salvador Ramos, the Robb Elementary shooter, is a "killing influencer" He pushes consumers to buy items, which benefits manufacturers and distributors. Like every previous AR-15 influencer, he profits Colt, the rifle's manufacturer, and 52,779 gun dealers in the U.S. Ramos and other AR-15 influences make us fear for our safety and our children's. Fearing for our safety, we acquire 20 million firearms a year and live in a gun culture.

So now at school, we want to arm teachers.

Consider. Which of your teachers would you have preferred in body armor with a gun drawn?

Miss Summers? Remember her bringing daisies from her yard to second grade? She handed each student a beautiful flower. Miss Summers loved everyone, even those with AR-15s. She can't shoot.

Frasier? Mr. Frasier turned a youngster over down to explain "invert." Mr. Frasier's hands shook when he wasn't flipping fifth-graders and fractions. He may have shot wrong.

Mrs. Barkley barked in high school English class when anyone started an essay with "But." Mrs. Barkley dubbed Abie a "Jewboy" and gave him terrible grades. Arming Miss Barkley is like poisoning the chef.

Think back. Do you remember a teacher with a gun? No. Arming teachers so the gun industry can make more money is the craziest idea ever.

Or maybe you agree with Ted Cruz, the gun lobby-bought senator, that more guns reduce gun violence. After the next school shooting, you'll undoubtedly talk about arming teachers and pupils. Colt will likely develop a backpack-sized, lighter version of its popular killing machine in pink and blue for kids and boys. The MAR-15? (M for mini).


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

More on Society & Culture

Enrique Dans

Enrique Dans

2 years ago

When we want to return anything, why on earth do stores still require a receipt?

IMAGE: Sabine van Erp — Pixabay

A friend told me of an incident she found particularly irritating: a retailer where she is a frequent client, with an account and loyalty card, asked for the item's receipt.

We all know that stores collect every bit of data they can on us, including our socio-demographic profile, address, shopping habits, and everything we've ever bought, so why would they need a fading receipt? Who knows? That their consumers try to pass off other goods? It's easy to verify past transactions to see when the item was purchased.

That's it. Why require receipts? Companies send us incentives, discounts, and other marketing, yet when we need something, we have to prove we're not cheating.

Why require us to preserve data and documents when our governments and governmental institutions already have them? Why do I need to carry documents like my driver's license if the authorities can check if I have one and what state it's in once I prove my identity?

We shouldn't be required to give someone data or documents they already have. The days of waiting up with our paperwork for a stern official to inform us something is missing are over.

How can retailers still ask if you have a receipt if we've made our slow, bureaucratic, and all-powerful government sensible? Then what? The shop may not accept your return (which has a two-year window, longer than most purchase tickets last) or they may just let you replace the item.

Isn't this an anachronism in the age of CRMs, customer files that know what we ate for breakfast, and loyalty programs? If government and bureaucracies have learnt to use its own files and make life easier for the consumer, why do retailers ask for a receipt?

They're adding friction to the system. They know we can obtain a refund, use our warranty, or get our money back. But if I ask for ludicrous criteria, like keeping the purchase receipt in your wallet (wallet? another anachronism, if I leave the house with only my smartphone! ), it will dissuade some individuals and tip the scales in their favor when it comes to limiting returns. Some manager will take credit for lowering returns and collect her annual bonus. Having the wrong metrics is common in management.

To slow things down, asking for a receipt is like asking us to perform a handstand and leap 20 times on one foot. You have my information, use it to send me everything, and know everything I've bought, yet when I need a two-way service, you refuse to utilize it and require that I keep it and prove it.

Refuse as customers. If retailers want our business, they should treat us well, not just when we spend money. If I come to return a product, claim its use or warranty, or be taught how to use it, I am the same person you treated wonderfully when I bought it. Remember that, and act accordingly.

A store should use my information for everything, not just what it wants. Keep my info, but don't sell me anything.

Hector de Isidro

Hector de Isidro

3 years ago

Why can't you speak English fluently even though you understand it?

Many of us have struggled for years to master a second language (in my case, English). Because (at least in my situation) we've always used an input-based system or method.

I'll explain in detail, but briefly: We can understand some conversations or sentences (since we've trained), but we can't give sophisticated answers or speak fluently (because we have NOT trained at all).

What exactly is input-based learning?

Reading, listening, writing, and speaking are key language abilities (if you look closely at that list, it seems that people tend to order them in this way: inadvertently giving more priority to the first ones than to the last ones).

These talents fall under two learning styles:

  • Reading and listening are input-based activities (sometimes referred to as receptive skills or passive learning).

  • Writing and speaking are output-based tasks (also known as the productive skills and/or active learning).

by Anson Wong

What's the best learning style? To learn a language, we must master four interconnected skills. The difficulty is how much time and effort we give each.

According to Shion Kabasawa's books The Power of Input: How to Maximize Learning and The Power of Output: How to Change Learning to Outcome (available only in Japanese), we spend 7:3 more time on Input Based skills than Output Based skills when we should be doing the opposite, leaning more towards Output (Input: Output->3:7).

