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Equity and Implied Odds

Many players calculate the equity of their hand at the current moment, compare it to the size of the pot, and base their decision solely on that calculation. Those decisions are correct if there is no future betting.

But when there is future betting or even the potential for future
betting, the equation isn’t correct. That’s because the “implied odds” of the future betting affects the price the future pot is laying you. That future betting can either increase or decrease the value of your hand.

Since implied odds are a “best guess estimate,” being realistic in your implied odds appraisal is key. Many people let their biases influence their judgement. Pessimists underestimate their odds and optimists overestimate them. If, in retrospect, you’re constantly misjudging your implied odds in one direction or another, take note and adjust to your bias.

Implied odds will decrease the value of your hand when you’re more likely to lose EV than gain it. Say you’re playing a capped hand (one your opponent knows is unlikely to be in the strong portion of your range) that has limited potential for improving, but may face sizeable future bets. In such cases you may end up folding a winner when your opponent is bluffing or pay off a superior hand when he’s not. If you’re not planning on taking the hand to showdown with further betting, you’re often faced with folding a small pot now or a big pot later against an aggressive bettor. The alternative is to pay off large bets with mediocre holdings, generally not a recipe for success either.

The good news is that, when your hand has potential for future value, your hand has value beyond its current equity. The greater the effective stack sizes, the greater the chance to obtain positive EV, the more your odds improve. That said, it’s important to include factors beyond just the math of the effective stack sizes.

The potential to realize those odds is an important component to the equation. The propensity of your opponent to call future bets will be largely determined by his looseness/tightness when faced with large bets. Keep in mind some players are very loose with small bets and tight with big ones. Drawing to hands that both beat your opponent’s big bet calling range and in situations where those hands are a significant portion of his current range has greater value than drawing to hands when your opponent is unlikely to possess a holding that he will call large wagers with. Also, keep in mind you may draw to a non-nut hand and still not win.

Additionally, an often overlooked element of implied odds is how your opponent(s) will read the situation if you make your hand. If you’re drawing to flush, make it, but it’s obvious to all the potential flush is out there, the chances of acquiring large bets from a marginal hand are significantly reduced. Compare that to having a card come with a hand you’ve played deceptively and your opponent has little chance of reading you for a big mitt. Obviously, your potential for payoff is greater the less of a threat you appear to your opponent(s). So, if when you hit your card(s), and you think your opponent(s) won’t read the card as strengthening your hand, your implied odds will be greater than if the card is an obvious threat. For example, hitting the straight on an Kd-8s-4d board with 7d6d will usually get stronger action than hitting the flush.

You should always try to predict what your hand is worth when drawing. What size of bet(s) and with what regularity do you think your opponent will call if you make your hand? It’s always a best guess estimate, but when you can approximately calculate correctly, you’ll make much better decisions on when to draw.


Understanding Equity and EV

Many people don’t know the exact difference between equity and EV. In fact, some people use the terms as if they were identical.
Equity is the percentage chance that a hand will win after all the cards are dealt. The percentage chance includes splits and is utilized when comparing your holding against opponent’s hand(s) or range(s).
The term is used in different ways, with or without more cards to come. Without cards to come and your opponent’s hand unknown, your equity is calculated against his likely range. But with cards to come, when all the cards are known, your equity is calculated by your chances after the river card is dealt. In other words, your percentage chances on a runout. But with cards to come and your opponents hand unknown, your equity is the percentage chance against his feasible range.
For example: AcKc has 45.76% equity against TcTh, which has 54.24% equity. That said, equity doesn’t include measuring the implied odds or economic value of the hand. A6o has more pre-flop equity than KsQs, as A6o has around 54% pre-flop equity. But KsQs ought to win more money over time if the stacks are deep because it has much better implied odds than A6o.
The reason being, among other things, is that KsQs plays better against your opponents’ big bet calling/raising range, whereas A6o is likely to get you in many trouble post-flop situations. And the true value of a hand is its propensity to win money, not have the highest equity (unless all-in). That’s because the EV or expectation of some hands is stronger than certain hands with higher equity due to the implied odds being better.
EV is your expectation. It’s different from equity in that EV is the average of what you can expect to win going forward with a given play. Folding at the decision point has an EV of zero even if you have already invested money in the pot. However, if you continue forward with your hand, the value of the chips in the pot at the decision point is calculated into the expected return on your play choice equation.
For example, if you’re heads-up, have a gut shot after the turn as your only win with $100 in the pot and are facing an all-in $30 bet, your EV is zero if you fold and -$18.19 if you call the $30. You’re 9.09% to make the straight and with $130 in the pot including your call, the $30 call returns an average of $11.81. Since your call cost you $30, the call loses $18.19 of EV.
That’s a simple example to explain the concept. Don’t forget to include the implied odds. In reality things get much more complicated as you can’t average together all the possible future scenarios in any given hand. That said, understanding the concept and estimating the EV going forward will formulate crisper decisions. And the closer you get to reality, the tougher you’re going to make it on your opponents.
Additionally, all gambling equations should be quantified in terms of EV/expectation. We’re taught to quantify things nominally. But, when gambling, if you bet $10 with $15 expected return on your investment (EV), you’ve made $5 whether you win the hand or not.
Yeah, I know it doesn’t feel that way, but just keep making those positive EV bets and those chips WILL end up in your stack!

