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Odds Simplified
By Paul Kammen

One of the first things a poker player learns is how the hands are ranked.  Many players stop there and dive right into the world of money poker.  Saying to themselves that itís "just gambling" and playing is "only for fun," they assume they can learn the rest as they go.  If you follow this approach, youíll soon find yourself wondering what happened to the extra money that used to be in your wallet.

Important parts of the game go overlooked by players, especially odds.  Some players donít want to take the time to learn about odds or find them intimidating; others dismiss them as relevant only for professionals.  Nothing could be further from the truth.  Get a grasp of basic odds, and youíre well on your way to becoming a solid poker player.

Odds defined.  In poker, there are three types of odds that you want to learn: basic odds, pot odds, and implied/reverse implied odds.  Letís look at these in a little more detail.

BASIC ODDS are the odds that something will happen.  Were you to bet a friend a dollar that a coin would come up tails, neither you nor he would have the advantage, as there is a 50/50 chance of this happening.  But suppose your friend had said, "Iíll give you $2 if the coin comes up tails and you only have to give me $1 if it comes up heads."  Here, you are "getting the best of it," because there is an equal chance of heads or tails coming up but you are risking less money than your friend.  "Getting the best of it" is a concept stressed by many a poker author, especially David Sklansky in The Theory of Poker ,a book well worth reading.

At the poker table, there are some basic odds youíll want to remember.  The ones that follow are among the most important.  (Note: The numbers are rounded off for simplicity.)

* When you flop a flush draw (after the flop comes, you find you have four cards to a flush), the odds are still 4.2-to-1 against your completing your flush on the Turn, and 4.1-to-1 against making it on the River if the flush didnít hit on the Turn. (Overall, the odds are 1.9-to-1 against making your flush by the River after you flop four to the flush).

* Flopping an open-ended straight draw is when you have a chance to make a straight by getting one of two ranks of cards coming on the Turn.  For instance, you hold 4-5 in the big blind, and the flop comes 2-3-9.  There are eight cards (four Aces, four sixes) that would give you a straight.  Here the odds are 4.9-to-1 against you making a straight on the Turn or River, and overall the odds are 2.2-to-1 against you making the straight by the River after the flop has come.

* When you do not hold a pair, the odds are about 2.1-to-1 against pairing one of your cards on the flop.

* When you hold a pocket pair, the odds against flopping one of the two remaining cards to give you a set are 7.5-to-1.

* When you start out with two suited cards, the odds against two or three of that suit showing up on the flop are 7.5-to-1.  (The odds against flopping a flush are 118-to-1).

* When four or fewer players remain in a hand before the flop, there is a better than 50% chance that no one holds an ace (including you).

* When you hold two pair after the flop, the odds against your making a full house by the River are about 5-to-1.  When you hold trips or a set after the flop, the odds against you making a full house or better by the River are about 2-to-1 against. (These are useful numbers when you put an opponent on a flush or straight).

To compute odds, simply count your outs (the number of cards that will help you) and compare them to the number of cards that will NOT help you, and come up with a ratio. In the flush draw example above, there are 9 cards that can complete your flush, which can come on the next card, and there are 38 cards do not help. The ratio is 38:9, or about 4.2-to-1 against.  It can be very difficult to make these calculations quickly, so your best bet is to memorize the flush and straight drawing odds first, because these come up the most often.  Work on memorizing other odds information as you go along, along with accurately counting your outs.  It can be easy to miss outs, such as when you have a straight draw.  If you miscount the outs, obviously, the odds you compute will be inaccurate.

There's more to odds than just knowing how many outs you have and getting a quick estimate. There's understanding POT ODDS.  These odds look at how much bang you are getting for your buck.  Suppose there is $20 in the pot, and it will cost you $4 to call.  That means the pot is giving you odds of 5-to-1.

(Note: Take that $20-to-$4 and reduce it by dividing both sides by the same number. Whenever possible, reduce it until the second number is 1. Here, with 20-to-4, we divide both sides by 4 to get 5-to-1. All odds should be reduced.)  With pot odds, the bigger this number, the better.  It means you are investing less for a bigger payoff.

HOW TO USE ODDS: Compare the pot odds to the basic odds of making your hand, which you were figuring out earlier.  You want the pot odds to exceed the odds you will hit the hand.  In the example of the $4 bet with a $20 pot, if the odds of your getting the hand you're drawing to were greater than 5-to-1, such as 10-to-1 or 12-to-1, you are making a bad bet.  But suppose you have a 4-to-1 chance of hitting your hand. Knowing you are getting pot odds of 5-to-1, you make the call.

