You don’t need to be a math genius to make it as a poker player, but a bit of math knowledge won’t hurt. Poker is a game where luck takes a back seat and skill takes center place. You must comprehend the difference between good and poor bets if you want to succeed in this game.
However, this is only possible with an appropriate understanding of the probability math behind poker. This article will show you how to crunch numbers to calculate your chances of hitting winning odds. You’ll also see the odds of winning when you have certain hands.
Poker Odds
Poker ranks as one of the top card games in the world, enjoyed both online and in physical casinos by newbies and professionals. When computing poker odds, it can be described in two words: “for” or “against.” This means you have the odds “for” an event and the odds “against” that event. Odds “against” is a ratio of the unfavorable choices to the favorable ones, while odds “for” is a ratio of the opposite.
Simply put, poker odds can be expressed for an event or against that event. Either one is okay, as the message they pass is still the same.
For example, the odds of hitting a royal flush when you’ve got three cards in your hands is 1-to-3. This means you’ve got one chance of hitting a royal flush out of every four times. The odds against hitting a royal flush in this case will be 3-to-1, which still passes the same message.
Converting Ratio Odds to Percentages
You can also express poker odds in the form of percentages and still tell the same story. So, a 3-to-1 odd is the same as a 25% chance of hitting or not hitting a card.
The math for expressing poker odds as a percentage is simple: add both odds first, and use the sum to divide 100. In this case,
3 + 1 = 4
100 / 4 = 25%
Converting Percentage Odds to Ratio
You can also convert percentage odds to ratio odds by using the percentage to divide 100. Subtract one from the quotient (the result of your division), and you’ll get your ratio odds. For example, converting 25% odds to a ratio will go like this:
100 / 25% = 4
4 – 1 = 3
Hence, the odds in ratio form are 3-to-1.
This isn’t the only formula for converting percentage odds to ratios. You can also subtract the percentage odd from 100 and divide the quotient by the percentage odds. If you’ve got a 25% chance of losing a game, the odds in the form of a ratio can be calculated like this:
100 – 25 = 75
75 / 25 = 3
As such, the odds in ratio form are 3-to-1.
Regardless of the form you are more familiar with, ratio and percentage odds convey the same message and you can convert vice versa. You only need to understand how odds work when they’re expressed as a ratio or a percentage.
Poker Outs
A card that will complete your hand is known as an “out” in poker. Let’s say you’ve got four spades in your hand, and you only need one more to get a straight flush, which is the second-best hand in the poker hand ranking chart. This means there are nine spades or nine outs in the deck that can make that happen.
You can also see an out as that card that gives you the chance to surpass your opponent’s hand. So, you’re hitting an out when you draw a card that turns an incomplete hand into a made hand.
An example of this is when you’ve got an eight and seven of hearts. The flop is an ace of hearts, a ten of hearts, and a three of spades.
At this point, any heart that you draw gives you a flush. With two hearts in your hands and two on the flop, nine hearts are in the deck. This means that you have nine outs in that game that can give you a flush.
Outs for common poker hands include:
- 2 outs: When you hold a pair and hope to make three-of-a-kind
- 4 outs: When holding two pairs with the intention of making a full house
- 4 outs: When you hold an inside straight and hope to make a straight
- 8 outs: When you hold an open-ended straight and hope to make a straight
- 9 outs: When you hold a four-flush and hope to make a flush
- 15 outs: When you hold a straight or flush draw and hope to make a straight or flush
Common Outs in Poker for Post-flop Play
To make things easier for you, we’ve created a table below with more poker hands and their outs for both online casino and physical games. This list will also offer the probable flops for those hands.