I can't tell you how he got those numbers, but I think he's not far off because, for example, think of how many people say they're learning a second language and are satisfied bragging about it by only watching TV, series, or movies in VO (and/or reading a book or whatever) their Input is: 7:0 output!

You can't be good at a sport by watching TikTok videos about it; you must play.

“being pushed to produce language puts learners in a better position to notice the ‘gaps’ in their language knowledge”, encouraging them to ‘upgrade’ their existing interlanguage system. And, as they are pushed to produce language in real time and thereby forced to automate low-level operations by incorporating them into higher-level routines, it may also contribute to the development of fluency. — Scott Thornbury (P is for Push)

How may I practice output-based learning more?

I know that listening or reading is easy and convenient because we can do it on our own in a wide range of situations, even during another activity (although, as you know, it's not ideal), writing can be tedious/boring (it's funny that we almost always excuse ourselves in the lack of ideas), and speaking requires an interlocutor. But we must leave our comfort zone and modify our thinking to go from 3:7 to 7:3. (or at least balance it better to something closer). Gradually.

“You don’t have to do a lot every day, but you have to do something. Something. Every day.” — Callie Oettinger (Do this every day)

We can practice speaking like boxers shadow box.

Speaking out loud strengthens the mind-mouth link (otherwise, you will still speak fluently in your mind but you will choke when speaking out loud). This doesn't mean we should talk to ourselves on the way to work, while strolling, or on public transportation. We should try to do it without disturbing others, such as explaining what we've heard, read, or seen (the list is endless: you can TALK about what happened yesterday, your bedtime book, stories you heard at the office, that new kitten video you saw on Instagram, an experience you had, some new fact, that new boring episode you watched on Netflix, what you ate, what you're going to do next, your upcoming vacation, what’s trending, the news of the day)

Who will correct my grammar, vocabulary, or pronunciation with an imagined friend? We can't have everything, but tools and services can help [1].

Lack of bravery

Fear of speaking a language different than one's mother tongue in front of native speakers is global. It's easier said than done, because strangers, not your friends, will always make fun of your accent or faults. Accept it and try again. Karma will prevail.

Perfectionism is a trap. Stop self-sabotaging. Communication is key (and for that you have to practice the Output too ).

“Don’t forget to have fun and enjoy the process.” — Ruri Ohama

[1] Grammarly, Deepl, Google Translate, etc.

The Velocipede

The Velocipede

2 years ago

Stolen wallet

How a misplaced item may change your outlook

Photo by Robert Isenberg

Losing your wallet means life stops. Money vanishes. No credit. Your identity is unverifiable. As you check your pockets for the missing object, you can't drive. You can't borrow a library book.

Last seen? intuitively. Every kid asks this, including yours. However, you know where you lost it: On the Providence River cycling trail. While pedaling vigorously, the wallet dropped out of your back pocket and onto the pavement.

A woman you know—your son's art teacher—says it will be returned. Faith.

You want that faith. Losing a wallet is all-consuming. You must presume it has been stolen and is being used to buy every diamond and non-fungible token on the market. Your identity may have been used to open bank accounts and fake passports. Because he used your license address, a ski mask-wearing man may be driving slowly past your house.

As you delete yourself by canceling cards, these images run through your head. You wait in limbo for replacements. Digital text on the DMV website promises your new license will come within 60 days and be approved by local and state law enforcement. In the following two months, your only defense is a screenshot.

Your wallet was ordinary. A worn, overstuffed leather rectangle. You understand how tenuous your existence has always been since you've never lost a wallet. You barely breathe without your documents.

Ironically, you wore a wallet-belt chain. You adored being a 1993 slacker for 15 years. Your wife just convinced you last year that your office job wasn't professional. You nodded and hid the chain.

Never lost your wallet. Until now.

Angry. Feeling stupid. How could you drop something vital? Why? Is the world cruel? No more dumb luck. You're always one pedal-stroke from death.

Then you get a call: We have your wallet.

Local post office, not cops.

The clerk said someone returned it. Due to trying to identify you, it's a chaos. It has your cards but no cash.

Your automobile screeches down the highway. You yell at the windshield, amazed. Submitted. Art teacher was right. Have some trust.

You thank the postmaster. You ramble through the story. The clerk doesn't know the customer, simply a neighborhood Good Samaritan. You wish you could thank that person for lifting your spirits.

You get home, beaming with gratitude. You thumb through your wallet, amazed that it’s all intact. Then you dig out your chain and reattach it.

Because even faith could use a little help.

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Alana Rister, Ph.D.

Alana Rister, Ph.D.

2 years ago

Don't rely on lessons you learned with a small audience.

My growth-killing mistake

Photo by Anthony DELANOIX on Unsplash

When you initially start developing your audience, you need guidance.

What does my audience like? What do they not like? How can I grow more?

When I started writing two years ago, I inquired daily. Taking cues from your audience to develop more valuable content is a good concept, but it's simple to let them destroy your growth.

A small audience doesn't represent the full picture.

