Expected Value [EV] Theory

1. Marvel Card Values

Expected Value (EV) in Poker is a very misunderstood concept. Our intention here is to explain “expected value” as simply as possible and to make you a better poker player by using expected value theory in your decision making process. Without going into a technical definition here is an example of an event that will have a zero expected value over time (EV = 0.00) so as to make this idea clear in your mind. Let’s say I asked you to pick a number between one and twenty and that each time you got it right I would pay you $20. You would expect to be able to correctly guess the number once out of every twenty tries. If I were to charge you $1 for each guess and you guessed at the number millions of times then the expected value under these circumstances would be zero. You would win $20 every twenty tries and since it would cost you $1 each try you would end up winning $20 for each $20 you gambled. If on the other hand I charged you more than a dollar for each guess you would be silly to bet against me (your expected value would be negative) and if I charged you less than a dollar for each guess then you would want to play against me all day long for the rest of your life. To put this idea into gambling terms you know that in Roulette there are 36 numbers and usually a 0 and even a 00 on a table. Clearly your EV would be zero if the casino paid you 37 to one (plus your original bet back) or 38 to one in total but in fact they give you 35 to one on your bet (and your bet back) so your expected value to make money over time is negative. And that is assuming you are betting on only one number for each spin. If you bet on multiple numbers on the same spin of the wheel then your expected value is even worse.

1. In Texas Holdem the expected value of your first two cards depend on the cards you have, your position on the table, and the number of players at the table. In other words you will be happy to know that in the dealer position (on the button) pocket aces yield an EV of 2.96.
2. High-Value Casino Denominations. Chip values above $5,000 are rarely seen by the public in casinos, since such high-stake games generally are private affairs. For very high-stakes games, casinos may use rectangular plaques that are about the size of a playing card.

Professional poker players demonstrate how to play poker and talks about the card values in Texas hold em. Transcript Rhett Butler: Hi Rick, we are here today to discuss texas hold em poker and the values of cards.

OK now you have a feeling for what we are talking about. How does all this relate to playing Texas Holdem? Glad you asked. In Texas Holdem the expected value of your first two cards depend on the cards you have, your position on the table, and the number of players at the table. In other words you will be happy to know that in the dealer position (on the button) pocket aces yield an EV of 2.96 when there are ten players at the table. This data is based on real data compiled over millions of hands and in real money games. So in the case of our AA in the dealer spot it goes without saying that you will make loads of money with pocket aces. Course we have all lost pocket aces but more often than not we will win the hand and if you have ever played Texas No Limit Holdem then you know that going all in pre-flop with pocket aces is the only time you can be sure to have the one up on all other players in the hand before you have seen a single card. It is expected value theory in Texas Holdem that can help you make a decision to go all in pre-flop (or not). Sometimes you are in a Texas Holdem Tournament and you are running out of chips and it is time to make a bold play (like the all in play). Wouldn’t you rather make a decision that at least you know that in the long run you have a positive expected value with a given hand and not a negative expected value? Sometimes it is just this little difference and this little bit of information that can help you stay in the Tournament until you are in the money as opposed to busting out early. We have taken the liberty to give you all the expected value data for 10 players all the way down to 2 players so that you can make an educated decision in the game at the crucial time instead of gambling blind on any two cards that are yours to play. Ultimately the all in play is the one situation the more talented Texas Hold’em players prefer to avoid in a pre-flop situation (unless they have pocket aces) and by using the all in strategy you will be able to improve your standing in a Texas Holdem Tournament without seeing a flop (hopefully). This is assumed that nobody calls your all in and that you pick up the blinds without a challenge.

