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August 2016

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!
 

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