Playing the Odds

Perhaps the most important factor in Texas Hold ‘Em is the value of your two card hand BEFORE the flop.  That value is closely aligned to the probability of your win. 

Here is a table you may find helpful.  This focuses on the pocket or hole card odds, and more specifically on the odds you will GET that particular set of two-cards. 

Now take a look at the table below to see the two-card hand values. 

You can afford to be more flexible if you are seated in a late position at the table, but be more conservative and selective if your position is an early position at the table. 

The following table will give you the odds of a win when using that particular two-card combination. 

We limited the results to those with least a 45% probability. 

Consider the odds!  There are over two and a half million possible hands in Texas Hold ‘Em, so the more familiar you are with the odds and probabilities (we will talk more about probabilities later in this book), the better your game will be and the more times you will win.

While we would never give short shrift to profiling behavior and other factors, the real core of the game is in understanding the chances you have to win when you are dealt a particular hand. 

Let’s say you play 100,000 hands of poker during your poker career – an admirable goal! 

What could you expect in the way of odds?  Just how many great hands would you be dealt?

50,000                       Pat Hands
40,000                       Hands with One Pair
20,000                       Hands with No Pair
5,000                        Hands with Two Pair
2,000                        Hands with Three of a Kind
400                           Hands with a Straight
200                           Hands with a Flush
170                           Hands with a Full House
25                             Hands with Four of a Kind
1.5                            Hands with a Straight Flush
.15                            Hands with a Royal Straight Flush

Good Texas Hold ‘Em players use the odds to make their playing decisions.  They don’t play be ‘feel’ or with their eyes closed. 

The chances of finishing a flush or a straight you think you could make, or the probability of getting a face card, or the percentage of times you might get a flop card to match your pocket (or hole) pair are all factors in how you will play the game, or whether you will fold.

The reason you need to understand the odds is so that you can know when to bet, when to raise, etc.  Without that knowledge, you are just guessing. 

Consider these examples for the pre-flop odds in a ten player game:

Example 1 - Let’s say you have two queens in your hand.  It is now time to call or raise the bet.  At this point, your chances of winning the hand are about 22%. 

If the pot was $60.00 and you had a 22% chance of winning, your ‘pot odds’ would tell you that you could safely bet up to $13.20. 

But what if someone decides to bet heavily?  What are the odds that they have a good hand?  Over half of all Texas Hold ‘Em pots are won with a pair of 9s or something better. 

How does that compare to what you have?  You should continue to play a tight game unless the players at your table are all big fish.

Example 2 - Your hole or pocket cards happen to be a pair of aces!  If you look at the 10 player table above, you will note that your chances of winning are about 31%.  

So, you have a distinct advantage pre-flop.  What should you bet?  Well, if you use the betting strategy we gave you earlier, you would not bet more than 31% of the pot, right?   

Let’s say the pot is $200.00.  Your highest bid would be $62.00 (31% of $200.00).  But here’s a question.  What if you did not need to bet that much to stay in the game?  Should you use the additional money you COULD bet to raise the bid? 

Before you make this decision, consider two things.  If you raise to your maximum bet, you may drive players out of the game, which would improve your odds of winning. 

However, if you WANT to keep more hands in the game so that the pot will increase even more in value, you should play it a little cooler so that you will not have a mass exodus. 

Remember that you are not 80-90% sure of winning.  Your hand is valued at 31%. 

So you might want to raise the bet to $40.00 to see who stays in the game.  If the table is strong, you might bet something less $20.00 or $25.00

Example 3 – Let’s say you draw a pretty bad hand, namely a 7 and a 2.  The odds are really against you. 

You have no high cards to build on and you have no real straight or flush prospects.   Your chances of winning are about four percent. 

You should ONLY stay in the game through the flop if it will cost you less than the value of your hand, which is four percent of the pot. 

If your maximum bet in a $100 pot is $4.00, and the blinds are established at five and ten dollars, you would need to have at LEAST a ten percent chance of winning to stay in the game. 

You don’t have that chance.  Your chances are limited to four percent. 

Under these circumstances, you will want to fold.  While it is true that you might be able to get a pair or two out of the flop, you have to weigh the probability that will happen against the odds you KNOW you have in your hand. 