As a rule the better the expected value of your first two cards in Texas Holdem the better the chances of you eventually winning the hand. In other words if you have an EV of 1.00 your bet in this situation will get you much more money more often than not as represented by such a strong expected value. You must note that even hands with an EV greater than 1.0 will lose sometimes. But in the long run you will make money with them. Actually the hands with an EV = 0.00 will break even over time so we suggest that you play the two first cards with a positive expected value as often as you can (depending on the situation). If you are in the dealer position with JJ and three people have gone all in for more chips than you have in total and it is your turn to play then you should fold immediately since there is a good probability that someone has a better hand and even though the EV of JJ in the dealer position is 0.89 you have to know that you are up against some very powerful hands.

In the above example we gave you the expected value of JJ in the dealer position in a ten player game. Below you will note the expected value of hands in a ten player game in the dealer position:

If you habitually play hands with large negative expected values you should not be surprised that you are losing more than you win. For example here are some seemingly good and bad starting hands in Texas Holdem and their associated negative expected values (in a ten handed game in the dealer position).

To show you the difference position makes in expected value please note below the same hands in the big blind position for a ten handed game:

In other words in the big blind an 8 7 off suit is much worse (you will lose much more money over time playing this hand) than in the dealers position.

Please send all your comments and questions about expected value to info@texasholdemgame.com. Enjoy Online Texas Holdem and play smart!

There are two different types of post-flop hands that have value in poker: made hands and drawing hands. Made hands are more straightforward than draws and typically much easier to play. In fact, learning what a drawing hand is and how to play it is an often misunderstood yet extremely important component of mastering Texas Hold’em or any poker game for that matter.

So what is a draw in poker? In poker, a drawing hand is when a player has an unmade hand that is not likely to be best on the current street but has the potential to “draw” to the best hand by the turn or river if a particular card comes. The most common draws that come to mind for most people is the flush draw or straight draw.

There are varying strengths of drawing hands ranging from a gutshot straight draw (4 potential outs) all the way up to having a powerful combo draw such as a straight draw that includes a flush draw (up to 15 outs).

What Is an Out?

An out is a potential future card that could be dealt on the turn or river that has the potential of improving a poker hand. Usually, outs are associated with cards that would likely improve a player to the winning hand. For example, if you held Ace King and the board was 952, then all Aces and Kings left in the deck would be considered “outs” since either of them would make you top pair.

What Is a Flush Draw?

A flush is when your hole cards and the community cards include 5 of the same suit. Therefore, a flush draw is when one or both of your hole cards have the possibility of making a flush on the next street.

Examples Two Card Flush Draws

Not all flush draws are created equally. The strongest flush draws are when you either have two of the same suit in your hand and two on the board, or have the Ace of one suit in your hand and 3 of the same suit on the board. Having a single card flush draw that is not to the nuts (the best hand possible) is often a sucker hand to play due to reverse implied odds.

What is Reverse Implied Odds?

Reverse implied odds means that you might improve your hand and still lose to a better draw. The weaker your flush draw the more likely it is that reverse implied odds is an issue. Therefore, unless both cards in your hand are suited, you generally do not want to invest a lot of chips chasing a flush draw. As a rule, straight draws tend to have fewer issues with reverse implied odds.

What Is a Straight Draw?

A straight draw is when one or both of your hole cards allow your hand to make a 5 card straight on the next street. The most common straight draw that most people are familiar with is the open-ended straight draw. This is where one or both of your cards are in between the community cards in such a way that you have 8 potential outs to make a straight.

While reverse implied odds problems are typically not that common with straight draws, it is still possible. If your cards are at the bottom of the potential straight and there are hands that can make a bigger straight, this is known as having the “dummy” end of the straight. The best straight draw to have is when all 8 cards are to the nuts, typically seen as open-ended straight draws.

Are There Any Other Drawing Hands?

Yes. In fact, any time you have a hand that has an obvious route to becoming the best hand on either the Turn or River, it is technically a drawing hand. Examples include:

• Bottom pair, which has 5 outs to make trips or two pair
• A gutshot straight draw, which has 4 potential outs to a straight
• A Backdoor flush draw, which can make a flush if the correct suit comes runner runner on the turn and river
  See the image below for examples of the above hands, respectively shown in the same order as written.

