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Figuring The Odds & Percentages
By Clonie Gowen
Clonie,
Everyone says the math is easy; maybe I am just not that smart. I don’t understand. I know what outs are, but when I try to compare them in a game I just get lost.
— Sandy2005
Sandy2005,
Figuring pot odds is a necessary part of any guy or gal’s game. By learning to understand the relationship between the mathematical odds against your hand and the money you win if you get lucky, you can play skilful, high percentage poker. It takes most people some time to really understand outs and odds, but figuring odds in Hold’em is easy compared to other forms of poker. Seven-card Stud and similar games, like Razz and Seven-stud/8, are more complicated, because each player’s hand has its own exposed cards and therefore it’s own calculation. But with Hold’em, the same similar situations come up again and again. So guess what? You can memorize the odds for common situations. That way you won’t have the need to perform calculations for each situation you find yourself in.
Odds give you the bad news first. If you have an open-ended straight with the turn and the river to come, so you have eight outs, the odds tell you that you are a 2:1 underdog. In other words, you will fail to make your hand twice for each time you do make it. Odds are useful because it is easy to compare the odds against making your hand to the money odds offered by the pot, and this helps you to make rational decisions about whether to fold, raise, call or reraise. If you don’t compare the odds against making your hand to the odds offered by the pot, you’re simply giving your money away. But how do you know if a 2:1 underdog is a good deal or not? It depends. If the pot is offering $60 dollars for a $20 call and you are only a 2:1 underdog, as Martha Stewart would say, “That’s a good thing.” This means the pot odds of 3:1 exceed the 2:1 odds against making your hand. If you repeated this situation over and over, you’d have the best of it by calling a bet in this situation. But if there was only $20 in the pot, and it cost $20 to call, you’d be better off folding, because an even money wager is a bad bet if you figure to win only once every three tries.
If you have 14 or more outs, the odds are no longer against you. In fact, with 14 outs or more you are oddson favorite to make your hand. And when you’re an odds-on favorite it seems easier to look at percentages rather than odds. If you’re a 2:1 underdog the picture is clear and easy to understand. But when the odds are in your favor – for example, if the odds of you making your hand are 0.4 to 1 – it is easier to express this as a 70% chance of making your hand.
Let’s say you hold the K-9 and the board on fourth street shows A-3-7-T. You have four cards to a heart flush: A-K-9-3. When you hold four cards to a flush on the turn in Hold’em, there are 46 unknown cards. Why 46? Because there are 52 cards total in the deck and you know for certain only the values of your two hole cards and the four exposed cards on board. Of the 46 unknowns, nine cards are the same suit as your flush draw and any one of them will make your hand. These nine hearts are called your outs. To figure the odds of making your flush, you first subtract your outs from the number of unknown cards: 46- 9=37. None of the 37 cards will make your flush. So now you divide the number of no-help cards by the number of outs: 37 ÷ 9 =4.1. Therefore, four times you will miss and once you will hit; the odds are 37:9, or roughly 4:1, against making your flush draw. Smart percentage poker players – and now you – will call a bet in this situation only if the pot is four times the size of the bet. In a game with betting limits of $20/$40, the pot would need to contain at least $120 for you to call here.
The chart provided makes it easy to learn the odds against all the common draws you’re likely to come up against in a hold’em game. If you memorize it, you won’t have to waste even a fraction of a second doing arithmetic at the poker table. There are simplified methods that allow you to approximate the percentages of times you’ll make your hand.
An easy method involves multiplying your outs by two, then adding two to that sum. The result is a rough percentage of the chance that you’ll make your hand on the next card. Suppose you have a flush draw on the turn. Since there are two suited cards in your hand and two more on the board, and a total of 13 cards of each suit in the deck, you have nine outs. A quick calculation, 9 x 2 = 18, and 18 + 2 = 20, comes pretty close to the 19.6% percent chance you’d come up with if you worked out the answer mathematically. If you have only four outs, this quick approximate measure, 4 outs x 2 +2 =10, is very close to the actual figure of 10.5%. If you have 15 outs, a quick calculation yields a figure of 32, while the precise figure is 32.6%.
The strategic implications of this are: If you have a 10 percent chance of winning, the cost of your call should not be more than 10% of the pot’s total. With a 32% chance, you can call a bet up to one-third the pot’s size.While the “outs x 2 + 2” method is an easy calculation to make at the poker table, it’s even easier to commit the chart to memory. That way, you never have to figure a thing. And anytime you find yourself fighting a tinge of self-doubt, you can always double-check yourself using the “outs x 2 + 2” approximation.
If you want to estimate your chances on the flop of making your hand by the river, try this: If you have between one and eight outs, multiply by four. 8 (outs) x 4 = 32, while the precise answer is 31.5%, the above method is about as close as you need to get. 4 (outs) x 4 = 16 percent, while the accurate answer is 16.5 percent. If you have more than eight outs multiply by four then subtract the number of outs above eight. For example, it you have 12 outs, you will multiply by four, which is 48, then subtract the number of outs over eight, so subtract four from 48.
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