| Type of draw | Hand | Number of Outs | Specific Outs | The Flop |
| Pocket pair to set | 2♢ 2♣ | 2 | 2♠ 2♡ | Q♢ 9♠ 4♡ |
| One overcard | 8♢ A♠ | 3 | A♢ A♡ A♣ | 2♢ J♣ 5♠ |
| Inside straight draw | 9♣ J♡ | 4 | 10♢ 10♡ 10♠ 10♣ | 4♣ Q♠ 8♢ |
| Two pairs to full house | Q♠ K♡ | 4 | Q♣ Q♡ K♢ K♠ | 5♠ Q♢ K♣ |
| One pair to two pairs or set | Q♢ A♣ | 5 | Q♣ Q♠ Q♡ A♡ A♠ | 3♠ 10♣ A♢ |
| No pair to pair | 7♢ 9♣ | 6 | 7♠ 7♡ 7♣ 9♡ 9♢ 9♠ | J♣ 2♠ 3♢ |
| Two overcards to over pair | J♡ A♢ | 6 | J♣ J♠ J♢ A♡ A♠ A♣ | 8♢ 2♠ 10♣ |
| Four of a kind | 6♢ 6♣ | 7 | J♡ J♢ J♠ 6♡ 7♢ 7♠ 7♣ | J♣ 6♠ 7♡ |
| Open-ended straight draw | 8♢ 9♣ | 8 | 6♠ 6♢ 6♣ 6♡ J♣ J♠ J♡ J♢ | 3♠ 7♣ 10♡ |
| Flush Draw | J♠ K♠ | 9 | 10♠ Q♠ 2♠ 7♠ 5♠ | 8♢ 6♠ A♠ |
| Two Overcards or Inside Straight | K♣ A♡ | 10 | Any 10, K♢ K♡ K♠ A♠ A♣ A♢ | J♠ Q♣ 6♢ |
| Flush and Inside straight draw | K♣ J♣ | 12 | Q♡ Q♣ Q♢ Q♠ Any 10♣ | A♣ 2♣ 10♡ |
| Flush draw and open straight | 10♡ J♡ | 15 | Any♡ K♢ K♠ K♣ 8♣ 8♠ 8♢ | 3♡ Q♡ 9♣ |
Blockers and Anti-outs?
One more thing worth considering while learning poker outs is the presence of blockers or anti-outs. Outs have been defined as draws that’ll complete a hand and ultimately give you a win. Nevertheless, anti-outs are poker outs that are unlikely to help you win the game but will still strengthen your hand.
This concept would be best explained with an example. Let’s assume you have a four of diamonds and a five of spades. The flop in this case is a queen of hearts, a three of spades, and a six of hearts.
With this combination, you’ll be drawing for a flush, and a seven or two can help you achieve that. However, you can also get two of hearts or seven of hearts. The two or seven of hearts will give you a straight instead of a flush.
A flush is better than a straight. While you won’t necessarily lose the game, the winning hand in this case would be lower than the optimum value. So, getting two or seven of hearts is a bad out, as it’ll cut you off from getting a flush.
Calculating the Odds in a Poker Game
Now that you’ve seen that good and bad outs exist in a game, you can optimize your calculations to know your real odds. This can happen in three ways:
- The poker odds chart
- Doing the calculations
- The rule of four and two
The Poker Odds Chart
This is the easiest method of calculating your odds, as it provides a visual representation of the outs and their corresponding odds. It doesn’t require any calculations, so you can just memorize some of its answers.
| Flop to Turn | Turn to River | Turn and River | ||||
| Outs | Odds | Percent | Odds | Percent | Odds | Percent |
| 20 | 1.35-1 | 42.6% | 1.30-1 | 43.5% | 0.48-1 | 67.5% |
| 19 | 1.47-1 | 40.4% | 1.42-1 | 41.3% | 0.54-1 | 65.0% |
| 18 | 1.61-1 | 38.3% | 1.56-1 | 39.1% | 0.60-1 | 62.4% |
| 17 | 1.77-1 | 36.2% | 1.71-1 | 37.0% | 0.67-1 | 59.8% |
| 16 | 1.94-1 | 34.0% | 1.88-1 | 34.8% | 0.75-1 | 57.0% |
| 15 | 2.13-1 | 31.9% | 2.07-1 | 32.6% | 0.85-1 | 54.1% |
| 14 | 2.36-1 | 29.8% | 2.29-1 | 30.4% | 0.95-1 | 51.2% |
| 13 | 2.62-1 | 27.7% | 2.54-1 | 28.3% | 1.08-1 | 48.1% |
| 12 | 2.92-1 | 25.5% | 2.83-1 | 26.1% | 1.22-1 | 45.0% |
| 11 | 3.27-1 | 23.4% | 3.18-1 | 23.9% | 1.40-1 | 41.7% |
| 10 | 3.70-1 | 21.3% | 3.60-1 | 21.7% | 1.60-1 | 38.4% |
| 9 | 4.22-1 | 19.1% | 4.11-1 | 19.6% | 1.86-1 | 35.0% |
| 8 | 4.88-1 | 17.0% | 4.75-1 | 17.4% | 2.17-1 | 31.5% |
| 7 | 5.71-1 | 14.9% | 5.57-1 | 15.2% | 2.60-1 | 27.8% |
| 6 | 6.83-1 | 12.8% | 6.67-1 | 13.0% | 3.15-1 | 24.1% |
| 5 | 8.40-1 | 10.6% | 8.20-1 | 10.9% | 3.93-1 | 20.3% |
| 4 | 10.75-1 | 8.5% | 10.50-1 | 8.7% | 5.06-1 | 16.5% |
| 3 | 14.67-1 | 6.4% | 14.33-1 | 6.5% | 7.00-1 | 12.5% |
| 2 | 22.50-1 | 4.33% | 22.00-1 | 4.3% | 10.90-1 | 8.4% |
| 1 | 46.00-1 | 2.1% | 45.00-1 | 2.2% | 22.26-1 | 4.3% |
With the chart above, you’ll find it easier to estimate your chances of hitting a win and avoid making some of the common betting mistakes. For instance, you have a 14.9% probability of making a flush draw following a flop (7 outs). This also means you have a 5.71-to-1 against.