As the Poker Table Turns

Things change! At the poker table they can change abruptly. A loose-aggressive player goes broke and is replaced by a solid pro. A normally solid player beserko tilts after losing a big pot. You’ve nurtured a tight, nitty image for hours, but you just got caught bluffing. The texture of the game and/or your opponents’ perception of your table image has just changed dramatically and with it, the value of many plays.

You need to consistently monitor and adjust to these changes. If you don’t, you’re likely to make plays incongruent with your image or the table’s texture. And that ain’t likely to go well!

Keep track of how things progress at the table. Did a nine-handed game just become a six-handed game? Did a big pot just get played? How will it emotionally affect the participants? Did a stuck player just get even? Did a winning player just blow back his win? Did a player with an aggressive mentality just acquire a big stack? Did you suck out on a vindictive opponent? Did someone just call a big bet with a weak hand and get shown the nuts? If so, how is this likely to change their play?

Poker players are human beings (Yeah, I know some aren’t). All of these matters effect emotions and play. Someone who just called a big bet with a marginal hand and lost is less likely to want to call in the same spot again. The aggressive player with the big stack is likely to get even more aggressive. The player who just got even is likely to play more solidly and not risk his stack. A winning player who is about to leave is less likely to assume risks. The converse is true for a player who is stuck and leaving. The questions and methods to exploit them are endless.

And these issues aren’t just important in how they directly relate to you; they’re important in how they relate to the other players at the table. If one player is vindictive towards another, will situations present themselves that you can exploit? You bet they will!
So pay attention to the ebbs and flows of the game. Think about how you can exploit them. Think about how your opponents think and how it changes with events. And devise tactics to exploit their thoughts and emotions.

You’ll be amazed how much extra equity you’ll be able to find!


Deep Stack vs. Small Stack


Size matters! And it matters a lot! Your stack size designates the strategies you should use. And since you can control your stack size via buy-in amount, you can create game play situations that correspond to your strengths and evade your weaknesses.

Having a small stack tends to limit the number of streets you must make decisions on. Additionally, your decisions are apt to be for lesser amounts, making your decisions less critical. With a small stack you can play tightly pre-flop and have easier post-flop decisions. The largest component of your decisions will be assessing your hand’s value. Assessing your implied odds is not much of a factor. And hand reading, a tough element of poker, takes on much lower importance.

Among other things, playing a deep stack requires being able to read your deep-stacked opponents’ hands, estimate the implied odds that the deep stacks create, and have the internal fortitude to act on your evaluation. The nature of deep stack no-limit hold’em that causes pots to grow exponentially street by street means these decisions are often for big money, making the accuracy of your decision MUCH more critical. All this makes for MUCH more complicated equations.

Most novice players aren’t proficient at reading hands and situations. That correlates to being unable to accurately assess their implied odds. For them, buying-in short amounts, playing a tight hand selection strategy, and picking spots to play post-flop will be the best strategy. They won’t win as much as their skilled deep-stacked opponents, but they don’t have the skillsets to compete with them. And you must understand your limitations in both poker and life.

If you think your strategic decisions will be better than your opponents, play deep. You’ll both read and create positive implied odds situations for yourself. Your big bets, both made and called, will be favored to have an edge over your opponents’. Plus, the threat of your large stack will increase your fold equity as players will be less inclined to call your bets when you have a large stack left.

Another component of this equation is your ability to handle swings. If you’re prone to get emotional when stuck, buying in deep may not be the best strategy. Yeah, you can circumvent this by not rebuying, but there is a cost to that too.

Often, you’re not sure how your opponents play. This is particularly true when you are playing in a new location. Generally, the best play is to buy-in short and chip up if you like what you see. Keep in mind, it’s the deep stacks you want to base your decision on since you are already equivalent with the short stacks.

How deep you buy-in is an important decision. Realistically appraise the situation. Then determine your best buy-in strategy.

