This guide is for you if you have a basic knowledge of poker, but don't have a clue about Texas Hold'em poker odds or how they work. After reading this you'll find it easier to beat your friends and win in online poker rooms.
At first, poker odds can seem confusing, but if you're going to take poker seriously then having a basic knowledge of them is critical (it'll be clear why after reading this page). This short, practical guide and the tools within will give you everything you need to gain the upper hand on both real and online tables.
Right then buckle up because we are going to take a short drive through the world of poker odds. But before we pull off the driveway, let's start with a back to basics look at odds and what they mean.
When the odds are particularly large against you winning, you'll often be referred to as the "long shot", which generally means it will be a cold day in Hell before you succeed.
Before we can get into a discussion of poker odds while playing poker online, you need to know how to calculate your "outs." Outs are simply the cards that will help you improve your hand and make it better than what you think your opponent is holding.
We have already determined that you have nine "outs". Now there are 52 cards in a deck and two of those are in your hand, leaving 50. In addition, there are four cards exposed from the flop and turn, leaving 46 cards. Although your opponent is holding two others we ignore those. Our calculations in Internet Texas Hold'em poker are only based on the cards you can see and what could be left in the deck.
With nine outs and 46 cards unknown, there are nine cards that will let you win the hand and 37 cards (46 unseen cards - 9 winning cards) that will cause you to lose. Thus the odds of you getting one of the cards you need on the river are 37 to 9. This simplifies down to just about 4:1. In other words, you are four times more likely to lose this pot than you are to win it.
So we have odds of around 4:1 to win this hand. To decide whether or not we should call our opponent's bet depends on how much money is in the pot. No, we don't mean that if there's a whole bunch of cash you should just go for it. What you should be looking for is the ratio of money you could win compared to the size of your opponent's bet.
OK, we'll continue our example. Let's say there was $90 in the pot and your opponent bets $10. That makes a total of $100 in the middle of the table just waiting to be won. You need to match your opponent's bet of $10 to see the river card, so it's going to cost you $10 to see if that last card is going to be one of the nine you need to win.
In this example by betting $10 your opponent has effectively given you odds of 10:1, when your actual chance of winning is 4:1.
This is like a bookmaker giving you 10:1 odds on a horse that has a 4:1 chance of winning. So should you call that bet? Yes and you should do it faster than an eye can blink because the odds are offering you the chance to enjoy a great pay day.
Even if you make that call, you might still lose. It happens. Remember, your calculated odds were 4:1, meaning the poker gods say you will lose four times for every time you win. That's why it is important you are being offered at least the chance to win four times as much as your bet, because in the long run you'll break even. More importantly, if you are being offered the chance to win more than four times your bet, you'll eventually make money.
Now that you have worked through the math and seen the theory, it is time to introduce a handy shortcut. This will help you calculate your chances of winning a hand within the short period of time that Internet poker allows you to make a decision.
While this method is not super precise, it provides a clear enough guide when calculating odds in online poker. Of course, the purists out there will still want to do mental gymnastics to get the exact percentage figure, but for the rest of us mere poker mortals the rule of 4 and 2 is more than enough to give reasonable percentages.
When preparing these we have not included any odds that incorporate there being two cards to come (i.e. situations after the flop). Instead, all these poker odds assume that you're on the turn and want to see a river. So, without further ado:
For example, an 8-7 on an A-9-6-2 board. You have 8 outs: the four fives and the four tens. These hand odds of winning presume that there is no possible flush on the board, and that you're drawing to the best hand. Be aware that if you have 7-6 on a A-9-8-K board, the tens may not be outs for you, as they could possibly make someone who has QJ a bigger straight.
If your hole cards are suited, and there are two more of your suit on the board, you can most often treat any flush as the nuts since it's very rare that you will be up against another person with two hole cards of your suit. If you are drawing to a four flush on the board, however, you should be extremely careful if you do not have the ace. Poker players like drawing to flushes, and also like playing aces - these two facts combined make your odds of winning a lot lower if you chase anything but the nut flush.
Again, I'm assuming that you're drawing to the nuts, e.g. with 8-7 on a board of A-9-5-K. Any of the four sixes will give you the nuts. Unless you use both your hole cards to make the straight, however, you will not be drawing to the nuts. If the board is A-9-6-5 and you have 7-2, any 8 will give you a straight, but it's not the nut straight; someone with T-7 will have the nuts.
If you have J-T on a board of A-J-8-3, and you strongly suspect that you're up against someone with a pair of aces, you have five outs to beat him: three tens (giving you two pair), and two jacks (giving you trips). Your odds here are based on the assumption that your opponent does not have AJ or AT! This is a dangerous assumption to make, and you should realistically have better odds than 8:1 to profitably make this call to make up for the times when you are actually drawing to only half as many outs as you think you are.
Now we've really entered a dangerous assumption. If you have KQ on a board of 8-5-2-J, and you think your opponent has made a pair of eights, but without a queen or a king kicker, you have six outs (any queen or king will make you a better pair). The odds of 6.7 - 1 only hold true if your assumption is correct. It will often be the case that you're wrong, so be very careful with this situation.
If you're holding 7-7 on a A-K-9-2 board, and your only saving grace is a third 7. This is a really far fetched draw, and our only reason for including it is to show just how far fetched it is. We have (almost) never seen a pot big enough to warrant drawing to a set. Fold in all but the most extreme pot sizes.