Pot odds are especially helpful with draws in tight games, when often, hands that look good canít be played.  For instance, suppose you are in a $2/$4 holdem game, you're sitting in the big blind position with 8-4 of hearts.  The flop comes K-7-Q with two hearts, and three players have seen the flop.  The pot has $6 in it.  You check, the player to your left bets, the other player folds, and itís to you.  The pot now has $8, but weíll deduct $1 for a rake and make it $7.  The odds against your hitting your flush on the Turn are 4.1-to-1.  The pot is giving you odds of 3.5-to-1, meaning as tempting as it might be to see the turn card, youíve got to dump this hand.

Along with pot odds, thereís one more thing to consider (actually two parts of one concept): implied odds and reverse implied odds.  This can get a bit confusing at first, but when you consider these factors it can help clear up whether you can call or should fold.  These odds are based on the probability of winning more money later in the hand and make the pot odds appear better or worse.  You can look at implied odds as a ratio between what you expect you will win if you make your hand against what it might cost you to continue to play.  Returning to the example of $4 being required to call a $20 pot, the pot odds, you will recall, are 5-to-1.  Suppose heading into the River you are drawing to a flush, and you suspect your opponent is drawing to a straight.  If you miss your hand, you simply fold.  But if you hit your hand and your opponent hits his, you know you will be getting another $4 bet from him (or perhaps $8 if you check-raise him).  What this does to the pot odds is make them better for you, so your implied odds are now 6-to-1.

Implied odds can also be used to figure out if the pot odds are better than they seem.  This is known as reverse implied odds.  You want to consider these when you have a good hand, but one that is not likely to get much better.  If there is $20 in the pot and the bets are at $4 and your opponent has been calling, drawing to a hand you suspect if made will beat you, he is going to stay involved.  So you will have to bet $4 on the turn and river, making it $8 total.  (Youíll be betting if you think you have the best hand; if he raises you, you can dump it, but heíll call trying to outdraw you.)  What this does to the pot odds, though, is make them worse, because in reality it is costing you $8, so the implied odds make the pot odds 2.5-to-1 as opposed to 5-to-1.  Knowing reverse implied odds is useful when you know your opponents well, so you can dump a good hand when you suspect your opponent has made his.

Why important? At this point you may be thinking: "I just play for small stakes, why should I take the time to learn about odds? Isnít that just for the pros?" Nothing could be further from the truth. Knowing about odds helps you make good decisions at the poker table and avoid bad ones, and all those small decisions that you make over the course of session after session add up over time to increase or deplete your bankroll. Odds are the reasons casinos love the players who feed quarters into slot machines. These machines will make some big payouts on occasion, but the house will always win because the odds are in its favor. The odds never change, as they are set by a computer chip inside the machine. In poker, though, the odds are constantly changing, allowing you to "get the best of it" or "get the worst of it" and be on the losing side of a wager. Every time you hear a player whine about luck, remind yourself that poker is a game that is dictated by odds as well as players and what they do with those odds. How the cards come out will be random, and at times there will be long shots that hit. At the same time, if you play out the same hand time and time again, you will find that one hand has a clear edge over the other.

Useful simulations.  If you watch poker on TV, youíll notice there are percentages next to each hand to let you know who the favorite is.  Pay attention to those numbers, especially if you enjoy no-limit holdem tournaments, because when you put an opponent on a hand, you can calculate what the odds are if you are correct in your guess, and get an estimate of how much of an underdog or favorite you are.  You can also run simulations online.  One of my favorite sites is www.twodimes.net, where you can run simulations by keying in the hands.  You can do it for holdem, stud, stud hi-lo, razz, Omaha, Omaha hi-lo, and even deuce to seven lowball.  Simply key in the hands, and youíll get a list of stats telling you who will win the most.

Take the time to study the odds, and never neglect the size of the pot.  You donít have to have a PhD in math to learn odds: Itís just a matter of memorization, which you can do in your time away from the poker table.  This simple but oh-so-important concept is neglected by many a player -- donít be that player!  Instead, be the player who can size up each situation, knowing when the risk is right instead of just tossing in chips blindly, hoping for the best.

Paul Kammen is an avid low-stakes poker player from the Twin Cities of Minnesota. He has played regularly at the Canterbury Card Club since it opened in 2000, playing primarily in low stakes Stud and Holdem games.  Since then,  he has played at various other casinos in Minnesota and Las Vegas,  and also plays regularly at the low-stakes tables on PokerStars.  He is the author of two books on poker, How To Beat Low-Limit 7-Card Stud Poker  (2003,  Cardoza Publishing) and How To Beat Seven Card Stud Eight-or-Better  (also available at ebookmall.com)  and available soon in print.


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