You’ve got a decent hand. You’re sure of it, but you don’t want to bet everything on it because you know the game and know that you’ll lose. What do you do? That depends in part upon how strong your hand is (or isn’t). For example, if you have an ace low flush, you might be tempted to fold, knowing you probably won’t make money betting with it. On the other hand, if you hold a pocket pair, you may have enough confidence in the strength of your hand to bet all-in, hoping for a full house or better. In order to get the most from your hand, you need to understand what the odds are against each possible outcome. Here’s how you can figure out whether or not you should push your luck with a particular hand.

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**The Value of A Pair**

Let’s assume we’ve just dealt two cards and one player has three suited cards and another has four. If the first player bets, then he’s going to win about half the time (assuming everyone else folds), so his expected return is 50 percent. The second player has a much tougher time. He’ll have a good chance of winning only when he gets three of a kind, which happens 1/4th of the time. So he has a 25 percent chance of winning. When he makes the call, the third player has a 55 percent chance of winning. His expected return is 45 percent. Of course, if the first player loses, then the chances of the third player winning go way up — about 80 percent. All of these percentages are based on the assumption that all players will fold.

The value of the hand is calculated by taking the probability of winning times the amount you would win if you did win. This gives us a number between zero and 100. We’ll use $5 as our basic unit for calculating the value of the hands. If you had 10 chips and could choose any five, what would you pick? Well, we’d obviously take the top hand, which is worth $50. The second best hand is a little bit worse — $45 — since you’re giving up some equity for the opportunity to win more. So now let’s calculate the value of the remaining hands.

If the second player chooses a third card, his expected gain is $25, which represents the difference between the two hands. A fourth card increases the expectation to $30, while adding a fifth card drops it back down to $20. Since there are no sixth cards, the value of the hand is equal to the average of the five cards, which is $24.60.

**The value of a suit**

We can also figure out the value of a suit by looking at the value of each individual card within that suit. Let’s say we’re dealing a standard deck of 52 cards. One person holds a KQ; the next person has a 7D; and the third has a 2S. Each person has a 20% chance of winning. What is the expected return of having this group of cards? Well, the KQ has a 5% chance of winning, the 7D has a 4% chance, and the 2S has a 3% chance. So the total expected return is 25%. The same logic applies to the other suits, where the probability of winning goes up as the value of the card decreases. For instance, the Aces have a 9% chance of winning, Kings have 8%, Queens have 7%, Jacks have 6%, and Tens have 5%. So the expected returns add up to 36%.

Now let’s add all of these numbers together to get an estimate of the value of a hand. Assuming that each hand was equally likely to come up, our total would be 60 percent. But we know that’s wrong! Not every hand is created equal. It turns out that a royal flush beats the rest of the pack pretty consistently. So we’re going to adjust our calculations to reflect this fact.

**Royal Flushes**

So far, we’ve assumed that all of the cards were equally likely to come up. Actually, most poker players believe that Royal Flushes are extremely unlikely. In fact, many experts estimate their frequency at less than 0.1 percent. To account for this, let’s increase the probability of winning for each card in a Royal Flush by 10 percent. Now when we calculate the value of a Royal Flush, we’ll find that it’s actually worth 62.5 percent of what it used to be. The value of the cards in each rank will still add up to 100, but they’re now weighted differently.

So what does this mean for you? Well, if you hold a Royal Flush, you’re probably going to win about 75 percent of the time. And if you hold a hand like QJT, you’ll win about 75 percent of the time too. And if you hold a straight, you’ll win nearly 70 percent of the time. In short, the bigger your hand, the more likely you are to win. Of course, even though you’re getting a higher hit rate, you’ll also tend to lose more often. So if you hold a straight, you’re almost guaranteed to lose. But if you hold a Royal Flush, you’re going to win about one-quarter of the time, and you’ll win about twice as much money. So you’re almost certain to profit from such a hand, but you’ll also take a lot of losses.

Now, I mentioned that you’ll lose money on any hand. In fact, you’ll lose money roughly half the time. So if you hold a straight, you’ll lose about 25 percent of the time. If you hold a flush, you’ll lose about 40 percent of the time. And if you hold a pair, you’ll lose 35 percent of the time. In addition, if you hold a set — one of the two highest ranks — you’ll lose 35 percent of the time. Finally, if you hold a high card in the lowest rank, you’ll lose 30 percent of the time.

But the interesting thing is that you’ll lose less money on those losing hands than you do on winning hands. Why is that? Well, suppose you hold a straight. There’s a 65 percent chance you’ll win. But suppose you hold a pair instead. There’s a 65 percent chance you’ll win. But you lost on your last hand. So there’s now a 75 percent chance that you’ll lose again. On the other hand, if you hold a straight and lose, there’s still a 65 percent chance you’ll win again. So you’re only losing about 15 percent of the time.

This means that you can minimize your losses by playing only hands that are reasonably likely to win. So if you hold a straight, you’ll probably lose around 25 percent of the time. But if you hold a flush, you’ll probably lose around 40 percent of the time. And if you hold a pair, you’ll probably lose around 35 percent of the time. And if you hold a set, you’ll probably lose around 35 percent of the time. But if you hold a high card in the lowest rank, you’ll probably lose around 30 percent of the time.

In summary, the higher the probability that you’ll win, the lower your loss percentage will be. And the lower the probability you’ll win, the higher your loss percentage will be. So the optimal strategy is to play only hands whose probability of winning exceeds your expected return. If you hold a straight, there’s a 65 percent chance of winning, so you’ll lose around 25 percent of the time. If you hold a flush, there’s a 65 percent chance of winning, so you’ll lose around 40 percent of the time. And if you hold a pair, there’s a 65 percent chance of winning, so you’ll lose around 35 percent of the time. But if you hold a set, there’s a 65 percent chance of winning, so you’ll lose around 35 percent of the time. And if you hold a high card in the lowest rank, there’s a 65 percent chance of winning, so you’ll lose around 30 percent of the time.

Of course, you shouldn’t ignore your opponents’ actions entirely. You should always give them credit for being smart, making decisions, and doing whatever it takes to beat you. But just remember that you’re being punished for having a decent hand.