If you are always looking at the odds, you can use your knowledge of the odds when you want to decide whether to bluff.  This technique comes in handy when the pot is large with only 2-3 players at the table.

Bluffing to the Odds - Here is an example you might find useful:

You are in a two-person game (5-10 dollars), and you are on the river with $140.00 in the pot. 

You don’t make the river which you thought might reap you a straight or a flush, or perhaps you saw a flop that started with two hearts and a spade, and proceeded with two additional spades. 

If you have two hearts in your hand, you might want to bluff, even if your opponent checks you.  At this point, you know you have probably lost, but if you can get him/her to back down, your bluff will win you the game.

Rather than check at this point, you could plunk down another ten dollars to get you odds of 14 to 1, and hope they fold.  

If this strategy works for you at least seven percent of the time, you will make money in the LONG RUN.  If not, it is a strategy you should dump.  Perhaps you are just really bad at bluffing? 

Just remember that the more players who are seated at the table, the less likely the odds will support your bluff.  Stick to bluffing in smaller games and you are likely to come out the winner more of the time. 

When you consider whether it is worth learning and playing the odds, consider this:  If you change your odds of winning by only 5%, you can take a 10/100 record and change it to 15/100.

Using the 10 wins for every 100 games scenario, if you have a stake of $100.00, with the house taking a rake of $1.00 per pot, you would get $90.00 at the end of your poker session if you had played one hundred games.  So you lost $10 after 100 games. 

What’s the big deal? 

But if you increase your winning advantage by a mere five percent with a pot of $115.00 for the hundred games, you could make eighteen thousand dollars by playing three nights a week for twelve months. 

Not bad for a mere 5% advantage! 

Odds and Outs - To further explore the concept of ‘odds’ let’s look at the idea of ‘outs’.  Outs are cards you need to make the hand you want to create so you can win the pot. 

If you need four cards to make your hand, you have ‘four outs’. 

Let’s say that you have a six of clubs and a seven of diamonds and you find, much to your pleasant surprise, that there is a nine of spades in the flop. 

You can use this with an eight to create a straight, right?  The thing you have to consider is the odds of your getting that card. 

Before we leave the subject of out odds, we should tell you about the ‘rule of four-two’. 

This is an easy way to figure out the odds when you know the number of outs.  While it isn’t completely fool proof, it is a fast method and it will keep you playing with a good, solid idea of your odds for making your hand. 

With two cards to come after the flop you will multiply your outs by the number four. 

With one card to come, you will multiply your odds by the number two.

Here is an example: 

Your Hand                    # of Outs            # of Cards to Come
Four Card Flush           Nine                  Two

Do the math:  9 x 4 = 36. 

A rough estimate of your odds would give you a 36% chance of making your hand.  If you were to look at a true odds chart, you would find that the actual number is 35%. 

Not too far off for a ‘guesstimate’! 

Pot Odds – Let’s talk in more detail about analyzing pot odds.  When you look at the current size of the pot in your game and weigh that against your next call or bet or raise, you see that your decision can be important to whether you stay in the game or fold. 

Here are a few examples: 

Example 2 – You have $200.00 in the pot and you have a bet of $10 in front of you.  You need to fill a four card flush, so you have a one in four chance (or 25%) to get what you need. 

If the odds are about 25% and you only have to bet 5% of the current pot to stay in the game, you are OK.  You only have to bet $10 to stay in and you could afford to bet $50.00 and stay within your card odds. 

Example 1:  Let’s say you are in a $5.00 to $10.00 game holding a JT pocket with only one opponent left on the turn.  You have an outside straight draw with a board that looks like this:  2, 5, 9, QA, and only one river card left to make that straight. 

Any 9 or K will finish it. 

You have eight outs (four 8s and four Ks in the deck), and 46 unknown cards.  With an eight out of forty-six chance of getting your hand, you have about a 17% chance of winning.  

You can make that $10.00 bet when it comes around to you, and the odds are 17% so you are still ahead of the odds.  If your bet or call is smaller than the 17% odds you can get your next card at a discount.

Don’t just throw away what you consider a bad card. Figure the odds for the hand and the pot and play accordingly.  You may be able to build that great hand and win anyway.

By the same token, don’t just keep drawing in hopes for that flush or straight. 

