Hand examples of applying odds and ‘douts’ when making drawing decisions
A column I wrote a couple of months ago, titled “Outs vs Douts,” generated a lot of discussion, as I received more e-mail than usual about the topic. Given the interest, this column shows a couple of hands that apply the concept of a “dout,” taken from my book Texas Hold’em Odds and Probabilities.

First, let’s summarize the main concepts discussed in the aforementioned column. The term “out” is one that creates a lot of confusion among poker players. And, in many cases, players use a definition that will lead to incorrect decisions. One commonly used definition is that an out is a card that improves one’s hand. What you really want to know is the odds against improving to the winning hand.

Mike Petriv first introduced the term “dout” in his book, Hold’em Odds Book. He used the term to refer to an opponent’s outs. My definition is different, as I use it here to refer to discounted outs.

A dout is simply a value used to represent a card that improves your hand and then is discounted based on how likely it is to improve it to the best hand. The discounted out, or dout, can range from 0 to 1. A dout with a value of 0 means that you are drawing dead to that card, while a dout with a value of 1 means that you are drawing to the nuts.

The following hands walk through each step in how to apply odds and douts when making drawing decisions:

$10-$20 limit hold’em: A middle-position player calls and you raise from the cutoff with the Kclub Qheart. The big blind joins the action and three players see the flop of 10club 7diamond 5spade. The big blind, a tight rock who never bluffs, bets out, and the middle-position player folds. There is $75 in the pot. What should you do?

1. Determine the number of douts. Assume that your opponent has at least a pair, since he never bluffs; therefore, you need a king or queen to improve, which is six outs. You would be drawing dead against 10-10, 7-7, or 5-5, unless you hit a backdoor straight. Other likely holdings of your opponent include A-10, K-10, Q-10, and J-10. In this case, a king or queen would not help against either K-10 or Q-10. It is doubtful that your opponent would call a raise preflop with K-7, K-5, Q-7, Q-5, 10-7, 7-5, or 10-5; therefore, you need to discount your outs only for the probability that your opponent holds K-10, Q-10, 10-10, 7-7, or 5-5.

One other consideration is what could happen if you hit the king or queen on the turn. Your opponent could possibly win on the river by hitting two pair or better. You should discount your outs a little more for this possibility.

To determine how much you should discount your outs, it is helpful to evaluate the probable hands of your opponent. Probable hands that you could beat if you improve include J-J, A-10, A-7, A-5, J-10 suited, and 9-9. Discounting outs is always a matter of judgment, but you might expect to win this hand 50 percent of the time when you improve, considering the possibility that your opponent might have a set, K-10, Q-10, or improve on the river. Therefore, you should discount your six outs and play as if you had three douts.

2. Calculate the odds against improving your hand. There are 47 cards left in the deck. We have estimated three douts, so, on average, three cards will improve your hand and 44 will not. The odds against improving are 44-to-3, which is about 15-to-1.

3. Calculate the pot odds. The total pot at this point is $75; therefore, your pot odds are 7.5-to-1 for a $10 bet.

4. Calculate the implied pot odds. Do you expect to win more bets if the king or queen comes? You should win bets 50 percent of the time when you improve, but you will lose more bets the other 50 percent of the time when your opponent has a better hand. A simplified assumption would be that all future bets are break-even. Therefore, there are no implied pot odds.

5. Compare the implied pot odds to the odds against improving your hand. In this case, we look at the pot odds, since the implied odds are the same. The pot odds of 7.5-to-1 are compared to the odds against improving with three douts of 15-to-1. This is an easy fold.

This hand is worth discussing a little further, to show the importance of discounting outs. Many players draw to overcards on the flop, hoping to pair up. This example shows that this approach is often a big mistake. If you play your hand thinking you have six outs to the king or queen, your odds are 7-to-1 against improving. These odds compare favorably to the 7.5-to-1 pot odds and you would call, expecting to make a small profit. However, this assumes that you would always win when the king or queen comes. As discussed before, your opponent could very well have K-10, Q-10, 10-10, 7-7, 5-5, or beat you on the river. When you take into consideration the estimate of winning only 50 percent of the time when you improve, this is a clear fold.

Some players also justify calling by saying that they have implied odds of winning more bets should they improve. This is true if your hand wins, but sometimes you will lose bets. If your king or queen comes on the turn, you will probably raise, and quite possibly be faced with a reraise if your opponent has a set or two pair. Also realize that sometimes when you improve to the best hand, your opponents will simply fold. I realize that this does not happen very often in today’s hold’em world, but opponents do sometimes fold!

$10-$20 limit hold’em: You raise from early position with the Jheart Jspade. Two middle-position players, the button, the small blind, and the big blind call, for a total of six players. The flop is 10club 8diamond 8heart. It is checked to you, and you bet. One middle-position player, the button, and the small blind call. Four players see the turn card, the Qdiamond. The small blind checks and you bet. The middle-position player raises and everybody folds to you. There is $220 in the pot. What should you do?

1. Determine the number of douts. Assuming that the middle-position player is not a tricky opponent, he has at least a pair of queens with a hand like A-Q or K-Q. He also might have 10-10, 8-8, or A-8. Q-Q is unlikely, since he probably would have reraised preflop. Q-8, J-9, and 10-8 are unlikely, since he probably would have folded to a raise before the flop. You have four outs to a straight and two outs to a full house. Your two outs to the full house are strong, since the only two hands that would beat you are Q-Q and 8-8. Your four outs to the straight are relatively strong unless your opponent has Q-Q, 10-10, 8-8, 9-8, or a backdoor diamond draw. Q-Q and 8-8 are unlikely, but 10-10 is a decent possibility. Only a weak player would call a raise preflop with 9-8 suited. One other small possibility is that your opponent has Q-J. In such a case, you will split the pot if a 9 comes. Therefore, I would discount your six outs to a total of five douts to account for Q-Q, 10-10, 8-8, and Q-J.

2. Calculate the odds against improving your hand. There are 46 cards left in the deck. We have estimated five douts, so 41 cards, on average, will not improve your hand, while five cards will. The odds against improving are 41-to-5, which is about 8-to-1.

3. Calculate the pot odds. The total pot is $220 and the bet is $20, so your pot odds are 11-to-1.

4. Calculate the implied pot odds. You should expect to earn another bet on the river if you improve. You might lose two bets on the river if you come out betting with the straight and lose to a full house. You might estimate that you would win $15, on average, when improving; therefore, the implied odds are $235-to-$20, which is 11.75-to-1.

5. Compare the implied pot odds to the odds against improving your hand. You should call, as the 11.75-to-1 implied pot odds compares favorably to the 8-to-1 odds against improving with five douts.

By always focusing on douts, you ensure that you always take into account that you could improve your hand, only to lose. A simple change in terminology to distinguish an out from a dout can hopefully help players avoid making simple mistakes.

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