Then follow the correct game strategy based on your buy-in.  


Shut Up!

Recently, I played in a live WSOP $2-5 game mixed with young pros and weak recreational players. After every hand the pros all swapped strategies about the potential ranges of their opponents and what was the best play. In doing so, they openly criticized their recreational opponents’ play.

The pros were very well studied and knowledgeable. Some of the recreational players seemed astonished at the depth of thought. It was at a level they’d never heard before. Some left, some were made uncomfortable and tightened up. One thing for sure, the pros’ edge had been dramatically reduced by all the strategy conversation.

I see this type of behavior all the time. People want to show how smart they are, belittle their opponent’s, and play big shot. It’s bad etiquette and among the worst poker plays. It costs both you and other serious players big money. It educates your opponents on strategy, informs your opponents how you think and focuses their minds on strategy.

Yeah, I’m the wrong guy to say this. I publish articles about poker strategy all the time. But I’m no longer playing for a living, and I avoid strategy discussions at the table.  These pros must have worked hard to develop an edge and then diminish it so stupidly. Pointing out strategies and mistakes to your opponent’s is just stupid, particularly at the table.

Players need to control the discussion. Point out to unaware players that their discussion is hurting the game. Move the conversation onto other topics. Keep the focus off poker strategy.

Do the smart thing. Shut up, and do your best to prevent others from damaging your edge.




Odds Are, You Need to Know This!

Pot odds, implied odds, your odds, their odds, cards to come odds.…It all gets so damn confusing. And if you want to be a world-beater at the poker table, there’s much to know. But if you just want to beat on some recreational players, knowing the mathematical basics will take you a long way.

You should always be aware of how much is in the pot so you can easily calculate your current odds. And you should also estimate what you think your hand is worth.

How is the hand likely to play out? What are the differing plausible scenarios? Be aware of any actions that may take place behind you. Closing the action is far superior to having three players to act behind you whose actions may affect your price.  What is the blended value of all the possible scenarios? Yeah, it’s always an estimate. But the more you think this way, the better your estimates will become, making for crisper decisions.

Always understand that your bet is offering your opponent odds. If you raise a small amount with a big wired pair and both you and your opponent have large stacks, and you’re probably paying off if you’re beat, think about the implied odds you are currently offering your opponent. If the implied odds number is high, you may well want to bet more. Yes, I understand there are many other issues, but this is about odds.

Close enough is good enough in poker. For ease of calculation, I use rough justice numbers. You have about 2% per win per card or 4% for two cards coming. So if you have 8 wins with one card to come, you have about a 16% chance to hit. With two cards to come it’s about 32%.  Keep in mind that you may face bets on all streets, and you can’t always assume improving translates into winning.

Discounting straights and flushes, if you hold AK, or any other unpaired cards, you will flop a pair or better about 1/3rd of the time. Running AK out (5 cards) against QQ is about a 45%-55% proposition. If you hold a wired pair, you will flop a set about 12% of the time or 7 1/2-1. Are the implied odds right to draw to your pair pre-flop? Keep in mind you don’t always win and don’t always stack your opponent when you do. If you do flop a set, you will make a full-house or better about 1/3rd of the time. If you hold two suited cards, you will flop a flush less than 1% of the time and a four-flush about 11% of the time. If you hold two unpaired cards, you will flop two-pair about 2% of the time.

Additionally, you can use math to assist in reading your opponent’s ranges. There are 6 combinations of any pair, 16 of any unpaired hand of which 4 are suited. So, if an opponent’s range is AA, KK, QQ or AK…There are 6 combinations each of AA-KK-QQ and 16 of AK. Therefore, that opponent’s range has 18 pairs and 16 AK’s. So if you hold TT, you are an underdog to be good right now and not much of a favorite when your opponent holds AK. That equates to a blended large negative EV with TT against that range.

If an opponent would play J9s in a given position, but not J9o, then his range has the potential for 4 combinations of J9. Adjust a player’s range by the cards that come on the flop or any in your hand. If an A is removed, there are only 12 combinations of AK available. If you hold the Ah5h then the chances of AA being in your opponent’s range is reduced by 50% (3 combos) and AK is reduced by 25% (12 combos).

These are the basics, rough justice style. Get to know them, apply them to your thought process, they are your friend. And when you can utilize them correctly, you’ll be getting your money in with the best of it!




Let Them Bluff


You open with AA and are called by an aggressive opponent. The flop comes the Jd-9c-8d. You fire, and he calls. The turn is the 3c, you fire again, and he calls. The river comes the 4h. Should you bet again?

