Counting Outs - Part II

As I discussed in Part I of this column, calculating your outs is not always an easy task. In fact, it is very easy to make mistakes doing it. Despite the fact that counting your outs correctly is very important in determining your pot odds and whether or not you still belong in a hand, very few poker books have analyzed this aspect of the game the way they should. One of the first books to tackle this problem correctly was Ed Miller's excellent Small-Stakes Hold'em – Winning Big With Expert Play. He discussed not just the number of cards that improve your hand, but, more importantly, how you should estimate what is really important: your actual chances of winning. In order to do this, he introduced the concept of partial outs, cards that improve your hand but do not give you the nuts, and therefore cannot be counted for full value. On Page 101, he wrote:



"You must account for partial outs when you are counting. If you count them for full value, you will overvalue your hand and call too often. If you discount them entirely, you will undervalue your hand and fold too much."



And quoting from Page 106:

"Decide how likely each card is to make you a winner. Some cards give you the nuts and are full outs. Others, like overcards, that may not be enough to win if hit, or any card that may cause a split pot, should be counted as partial outs."



My Regular Game

In my regular pot-limit Omaha game, quite a few players obviously have not read this section. On numerous occasions, I have heard my opponents claim things such as, "Gee, 13 outs twice, how much better can things get," when the situation is entirely different than would appear from their description. Here's an example: A favorite play of mine is to raise or check-raise all in on the flop with a hand like aces plus the nut-flush draw, especially with semicoordinated boards like J-8-5 with two of a suit. Now, if I am up against someone with 10-9-7-6, he will often think he has an absolute monster hand (any 4, 6, 7, 9, 10, or queen will complete his hand), and even a smaller wrap like 10-9-7-X or 9-7-6-X will often think he has a premium draw. But this is mostly because of the common mistake of thinking only about his own hand, automatically assuming that making his hand equals winning the pot. But there are two problems here:



1. In a multiway pot, it is quite likely that someone will be in there with a Q-10-9-X type of holding. If indeed the player with one of the wrap hands mentioned is up against this "higher" straight draw, quite a few of the cards that will make his straight will give his opponent the same straight or even a better one.



2. Even when heads up against my weak-looking aces plus the nut-flush draw, the big wrap is by no means the favorite! If my flush card comes on either the turn or the river, my opponent is entirely dead, and it doesn't matter if he completes his hand at any stage in the hand. In addition to that, both of the card combinations blank-blank and runner-runner full house will also give me the pot. This means that while the player with the big wrap will think he's very unlucky if he loses the pot, it is actually the aces plus the nut-flush draw that has made the correct decision to move in on the flop. For the wrap, it probably would have been better to wait for the turn card to make his move, most of all because he could have released his hand if the flush card had come. Here is an extremely important pot-limit Omaha concept when it comes to playing draws correctly: If your opponent is probably drawing to a bigger hand than yours, it is often best to play your hand in a passive manner on the flop. This way, you can get rid of your hand cheaply once the turn card may have completed one of these higher draws, and if you complete your draw on the turn, you can then charge your opponents to try to outdraw your hand with one card to come. Playing your hand in this seemingly weak manner is more often than not correct if you are drawing to a straight when your opponent may be drawing to a better one, or you have a big straight draw but your opponent is probably drawing to a flush or full house.


Redraws

In pot-limit Omaha, it is always important to be aware of the fact that if your opponent is strong, he may have a lot of redraws – meaning there are still several cards to beat you even if you make your straight on the turn. This is one of the main reasons why, in this game, it is especially the straight draws that cause people to make both playing and calculating mistakes. In hold'em, the danger of redraws exists with straight draws, as well, but to a lesser degree. It is often the one-pair holdings that are vulnerable to getting outdrawn on the river. For instance, if you call a bet on the flop with an unimproved A-K because you think the bettor has "just" top pair, you may think you've got six outs, and that based on pot odds, this call is correct. But it is important to take into account two things:



1. The possibility of hitting your hand and still be trailing.



2. The possibility of gaining the lead on the turn and then losing it on the river.



A Limit Hold'em Example

The best example of the problems with counting outs is an example that Miller gives in his own book, in which it seems that even he falls into the trap of overvaluing the strength of a hand. Why? Well, most of all because he fails to take into account his own concept of partial outs. Here is the situation:



On Page 123, in what is described by him as a multiway pot, he defines the 3 2 on a flop of Q 8 2 (bottom pair, low kicker, 3-high flush draw) as a "strong" hand, a "robust holding," and, most importantly, a 14-out draw. Now, in a multiway pot, this can never be correct. When there is significant action on a flop like this, one should always take into account the possibility of being up against a higher flush draw, especially when holding the smallest possible flush cards. This is even more true if you are in a game in which lots of people play any two suited cards – which is the case in the type of games Miller describes. Now, even if you are not up against the higher flush draw that would instantly turn your robust holding into a very poor one, you still can't count this hand as having 14 pure outs – exactly because of the reasons the author himself had given in earlier sections. Especially important in this regard are his words from Page 106: "Decide how likely redraws are if you make your hand on the turn. Potential redraws devalue your hand." Now, in this case, it should be clear that regardless of which of your 14 outs comes on the turn, you will always be up against at least some redraws on the river – and possibly even several. So, one should not simply count the number of possible good cards, but should come up with an estimate of the chances of ending up with the best hand on the river. Now, of course, this cannot always be done accurately, but if you have a good read on the cards that your opponents probably hold, based in large part on the betting up to that point, it will be easier for you to determine whether you still belong in the hand – and if you do, whether you should just call or raise for value.



Some Final Words

One of the biggest mistakes in poker is confusing your number of outs with your actual chances of winning. Those who habitually overestimate their pot odds ("Nine cards out of 45 improve my hand; therefore, I have a 20 percent chance of winning") will make many costly mistakes. For instance, in the 3 2 example, if you are up against both a higher flush draw and a set – which is highly unlikely but far from impossible – you may be drawing dead while thinking you actually hold a premium draw! All in all, counting your outs correctly is not always easy, because it involves not just the mathematics of calculating pot odds. It also requires good reading skills and an evaluation of how the range of possible cards that your opponents could hold might influence the strength of your own cards – either in a positive or negative manner.



Rolf "Ace" Slotboom has been a professional money player since 1998, specializing in limit hold'em and pot-limit Omaha. He is the tournament reporter for almost all major European tournaments, and is the Dutch commentator for Eurosport's EPT broadcasts. His first book, Hold'em on the Come: Limit Hold'em Strategy for Drawing Hands, discusses in depth the process of counting your outs properly. The book can be ordered through http://www.danbpoker.com/, Amazon, or Rolf's own site, http://www.rolfslotboom.com/.