Say you've moved all in and the opponent called although he wasn't supposed to.
What are your chances now?
Photo courtesy of Piotr Dorabiala
Thing is, even if you get the money in with the worst hand, you often have some winning cards among the cards that remain to come.
In general, a number of cards can come on the board that will turn your hand into a winner. In poker, these winning cards are called "outs".
Counting outs
Counting outs means figuring out how many cards will make your hand a winner. (The next step is to translate outs into winning odds and decide if you should call or fold, more on that later.)
Example: You have two hearts in your hand and there are two hearts on the board. You need another heart to fill your flush and beat the opponent's straight. How many outs do you have?
There are a total of 13 hearts in a deck of cards, and four of them have been dealt out. Logically, then, nine more hearts are available. If any of them comes on the board, you fill your flush. You have nine outs.
Note: How can we be so sure that these nine hearts are still in the deck and available to us? Other players may have folded some hearts before the flop, right? Or they may be in an opponent's hand. See our article on outs and opponents' cards for an explanation of this often overlooked difficulty.
Adjusting for monsters and redraws
When you're counting your outs, you need to remember that even if you hit one of them, winning may not be guaranteed. You need to watch out for redraws and monsters.
If the third heart comes on the turn, a fourth may come on the river and fill up someone else's backdoor flush. Or even if you fill your flush, an opponent who flopped a set may fill up to a full house and beat you.
That's two examples of redraws - opponents drawing out on you after you hit your own draw.
The other possibility is if the hand you're drawing to isn't really a winner. For example, if you hit your king high flush, someone else may have the ace high flush. Or when you flop a middle set, there's always a chance that an opponent has flopped a higher set.
That's why drawing to the nuts is the superior alternative.
Counting your exact outs for these cases is tedious. Instead, poker players usually adjust their outs "a bit" to accommodate the risk of redraws.
Example: The flush draw again. Unless you know something I don't, there's a chance the opponent has flopped a set. If so, your flush won't be a winner if the board pairs (because then he'll have you beaten with his full house or quads).
This means that one or two of your outs are no good. One on the flop and two on the turn. To avoid long calculations, just think of it as 1.5 outs that aren't good. Your remaining outs are 7.5. But since he may very well NOT have a set, maybe 8 outs is a good compromise for your decision.
Shortcuts - The easy way of handling this is to reduce the number of outs a bit. Instead of nine outs, do your math using eight or seven or any other number you feel corresponds to your real chances.
Converting outs to winning odds
Once you have an idea of your outs, you can start making a poker decision.
As described in The Math behind Calling and Folding, to find your EV and make a correct decision, you need to know the probability that you'll win the hand - your winning odds.
So you need to convert your outs to a percentage or odds number. This isn't hard to do with a pen and paper, but when you're in a hand you may not have the time. Luckily there are a few rules of thumb for this.
The 2 and 4 rules
To get an idea of your winning chances, just take your outs and multiply them by twice the number of cards that remain to come - that is, by 4 on the flop and by 2 on the turn.
Example: You have nine outs. You're on the flop. Multiply your outs by 4. Your winning chances are close to 4*9 = 36%.
Example: You have nine outs. You're on the turn. Multiply your outs by 2. Your winning chances are close to 2*9 = 18%.
These are the standard rules that most players use at the table.
If you want to be a bit more on target, and if you don't bother bogging down your brain a little more, the following modified rules add some precision to the above simple rules.
The modified 4 rule
On the flop, if you have nine or more outs, subtract one from the result for each out over eight.
Example: You have nine outs on the flop. The 4 rules gives you winning chances of 36%. Since 9-8=1 you now subtract 1 from this and get 35%. The true value is 35%.
Example: You have 15 outs on the flop (perhaps you're playing PLO). The 4 rule gives you 60% winning chances. You subtract 15-8=7 and get 53%. The true value is 54%.
The modified 2 rule
To get closer to the real winning chances on the turn, you could multiply the outs by 2.2.
While this may sound tedious, it's actually really simple even if you're not a math geek.
First perform the multiplication by 2 as above. Then add the result divided by 10. It's easier than it sounds.
Example: You have 4 outs on the turn. Multiply by 2 and you get 8. Divide 8 by 10 and you get 0.8. Add the two and you have 8.8%. The true value is 8.7%.
Example: You have 13 outs on the turn. Multiply by 2 and you get 26. Adding 2.6 brings you up to 28.6%. The true value is 28.3%.
Outs in Omaha
When it comes to Omaha, things change little bit. Thing is, since we have four hole cards in Omaha, we have a little more information. Two fewer cards are unknown, 46 on the flop and 45 on the turn.
As a result, your winning chances are about one percentage unit better than in holdem on both the flop and the turn.
On the flop with nine outs, you have 36% rather than 35%. On the turn, you have 20% rather than 19%.
So, not only can you have more outs in Omaha, they are a tad more valuable, when measured in winning chances.
Conclusions
Outs are essential in poker. If you have an idea of what's going on in the hand, counting outs is pretty straightforward, and converting them to a percentage number is easy using the rules of thumb.
And remember, what's true in poker is true in life. Always leave yourself some outs.
/Charlie River
-
This article is part of the poker math series:
- Basic Probability Theory
- Where do Probabilities Live?
- Average, Expected Value, Variance and More
- What Is Odds?
- What is Outs in Poker?
- The Math behind Calling and Folding
- EV - How To Calculate It
- Variance - How to Calculate It
Comment