Look at the options and weigh them against the odds.  In other words, is there enough money in the pot to justify the risk or should you just fold? 

If there is a reasonable chance of winning, you may want to stay in the game and shoot for the big pot.  Knowing the card and pot odds will help you make that decision.

For a pot of $100.00 with a $10.00 call, you should win at least once every eleven times if you are going to break even. 

If you have to draw for a flush, your odds would be about 35%.  If the bet is $5.00 to you, should you call?  What are the pot odds?  With fifteen dollars in the pot and a $5.00 bet to you, your odds are 25%. 

To break even, you would have to win once out of every five times you play this combination. Your chances of making that draw are better than that! 

Your chances are about one in three, so you can go ahead and play for the profit margin! 

If you do not win this time, you will win when you make this play in the long run and you will make money.  If your pot odds are better than the five to one required, why not take the chance?

But if your pot odds become an even bet, you probably don’t want to take the 50-50 chance you will win.   You might fold or try a partial bluff to see if you can stay in long enough to improve your hand.

While it is a great idea to memorize the odds so you can quickly calculate your cards and pots, the basic idea is more important.  Play draw hands when your POT ODDS are better than your CARD ODDS.

Implied Odds – This technique uses odds coupled with a prediction about how other players will react in the game.  

If for example you are in a $5.00 to $10.00 game with a four flush at the flop, and your neighbor bets, you might see that everyone else folds. 

If the pot is $50.00, you first have to do your math to figure out the chances that you will get your flush on the turn (19% - or about a 1 in 5 chance). 

To stay in the game, you will have to call the $5.00 bet and when you consider the $50.00 pot that is OK.  A one in five chance is better than a one in ten chance so the odds are OK. 

But you still have to consider what the opponent will do.  He is going to bet on the turn and the river so that’s another $10.00 for each bet, bringing your total bet to $25.00.

Your chances of hitting the flush on the turn or the river are about 35% (a better than one in three chance now) but you have to pony up that $25.00, bringing the total of the pot to $100.00. 

You have a one in four chance of winning when you consider your investment in the pot versus the pot size. 

That’s still OK.

But what if you don’t make the hand on the turn.  You’d have to change your outs and your odds to reflect the game you are now both playing. 

Your chances of getting the flush now stand at 19.6%, but your chance of winning when you consider the pot odds, seem OK. 

You have to make a $20.00 investment but you’ll get the $100.00 pot if you do and you can figure a one in five chance of that.  

If you decided to take your chances and stay in, you might consider raising your opponent to get another $20.00 to $40.00 in the pot. 

As you can see, if you master the outs and the  pot odds, you can use these to your advantage in trying to predict the implied odds and player behavior. 

Before we leave the subject of odds, let’s look at a few more examples so you can test your ability to judge and strategize. 

Example 1 – You are dealt a pair of Jacks.  But the flop does not reveal another Jack.  What are the chances that you will get a Jack on the turn?  Here’s a hint:  calculate the number of outs and divide it by the number of cards in the deck. 

With two more Jacks in the deck, you have 47 more cards to see.  You have already seen five of them (your two pocket cards, and the flop).  Under these circumstances you would have about a 4.3% chance of pulling another Jack (.0426%).

What if there is no Jack on the turn?  You still have the river, right?  And there are still two Jacks left somewhere, but there is one less card in the deck.  The odds remain about the same for those 46 remaining unknown cards (about 4.3% or .0434%). 

But what if you wanted to get BOTH the remaining Jacks on the turn or the river.  If the chances of getting ONE Jack are 1 in 47 at the turn, what are your chances of getting that second Jack at the river?  

Since you already have the first one you wanted, you would be looking at only one Jack left in the deck.  So the chances are still 1 in 46 or 2.2% (.0217%).  If you multiply the .0426 x .0217, you get .0009 (1/10th of a percent).  That is not a bet we would suggest you make! 

Example 2 – You try this one!  You have a straight draw.  What are your chances of hitting the straight on your next card?  A K or 8 will complete your hand and you can assume there are four left in the deck.  You have eight outs at the flop. 

What are the chances of getting what you want at this point? 

a.     12%
b.     15%
c.      17%
d.     20% 

You will find the answers for these questions at the end of this chapter! 