This is the generic formula. If you have a draw other than the ones we've listed above, and want to figure out your odds for it, this is the way. Count the number of outs you have and then subtract this number from 46. Divide the result by the number of outs, and voila - you have your odds. For example, if I'm drawing both to a set and to a flush, e.g. I have reason to believe my opponent has two pair, and I have AA, with four to a flush, my outs are any ace (giving me a set) plus 9 flush cards (giving me a flush), totalling 11 outs. This gives:
46 - 11 = 35.
35 / 11 = 3.2
My odds of drawing a winner are 3.2 : 1
Don't forget that you can always use our poker odds calculator, especially when reviewing your poker hands and studying.
Here's our at-a-glance guide to pot odds in poker and which hands to play. You can download and print out this Texas Hold'em poker odds guide to have next to you when you play. Click the image below to enlarge the poker odds chart or download the pdf here.
There are many ways to calculate different kinds of poker odds. Sometimes, rote memorisation helps – for example, knowing that a small pair against two overcards before the flop is roughly 50/50; knowing that a small pair against a big pair is a 4/1 underdog, etc.
Other odds calculations require more effort and practice. It's best to routinely use an odds calculator to check what your odds were after the fact; you can then adjust your play based on this information in future, similar hands.
The rule of four and two is the easiest way to know roughly what your odds of winning the hand are.
It's a simple process: first, work out how many cards you can hit to improve your hand (outs). For example, if you have a flush draw, there are nine cards you can hit to make a flush.
To know the odds of making your flush on the turn, simply multiply your outs by two and add two. To know the odds of making your flush on the river, multiply your outs by four and add four. In this case, you have a roughly 40% chance of making your flush by the river.
The best way to calculate precise preflop odds is to use a dedicated odds calculator. However, here are a few quick and dirty tricks to know rough odds on the go:
Pot Equity refers to your percentage chance of winning the pot. It is the amount that may belong to you depending on what cards you have. This could be at any stage of the game. For example, if there is a 70% chance you'll be successful and win, you have 70% equity in the hand.
Pot odds refers to the price of calling a bet relative to the size of the pot. For example, if the pot is $100 and your opponent bets $100, then you have to call $100 to win $200 (their bet plus the pot). This means you're getting odds of $100 to $200, or 2/1. It can be tricky to work out pot odds exactly, but estimating is usually fine.
To calculate Pot odds, you'll first need to know your outs. Outs are the cards that can improve your hand. There are many ways to calculate Pot Odds but here's a simple one. Rather than using a formula, poker players around the globe use the Rule of 2 and 4. The rule says that if you have two cards to come, you can multiply the number of outs you have by four and you'll come to an approximate percentage of making your hand. If you have only one card to come, you can multiply your outs by two to reach an estimated percentage.
Good odds simply means that the odds you have to call are better than the odds of making your hand. For example, if you have a flush draw and face an all-in bet on the flop, you will have a roughly 40% chance of making your flush and winning. That 40% is around 3:2, so if you have to call a bet of $200 to win $300 or more, you're getting good odds and should call.
If you have a pocket pair, you will flop a set roughly one time in nine.
If you have two suited cards, you will flop a flush roughly one time in 118. You'll flop a flush draw around one in ten times, though.
On average, you'll be dealt pocket aces once every 220 hands.
Some common poker hand odds are open-ended straight draws at 4.8:1, four to a flush at 4.1:1, inside straight (belly buster) at 10.5:1, one pair drawing to two pairs or trips at 8.2:1, overcards on a ragged board on the turn at 6.7:1, drawing to a set at 22:1, and drawing to X outs at (46-X) / X:1.
The more players that are involved in the hand, the lower your chances of winning the pot – even if you're a favourite. For example, the most powerful starting Hold'em hand is pocket aces. If you're up against a random hand, you'll be a huge 85% favourite. If you're up against five random hands, you'll still be a huge favourite, but you'll only win the pot 49% of the time.
On top of that, the more players in the pot, the higher the chances that they hold some of your outs. If two players have flush draws, they only have seven outs (not nine) to hit their flush – and one of them will lose a big pot!
If you do not distinguish between suits (which are not ranked in most poker games), then there are 169 different starting hands in Texas Hold'em. The best is A-A and the worst is either 7-2 or 3-2 unsuited. If you do differentiate between suits, there are 1,326 possible combinations of two cards.
"Outs" are simply the technical term for the number of cards that can make you the winning hand. For example, if you have Ah-Qh against Jc-Jd on a flop of 8h-5h-2c, you can win with any heart, queen or ace for a total of fifteen outs.
An out card is simply a card that will help you win. To calculate, take a look at this example. If you're planning on winning with a flush and you have four spades, then there will be nine spades left in the deck. So you can win with any of these nine spades. There are thirteen cards in a suit, so you can easily calculate that because you have four spades there will be nine left (13 – 4 = 9).
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If you would like more information on the math involved in figuring out probability when it comes to poker, check out this article on poker math.
For more on poker odds and implied odds in general, see "Theory of Poker" by David Sklansky. For a good discussion on how to figure out your poker odds in No-Limit Texas Hold'em situations, have a look at "Harrington on Hold 'em", volumes I and II, by Dan Harrington and Bill Robertie. For more discussion on counting your outs and specifically how to discount them, see "Small Stakes Hold 'em" by Ed Miller, David Sklansky and Mason Malmuth.
The Fundamental Concepts of Poker article series starts with Expected Value.
ProblemGambling.ca Math of Gambling PDF
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