When you’re heads-up on draw-heavy boards against aggressive opponents, you’ve bet, and the draws missed, and your opponents’ calling range on the flop/turn included many draws, don’t value bet the river out of position.

Since he can’t call with his missed draw hands, and the ratio of drawing hands to calling hands in his range is weighted toward the missed drawing hands, give him an opportunity to bluff his whiffed draws. The more aggressive and bluff-happy your opponent is, the greater the strength of the play. The more passive, call prone, and bluff adverse your opponent, the more you should be inclined to value-bet.

Conceptually: When the overall value you will lose from the hands he would check that he would have called a river bet with and you would have won, is less than the overall value of the bets he will bluff and you will call with, you should check and call. Simply put, you should check and call when you gain more from inducing bluffs than you lose by not value betting.

I understand this is often hard to calculate at the table. Because this situation occurs frequently, this knowledge has significant value. It’s not uncommon for aggressive opponents to bet many of their whiffed draws on the river. And since those bets are river bets, their value is often high.

So induce them to bet. And don’t chicken out and fold. You’ll find yourself obtaining better value on the river.

I’ve Got to Get Even


That thought has been the death of many bankrolls. We all hate to lose. And it’s no fun to give up. That head-down walk away from the table can get mighty distasteful.

You see it all the time. Players barely able to keep their eyes open, playing in a desperate attempt to “get out,” often in games they wouldn’t be in if they weren’t stuck. Even with some extremely knowledgeable players, this is a fatal flaw, and turns an otherwise good player into a perennial loser. With poker, you have to learn to take your beating and return when you’re strong to fight another day.

I’ve heard all the money-management theories. Play until you win x amount of dollars. If stuck,  play until you get even. Some put a stop-loss on their losses. But “Father Time” has no bearing on how you do. He doesn’t know how you’re doing. He doesn’t know or care if you picked up your last hand one minute ago or two days ago.

The problem with the money-management model is that you tend to leave good games small winners when your image and play level are at their best. And stay and play in poor games when your image and playing ability are downgraded due to being stuck and tired. On top of that, your image is bad and your opponents are empowered by their success. Poker is one long war, a cumulative score game, one where the score of money adds up over time. Your win/loss record is meaningless. It’s better to be 1-9 and $1,000 ahead, than 9-1 and a $1,000 behind. While that may seem like an exaggeration, I’ve seen such cases.

Your lifetime poker record will be dictated by the edge you attain. Play when your edge is large and not when it is thin or non-existent. That equation isn’t a calculation of just the ability of your opponents, but also your own. Don’t play bad games or when your facilities have been weakened just to get even. And don’t quit good spots just to book a winner.

There is something about that cashing in moment when you’ve lost. Yeah, it totally sucks! But “swallowing that bitter pill” at the right time will transform in your long-term poker career.

Play with strong character. Identify when you’re tired, beaten, off your game or the game is deficient and get up. And when the game is good and you’re feeling strong, don’t quit to ensure a small win.

If you play well, you’ll find your bigger wins will more than make up for your smaller losses.

Defending Against Floating

You raise pre-flop with a moderately strong hand in middle position, say AJ. You’re called by the button, whose range is wide. The flop comes down Ts-7s-2h, and you continuation bet, hoping to end the hand right there. He calls, a play he is likely to make with a wide range of hands, many of which he doesn’t want to get a lot of chips in with.

A lot of the value of Mr. Button’s call, and the reason he often calls the flop, is that, if you check the turn, he will bet and pick up a lot of pots in which you whiffed and continuation bet. It’s called a “float” and is a good play on Mr. Button’s part, particularly if you are a common continuation better, which you should be. It’s important that you take the value of “float” plays away from your opponents. Do that successfully, and not only does it give your made flop hands greater value, but in future situations they will be less likely to mess with your aggressive plays both pre-flop and post-flop.

The key to defending your continuation bets against a habitual floater is to check your high equity hands on the turn. You can call or check-raise depending on the texture of the situation. Calling is better the less vulnerable your hand is, the smaller the pot, the lower any implied extra costs, and the greater your opponent’s propensity to bluff the river. The larger the pot, the more vulnerable your holding, the larger your implied loss if he draws out, the less likely you’ll be rerasied–bluffed, the less  you want your opponent to realize his equity, making raising a stronger play.

By charging him the extra bet(s) the times you hit the flop, you take away some or all of his value of making the play. Often those bets by your opponent are with very weak hands, and the equity you gain is considerable. But, only make this play only against opponents you know to be “floaters.”

Don’t let your opponents float you profitably; check the turn into them with your made hands and raise or call based on the current situation.

There’s a lot of value in this play!






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