These odds get better when the play shifts from turn to river, and with both turn and river. You’ll see it in the increased odds that go from 14.9% to 15.2% and 27.8%.
Doing the Calculations
This is a method for players who are good with math. Let’s pick one of the odds shown in the chart above and get its value using calculations. We’ll choose 1.86-1, which is the odds of hitting a flush when you go from flop to river.
Let’s assume there are nine hearts in the above scenario. This means you have 36 probabilities of getting two hearts and hitting a royal flush with five hearts, as shown below:
(9 x 8 / 2 x 1) = 72 / 2 = 36.
The 36 that we’ve got in this case is the chance of hitting two running hearts. However, we only need one.
Out of those 47 cards, only 38 can be combined with the remaining 9 hearts. Hence, 38 x 9 = 342, and this means that there are 342 heart/non-heart combinations present in the deck.
When you combine this with the 36 probabilities calculated earlier, you get 380. This gives you the total number of combinations that can give you a flush.
On the other hand, the total river and turn combos (or possible outcomes) available in the chart are
(47 x 46 / 2 x 1) = 2162 / 2 = 1081.
Next, divide the 1081 possible outcomes by the 380 probabilities of getting a flush.
380 / 1081 = 35.18518% or 0.3518518
When you round up this figure, you’ll get 0.352 or 0.35. The reciprocal of 0.35 is 0.65 (that is, 1 – 0.53). Divide 0.65 by 0.35, and you’ll get 1.8571428.
Approximating this will give you 1.86, which is the same as the 1.86-1 shown above. As we said earlier, this method is very confusing for people who aren’t good with math.
The Rule of Four and Two
If you don’t want to work with complex math, you can use this method to easily calculate your odds. The rule of four and two works with three simple steps:
1. First, calculate the number of outs on the deck after the flop.
2. To calculate the likelihood of striking a winning card on the turn or river, multiply the value you receive by four.
3. Multiply the number of outs on the deck after the turn by two. This will narrow things down and give you the probability of hitting a winning card on the river.
After the flop, if we apply the exact same scenario as earlier, you will have nine outs. The following step is to multiply nine by four, which results in a result of 36%. You can then calculate your chances of getting a winning card on the turn or river.
Then multiply nine by two to get 18%, i.e.; (9 x 2). You’ll notice that this number differs a bit from the precise answers shown on our chart. That’s because this shorthand method isn’t very precise, but it’s good for estimations and gets the job done.
Conclusion
Calculating the odds in poker is a skill that all good poker players must learn as it can be the difference between winning and profiting or losing. To maximize your chances of winning at the poker table and make the greatest selections, it’s essential to know this information.
While counting outs, you should also bear a few factors in mind. First, stronger hands give you more outs. The second is that outs cannot be counted more than once.
So, if you’ve got the same outs appearing in two types of draws (like flush draw and open straight), you’ll count them once. That’s why we got 15 outs in our example in the article instead of 17.
Avoid slow playing until you have a solid understanding of table behavior, as itker. Here are so doesn’t improve your odds in pome scenarios where it’s acceptable to consider slow playing.
Consistently play poker logically and according to your odds of winning, not out of anger or pride. Remember that you don’t need to “defend your way through the hand.”