Wizard Recommends

1. Poker Odds And Outs
2. Poker Odds On The Flop
3. Pre Flop Hand Odds
4. Pre Flop Odds

After the flop, the usual starting bet is two-thirds the size of the pot (the total that has already been bet). So if the pot stands at $9, you should bet around $6. If you want to re-raise, you should aim for two and a half times the previous player’s bet. So if they bet $6 you should raise to $15.

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Introduction

Flop Poker is a poker variant I have seen in many of the casinos in Biloxi. I've had reports of the game in other parts of the country too, like Atlantic City and Indiana. The game is easy to learn, community cards cause players to often win or lose in unison, and there is a possibility of a large win. A unique feature is the 'pot' bet, which carries a zero house edge.

Rules

1. Game uses a single deck of cards and all hands are scored according to traditional poker rules.
2. Play starts with the player making an Ante wager and a Pot wager. The ante wager may be any amount subject to table limits. The Pot wager is always the table minimum, which in my experience is usually $5.
3. Each player gets three cards dealt face down. The player may look at his own cards but sharing of information is not allowed.
4. Player has two options, raise or fold. If the player folds he forfeits his Ante but but retains his cards for purposes of the Pot bet. If player raises it is in the form of a Flop bet equal to his Ante bet.
5. The dealer then deals a three card flop face up. These are community cards and may be used by all players.
6. The dealer will determine the best poker hand using the player's three cards and any two of the flop cards. If the player has at least a pair of jacks the Ante wager will pay even money and the Flop bet according to the pay table below.
7. Finally, the player with the highest poker hand, again using his own three cards and any two flop cards, shall win all Pot bets. If two or more players have the exact same valued hand then the Pot bets will be chopped by the players with the high hand.

Liberal Pay Table

Hand	Pays
Royal flush	1000 to 1
Straight flush	500 to 1
Four of a kind	100 to 1
Full house	30 to 1
Flush	20 to 1
Straight	11 to 1
Three of a kind	4 to 1
Two pair	2 to 1
Jacks or better	1 to 1
All other	Loss

There is also a stingy pay table, that pays 10 to 1 on a straight, instead of 11.

Strategy

The player should raise with any of the following hands.

1. At least one card jack or higher.
2. A pair
3. 3 to a flush
4. 3 to any straight

The player will have one of these hands 86.4% of the time.

House Edge

The following table shows all the possible events in Flop Poker, the probability, win/loss, and the contribution to the total return, based on the liberal pay table. The lower right cell shows a player return of -0.054237. This means the house edge, which is defined as the ratio of expected player loss to initial wager, is 5.42%. The element of risk, which is defined as the ratio of expected loss to the total amount wagered, is 2.91%.

Return Table in Flop Poker

Event	Combinations	Probability	Pays	Return
Royal flush	1880	0.000005	1001	0.004622
Straight flush	16776	0.000041	501	0.020642
Four of a kind	234624	0.000576	101	0.058199
Full house	1676064	0.004116	31	0.127607
Flush	2126344	0.005222	21	0.109667
Straight	4321584	0.010614	12	0.127364
Three of a kind	14197576	0.034869	5	0.174344
Two pair	37615896	0.092384	3	0.277151
Jacks or better	62578504	0.153691	2	0.307382
Tens or less	229129152	0.562735	-2	-1.125471
Fold	55272000	0.135747	-1	-0.135747
Total	407170400	1	-0.054237

The house edge on the pot bet is obviously 0%.

The house edge under the stingy pay table is 6.49%.

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%

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.

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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.

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:

Poker Odds And Outs

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.

Poker Odds On The Flop

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 decimal terms. You divide .35 into its reciprocal of .65:

0.65 / 0.35 = 1.8571428

And voila, this is how we reach 1.86. If that made you dizzy, here is the short hand method because you do not need to know it to 7 decimal points.

The Rule of Four and Two

A much easier way of calculating poker odds is the 4 and 2 method, which states you multiply your outs by 4 when you have both the turn and river to come – and with one card to go (i.e. turn to river) you would multiply your outs by 2 instead of 4.

Imagine a player goes all-in and by calling you’re guaranteed to see both the turn and river cards. If you have nine outs then it’s just a case of 9 x 4 = 36. It doesn’t match the exact odds given in the chart, but it’s accurate enough.

What about with just one card to come? Well, it’s even easier. Using our flush example, nine outs would equal 18% (9 x 2). For a straight draw, simply count the outs and multiply by two, so that’s 16% (8 x 2) – which is almost 17%. Again, it’s close enough and easy to do – you really don’t have to be a math genius.

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Conclusion

Pre Flop Hand Odds

In this lesson we’ve covered a lot of ground. We haven’t mentioned the topic of pot odds yet – which is when we calculate whether or not it’s correct to call a bet based on the odds. This lesson was step one of the process, and in our pot odds lesson we’ll give some examples of how the knowledge of poker odds is applied to making crucial decisions at the poker table.

As for calculating your odds…. have faith in the tables, they are accurate and the math is correct. Memorize some of the common draws, such as knowing that a flush draw is 4-to-1 against or 20%. The reason this is easier is that it requires less work when calculating the pot odds, which we’ll get to in the next lesson.

Pre Flop Odds

By Tom 'TIME' Leonard

Tom has been writing about poker since 1994 and has played across the USA for over 40 years, playing every game in almost every card room in Atlantic City, California and Las Vegas.