Getting a royal flush = 1 in 649,740 odds Starting with 4 royal flush cards = 1 in 2,777 3 RFCs = 1 in 92 2 RFCs = 1 in 13 1 RFC = 1 in 6. Drawing to a Royal. We just discussed how players can receive certain parts of a royal flush and improve their opportunities of getting video poker's best hand. Calculate the probability of a Royal Flush: First calculate the total number of possible hands in a 52 card deck: From a deck of 52 cards, we want the number of possible unique ways we can choose 5 cards.

In our poker math and probability lesson it was stated that when it comes to poker; “the math is essential“. Although you don’t need to be a math genius to play poker, a solid understanding of probability will serve you well and knowing the odds is what it’s all about in poker. It has also been said that in poker, there are good bets and bad bets. The game just determines who can tell the difference. That statement relates to the importance of knowing and understanding the math of the game.

In this lesson, we’re going to focus on drawing odds in poker and how to calculate your chances of hitting a winning hand. We’ll start with some basic math before showing you how to correctly calculate your odds. Don’t worry about any complex math – we will show you how to crunch the numbers, but we’ll also provide some simple and easy shortcuts that you can commit to memory.

Basic Math – Odds and Percentages

Odds can be expressed both “for” and “against”. Let’s use a poker example to illustrate. The odds against hitting a flush when you hold four suited cards with one card to come is expressed as approximately 4-to-1. This is a ratio, not a fraction. It doesn’t mean “a quarter”. To figure the odds for this event simply add 4 and 1 together, which makes 5. So in this example you would expect to hit your flush 1 out of every 5 times. In percentage terms this would be expressed as 20% (100 / 5).

Here are some examples:

2-to-1 against = 1 out of every 3 times = 33.3%
3-to-1 against = 1 out of every 4 times = 25%
4-to-1 against = 1 out of every 5 times= 20%
5-to-1 against = 1 out of every 6 times = 16.6%

Poker Probability Royal Flush Valve

Converting odds into a percentage:

3-to-1 odds: 3 + 1 = 4. Then 100 / 4 = 25%
4-to-1 odds: 4 + 1 = 5. Then 100 / 5 = 20%

Converting a percentage into odds:

25%: 100 / 25 = 4. Then 4 – 1 = 3, giving 3-to-1 odds.
20%: 100 / 20 = 5. Then 5 – 1 = 4, giving 4-to-1 odds.

Another method of converting percentage into odds is to divide the percentage chance when you don’t hit by the percentage when you do hit. For example, with a 20% chance of hitting (such as in a flush draw) we would do the following; 80% / 20% = 4, thus 4-to-1. Here are some other examples:

25% chance = 75 / 25 = 3 (thus, 3-to-1 odds).
30% chance = 70 / 30 = 2.33 (thus, 2.33-to-1 odds).

Some people are more comfortable working with percentages rather than odds, and vice versa. What’s most important is that you fully understand how odds work, because now we’re going to apply this knowledge of odds to the game of poker.

The right kind of practice between sessions can make a HUGE difference at the tables. That’s why this workbook has a 5-star rating on Amazon and keeps getting reviews like this one: “I don’t consider myself great at math in general, but this work is helping things sink in and I already see things more clearly while playing.”

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Counting Your Outs

Before you can begin to calculate your poker odds you need to know your “outs”. An out is a card which will make your hand. For example, if you are on a flush draw with four hearts in your hand, then there will be nine hearts (outs) remaining in the deck to give you a flush. Remember there are thirteen cards in a suit, so this is easily worked out; 13 – 4 = 9.

Poker Probability Royal Flush Rules

Another example would be if you hold a hand like and hit two pair on the flop of . You might already have the best hand, but there’s room for improvement and you have four ways of making a full house. Any of the following cards will help improve your hand to a full house; .

The following table provides a short list of some common outs for post-flop play. I recommend you commit these outs to memory:

Table #1 – Outs to Improve Your Hand

The next table provides a list of even more types of draws and give examples, including the specific outs needed to make your hand. Take a moment to study these examples:

Table #2 – Examples of Drawing Hands (click to enlarge)

Counting outs is a fairly straightforward process. You simply count the number of unknown cards that will improve your hand, right? Wait… there are one or two things you need to consider:

Don’t Count Outs Twice

There are 15 outs when you have both a straight and flush draw. You might be wondering why it’s 15 outs and not 17 outs, since there are 8 outs to make a straight and 9 outs for a flush (and 8 + 9 = 17). The reason is simple… in our example from table #2 the and the will make a flush and also complete a straight. These outs cannot be counted twice, so our total outs for this type of draw is 15 and not 17.

Anti-Outs and Blockers

There are outs that will improve your hand but won’t help you win. For example, suppose you hold on a flop of . You’re drawing to a straight and any two or any seven will help you make it. However, the flop also contains two hearts, so if you hit the or the you will have a straight, but could be losing to a flush. So from 8 possible outs you really only have 6 good outs.

It’s generally better to err on the side of caution when assessing your possible outs. Don’t fall into the trap of assuming that all your outs will help you. Some won’t, and they should be discounted from the equation. There are good outs, no-so good outs, and anti-outs. Keep this in mind.

Calculating Your Poker Odds

Once you know how many outs you’ve got (remember to only include “good outs”), it’s time to calculate your odds. There are many ways to figure the actual odds of hitting these outs, and we’ll explain three methods. This first one does not require math, just use the handy chart below:

Table #3 – Poker Odds Chart

As you can see in the above table, if you’re holding a flush draw after the flop (9 outs) you have a 19.1% chance of hitting it on the turn or expressed in odds, you’re 4.22-to-1 against. The odds are slightly better from the turn to the river, and much better when you have both cards still to come. Indeed, with both the turn and river you have a 35% chance of making your flush, or 1.86-to-1.

We have created a printable version of the poker drawing odds chart which will load as a PDF document (in a new window). You’ll need to have Adobe Acrobat on your computer to be able to view the PDF, but this is installed on most computers by default. We recommend you print the chart and use it as a source of reference. It should come in very handy.

Doing the Math – Crunching Numbers

There are a couple of ways to do the math. One is complete and totally accurate and the other, a short cut which is close enough.

Let’s again use a flush draw as an example. The odds against hitting your flush from the flop to the river is 1.86-to-1. How do we get to this number? Let’s take a look…

With 9 hearts remaining there would be 36 combinations of getting 2 hearts and making your flush with 5 hearts. This is calculated as follows:

(9 x 8 / 2 x 1) = (72 / 2) ≈ 36.

This is the probability of 2 running hearts when you only need 1 but this has to be figured. Of the 47 unknown remaining cards, 38 of them can combine with any of the 9 remaining hearts:

9 x 38 ≈ 342.

Now we know there are 342 combinations of any non heart/heart combination. So we then add the two combinations that can make you your flush:

36 + 342 ≈ 380.

The total number of turn and river combos is 1081 which is calculated as follows:

(47 x 46 / 2 x 1) = (2162 / 2) ≈ 1081.

Now you take the 380 possible ways to make it and divide by the 1081 total possible outcomes:

380 / 1081 = 35.18518%

This number can be rounded to .352 or just .35 in