Odd Man Out
The Outs, Odds, and the Rule of 2 & 4
“When I was young, people called me a gambler. As the scale of my operations increased I became known as a speculator. Now I am called a banker. But I have been doing the same thing all the time.” — Sir Ernest Cassel
Imagine we have a drawing hand and someone bets into us on the flop. How do we decide whether to call or fold? Should we chase the draw or not? Remember that poker is a game of decisions, not results. If we can make the right decision, we will win the hand, regardless of the actual outcome. So, how do we do this?
Answer: we have to compare the probability of hitting our hand and getting paid against the price we’re offered to chase and potentially miss. If the reward is greater than the risk, we should call. If it’s not, we shouldn’t. So, how do we know if the price is right to chase?
Answer: There are several ways of making this comparison, but one of the simplest is to count your outs and determine what the probability of making our hand is. There are two ways to determine the probability. The first is via a standardized chart, like the one shown here in the image. The other is to use the so-called “rule of 2 & 4.” Let’s look at both approaches.
How to Use the Chart:
Imagine that we have A♣2♣ on a Q♣K♥5♣ flop. The pot is $100 and our opponent moves all-in for his remaining $50. We are relatively confident he has a moderately strong hand like top pair. We have him covered. Is it correct (read: profitable) for us to make the call or not?
Given our read of the villain, we assume that if we hit a flush, we will win the hand. There are nine unseen club cards, or outs, available to make our flush (K♣, J♣, T♣, 9♣, 8♣, 7♣, 6♣, 4♣, & 3♣).
After the villain shoves, the pot is $150, and it will cost us $50 to call. We’re getting $150:$50, or 3:1 on our money to make the call. Converting this to a percentage form gives us: 1/(3+1) = 25%. This means we need more than 25% equity to make this a profitable call.
Per the chart, the probability of making our hand with nine outs and two cards to come is 35% (i.e., we can make our hand on the turn or the river). Since our equity (35%) is greater than the pot odds (25%), this is a profitable call to make. In fact, not making the call is a mathematical mistake. Even if we don’t make the flush, we will have still made the correct “+EV” decision. This is all that matters in poker: making the right decision. The results of a single hand don’t matter a whit. The only thing that matters is that we make +EV decisions, over and over.
In this situation, calling $50 on the flop is correct. But imagine that our opponent shoved on the turn instead of the flop. Here, we still have 9 outs, but per the chart, the probability of us making our hand on the river (i.e., with just one card to come) would drop to only 19.6%. And since 19.6% is less than 25%, this would not be a profitable call for us to make. The most positive EV play you can make in this situation would simply be to fold.
A Shortcut to Memorization: The Rule of 2 and 4
The ideal approach to outs and odds is to memorize the key probabilities of the most common situations, like flush and straight draws, hitting a set, and so on. Armed with this knowledge, we can make instant, on-the-fly decisions with relative ease. We simply calculate the pot odds and compare to the memorized probabilities.
Instead of memorizing numbers from a chart, however, there is a simple shortcut that approximates the probability of making our hand. This is called the “Rule of 2 and 4.” Here’s how it works:
Imagine that we are on the flop and plan to stick around and see both coming cards (turn and river) if we call. To calculation our probability, simply multiply the number of our outs by the number four. The result is the approximate probability of making our draw. In the first example, above, we’re facing a shove on the flop with two cards yet to come. We’re on a flush draw with nine out, so we multiply 9×4, which equals 36, or 36%. Note that this estimation of our equity is very close to the actual correct value of 35%.
Similarly, if we will only see one card (e.g., we’re on the turn and there’s just the river card to come), multiply our outs by two. Again, the result is a rough approximation of making our hand. For the second example, with just one card to come and facing the shove, we would multiply the number of outs by two, which gives us: 9×2 = 18%. Again, this is pretty close to the correct value of 19.6%. While not exact, most times, this will get you close enough to make the right decision.
The Bottom Line:
Learning to count outs and determine the probability of making a draw is one of the most basic skills every poker player should be capable of doing at the table. Taking the time to memorize key percentages from a table, or at least learning the rule of 2 and 4, can and will make the difference between long-term profit or loss. Poker is a game of math. If you’re not doing the math in real time at the tables, you’re just guessing.
As you say, making the correct decision is key, win or lose. It is sometimes cold comfort though when you lose a good hand, to someone who shouldn't have been in it :)