Weak Draws

The possibilities are endless. What is really important is in determining which draws have enough value to continue with and then choosing the correct lines to maximize the expected value. Mastering tactical play in these spots takes lots of time and effort.

What Are the Odds of Making a Draw by the Turn or River?

Understanding the odds of drawing hands is one of the basic fundamental concepts of texas hold’em. The probability of completing a draw is based on the number of outs you have. Here is a poker outs probability chart showing the odds of making a few of the common draws on the turn or river, based on the number of outs.

An Easy Math Shortcut to Help You Figure out the Odds

If you can remember the numbers 4 and 2, you can figure out your approximate chances of hitting a flopped draw on the turn or by the river. For your chance of improving by the river, multiply your expected number of outs by 4. For your chance of improving on the turn, multiply your expected number of outs by 2. That’s it, easy peasy.

Of course, the numbers won’t be exactly correct and are going to be off by around 1% most of the time. Even so, it’s close enough to make intelligent decisions at the table. Let’s test it out, just to be sure. Say you have an open-ended straight draw and are curious how often you will hit your straight by the river. Since an open ender is 8 outs, we multiply that by 4 and end up with 32. If you check the chart above, you will notice that the actual number is 31.5%; pretty dang close. Feel free to test a few other possibilities to get the hang of it.

Why Are Drawing Hands so Valuable?

Now, let’s briefly get a bit more advanced and discuss the theory of why drawing hands are so valuable. In short, it’s because they tend to do very well against the strong made hands and have much better equity against the nuts (the strongest hand possible) or near nuts, even on the turn.

Equity is basically what percentage of the pot your hand is going to win if everyone involved in the pot happened to get all-in right now at this very moment on this street. If you compare the equity of a made hand like top pair versus the nuts, you will see that that type of hand has very little chance of winning by the river. On the other hand, your run of the mill low flush draw will usually beat the stone cold nuts more than 1 in 3 times by the river.

As an example, 32s, with a two card flush draw, has over a 33% chance of winning the pot by the river versus QJo on an AKT, 36% if your opponent doesn’t share a suit with you. See the results below, as shown in a program called Pokerstove, which calculates raw flop equity based on known hole cards and the board.

Now, look at how top pair does versus the same hand.

Only 7.5% equity! Now you see the full impact of draws. Versus an opponent who likely has a really strong range, it is much better to have a draw than a medium strength hand, like top pair.

While it’s better to have a draw over a made hand when up against a really strong hand, the real power of a draw is the fact that sometimes your opponent(s) will fold and you take down the pot uncontested. This extra money you win the times that you get a fold is known as fold equity.

The Power of Fold Equity

The entire reason a draw is profitable has nothing to do with actually making your hand. Even most of the stronger draws will have less than 50% equity on the flop. If no one ever folded, then it would be virtually impossible to show a profit with a draw. Take a look at this screenshot of the graph from my recent play while holding either a flush draw or straight draw.

Hold’em Manager Graph Showing My Results With Flopped Draws

As you can see, I won a lot of money with my draws but would have been a loser if it were not for the non-showdown earnings I achieved via fold equity. These “red line” earnings were made when I bet and my opponents folded. This is known as “Semi-Bluffing.”

What is a Semi Bluff?

When you represent a made hand by betting or raising while on a draw, it is known as semi-bluffing. One of the reasons that good poker players win is not because they have the best hand at showdown more than everyone else, but rather how they make opponents fold the best hand. The best hands to “bluff” are ones that are most likely to improve on a later street; namely draws. Therefore, the most effective bluffs are ones that have a lot of equity, such as flush draws or straight draws via semi-bluffs.

Summary

Marvel Card Values

One of the keys to learning how to play winning poker is to master how to play a variety of hands after the flop. Not only do you have to know how to get value from made hands, you also have to learn how to maximize your drawing hands as well. In fact, learning how the equity of made hands versus draws works can make the difference between being a losing and a winning player. This makes mastering how to play a drawing hand of utmost importance.