What if you didn’t get the card on that turn and you want to calculate your chances now?  There are now 46 cards left in the deck and eight that will help you win.  What’s the chance you will win now? 

What are your chances of getting that card on the turn or the river? To get that information, you will have to calculate the chances of NOT getting the K or 8.  Invert the probabilities (by subtracting them from one), and then multiply them to get your number. 

{39/47}  x  {38/46} results in what odds?

Example 3 – Let’s say you are dealt the Kd and the 9h.  The flop contains a Ks, a 9c and a 4c.  What are your chances of getting the full house on the turn?  You will need a K or 9 and there are two of each of these left in the deck so you have four outs. 

With 47 cards left after the flop your chances are four out of forty seven or about 8.5% (.085). 

Can you get a full house on the river?  Those chances are not going to change much with one card (four in forty six), so your shot here is about 8.7% (.087). 

What about your chances on the turn OR the river?  It WON’T happen on the turn 43 out of 47 times (.915).  On the river, it WON’T happen 42 out of 46 times (.835). 

If you invert those numbers, you get a 16.5% chance that you will get your hand by the river. 

What are your chances of getting four of a kind?  You’ll need to get the full house on the turn and if you recall, the chances of that are .085.  The chances of your getting the same card again are 1 in 46 or 2.2% (.022). 

If you multiply these two (.085 x .022), you get 1/5 of one percent.  Half the time it will be K and the other half of the time it will be a 9. 

Return on Investment (ROI) - When  the  stakes increase, it stands to reason that there will be an increase in the average winnings. 

Players will play tight games at the beginning of play, so the pots will not grow as fast.  If that is the case, your ROI will go down as the small blind goes up.

Take at look at this table to see what we mean:

One of the benefits of playing Texas Hold ‘Em in an online casino is that these casinos release data to show the ROI on various hands versus the bets made.  For example, in a $2.00 game, the winning pot was 28-37 times the big blind.  

Average pots were about $60.00.  So, if you have the right hand, you can expect a 3,000% return on your investment!

If you are in a high-stakes game ($200), while the pots may average anywhere from six to twelve hundred dollars, the risk is also much greater, and the games will be much tighter. 

Pots will only be about five or six times the big blind.  

The low stakes tables seem to be a better bet, especially for the fish! 

You should consider that while the high-stakes tables play a tighter game, that does not mean they play a slower game.  If you are not ready for the action and you find it hard to make decisions quickly, you should beware.  

A recent study revealed that a large percentage of games with pot totals over one thousand dollars were completed in less than one minute, and many more in less than six minutes. 

If you look at the speed on the low-stakes tables, you will find about the same statistics, so there isn’t much difference in the pace of play. 

When you consider the hand odds, the pot odds and other strategies and information you will use to make your decisions, think about this:  Most Texas Hold ‘Em online casinos report an average of 50-60 hands each hour, PER TABLE.

When you consider risk versus reward, the $5.00 to $10.00 limit tables are the best bet for a novice or minimally skilled player

Before we leave this section on Playing the Odds, we will offer one last encouraging note. 

Before you get crazy trying to memorize odds or decide to quit the game because you are discouraged by the need to keep all these numbers in your head, you should know that you can get odds charts that will easily help you figure out odds in your hand and odds for modified strategies as the game proceeds.

Oh, yes and for those of you who are keeping score, here are the correct answers to that little test we gave you above in Example 2 of the Implied Odds section!

The correct answers appear in bold, below:
 
Example 2 - You have a straight draw.  What are your chances of hitting the straight on your next card?  A K or 8 will complete your hand and you can assume there are four left in the deck.  You have eight outs at the flop. 

What are the chances of getting what you want at this point? 

a.     12%
b.     15%
c.       17%
d.     20% 

What if you didn’t get the card on that turn and you want to calculate your chances now?  There are now 46 cards left in the deck and eight that will help you win.  What’s the chance you will win now? 

What are your chances of getting that card on the turn or the river? To get that information, you will have to calculate the chances of NOT getting the K or 8.  Invert the probabilities (by subtracting them from one), and then multiply them to get your number. 

{39/47}  x  {38/46} results in what odds?

      
The Wonderful World of Poker Probability