When I had fewer than 100 YouTube subscribers, I tried several video styles and topics. I looked to my audience for what to preserve and what to change.

If my views, click-through rate, or average view % dropped, that topic or style was awful. Avoiding that style helped me grow.

Vlogs, talking head videos on writing, and long-form tutorials didn't fare well.

Since I was small, I've limited the types of films I make. I have decided to make my own videos.

Surprisingly, the videos I avoided making meet or exceed my views, CTR, and audience retention.

Recent Video Stats from YouTube studio — Provided by Author

A limited audience can't tell you what your tribe wants. Therefore, limiting your innovation will prohibit you from reaching the right audience. Finding them may take longer.

Large Creators Experience The Same Issue

In the last two years, I've heard Vanessa Lau and Cathrin Manning say they felt pigeonholed into generating videos they didn't want to do.

Why does this happen over and over again?

Once you have a popular piece of content, your audience will grow. So when you publish inconsistent material, fewer of your new audience will view it. You interpret the drop in views as a sign that your audience doesn't want the content, so you stop making it.

Repeat this procedure a few times, and you'll create stuff you're not passionate about because you're frightened to publish it.

How to Manage Your Creativity and Audience Development

I'm not recommending you generate random content.

Instead of feeling trapped by your audience, you can cultivate a diverse audience.

Create quality material on a range of topics and styles as you improve. Be creative until you get 100 followers. Look for comments on how to improve your article.

If you observe trends in the types of content that expand your audience, focus 50-75% of your material on those trends. Allow yourself to develop 25% non-performing material.

This method can help you expand your audience faster with your primary trends and like all your stuff. Slowly, people will find 25% of your material, which will boost its performance.

How to Expand Your Audience Without Having More Limited Content

Follow these techniques to build your audience without feeling confined.

  • Don't think that you need restrict yourself to what your limited audience prefers.

  • Don't let the poor performance of your desired material demotivate you.

  • You shouldn't restrict the type of content you publish or the themes you cover when you have less than 100 followers.

  • When your audience expands, save 25% of your content for your personal interests, regardless of how well it does.

DC Palter

DC Palter

2 years ago

How Will You Generate $100 Million in Revenue? The Startup Business Plan

A top-down company plan facilitates decision-making and impresses investors.

Photo by Andy Hermawan on Unsplash

A startup business plan starts with the product, the target customers, how to reach them, and how to grow the business.

Bottom-up is terrific unless venture investors fund it.

If it can prove how it can exceed $100M in sales, investors will invest. If not, the business may be wonderful, but it's not venture capital-investable.

As a rule, venture investors only fund firms that expect to reach $100M within 5 years.

Investors get nothing until an acquisition or IPO. To make up for 90% of failed investments and still generate 20% annual returns, portfolio successes must exit with a 25x return. A $20M-valued company must be acquired for $500M or more.

This requires $100M in sales (or being on a nearly vertical trajectory to get there). The company has 5 years to attain that milestone and create the requisite ROI.

This motivates venture investors (venture funds and angel investors) to hunt for $100M firms within 5 years. When you pitch investors, you outline how you'll achieve that aim.

I'm wary of pitches after seeing a million hockey sticks predicting $5M to $100M in year 5 that never materialized. Doubtful.

Startups fail because they don't have enough clients, not because they don't produce a great product. That jump from $5M to $100M never happens. The company reaches $5M or $10M, growing at 10% or 20% per year.  That's great, but not enough for a $500 million deal.

Once it becomes clear the company won’t reach orbit, investors write it off as a loss. When a corporation runs out of money, it's shut down or sold in a fire sale. The company can survive if expenses are trimmed to match revenues, but investors lose everything.

When I hear a pitch, I'm not looking for bright income projections but a viable plan to achieve them. Answer these questions in your pitch.

  • Is the market size sufficient to generate $100 million in revenue?

  • Will the initial beachhead market serve as a springboard to the larger market or as quicksand that hinders progress?

  • What marketing plan will bring in $100 million in revenue? Is the market diffuse and will cost millions of dollars in advertising, or is it one, focused market that can be tackled with a team of salespeople?

  • Will the business be able to bridge the gap from a small but fervent set of early adopters to a larger user base and avoid lock-in with their current solution?

  • Will the team be able to manage a $100 million company with hundreds of people, or will hypergrowth force the organization to collapse into chaos?

  • Once the company starts stealing market share from the industry giants, how will it deter copycats?

The requirement to reach $100M may be onerous, but it provides a context for difficult decisions: What should the product be? Where should we concentrate? who should we hire? Every strategic choice must consider how to reach $100M in 5 years.

Focusing on $100M streamlines investor pitches. Instead of explaining everything, focus on how you'll attain $100M.

As an investor, I know I'll lose my money if the startup doesn't reach this milestone, so the revenue prediction is the first thing I look at in a pitch deck.

Reaching the $100M goal needs to be the first thing the entrepreneur thinks about when putting together the business plan, the central story of the pitch, and the criteria for every important decision the company makes.

Matthew Cluff

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.