This may help, an article I have in my documents......
Hand odds are the chances of you making a hand in texas hold'em poker. For example, if you hold two hearts and there are two hearts on the flop, your hand odds for making a flush are about 2 to 1. This means that for approximately every 3 times you play this hand, you will hit your flush one of those times. If your hand odds are 3 to 1, then you would hit your hand 1 out of every 4 times.
X to 1 odds = You hit your hand 1 out of (X + 1) times
X to 1 odds = 1 / (X + 1) = % chace to hit your hand
(Example: 3 to 1 odds = 1 / 4 = 25% chance to hit your hand)
Outs Flop% Turn% Flop Odds Turn Odds Draw Type
2 8% 4% 12 22 Pocket Pair -> Set
3 13% 7% 7 14 Single Overcard Draw
4 17% 9% 5 10 Gut Shot, Two Pair -> Full House
5 20% 11% 4 8 One Pair -> Two Pair or Set, Gut+Backdoor
6 24% 13% 3.2 6.7 No Pair -> Pair, Two Overcard Draw
7 28% 15% 2.6 5.6 Set -> Full House or + (not counting extra turn outs)
8 32% 17% 2.2 4.7 Open Straight Draw
9 35% 19% 1.9 4.1 Flush Draw, Open+Backdoor Draw
10 38% 22% 1.6 3.6
11 42% 24% 1.4 3.2
12 45% 26% 1.2 2.8 Flush+Gut Draw
13 48% 28% 1.1 2.5
14 51% 30% 0.95 2.3
15 54% 33% 0.85 2.1 Flush+Open Draw
16 57% 34% 0.75 1.9 Flush+Open+One Overcard
17 60% 37% 0.66 1.7
[ The above chart represents your percentage and odds of hitting an out by the river ]
To calculate your hand odds, you first need to know how many outs your hand has. Outs are defined as a card in the deck that help you make your hand. So if you hold AK of spades and have two spades on the flop, that leaves 9 more spades in the deck, since there are 13 cards of each suit. This means you have 9 outs to complete your flush - but not necessarily the best hand! Usually you want your outs to count toward a nut draw, but this is not always possible.
The quick amongst you might be wondering "But what if someone else is holding a spade, doesn't that decrease my outs?". The answer is yes and no. If you know for sure that someone else is holding a spade, then you will have to count that against your total odds. However, in most situations when you do not know what your opponents hold, you can only do calculations with the knowledge that is available to you. That knowledge is your pocket cards and the cards on the table. So, in essence, you are doing the calculations as if you were the only person at the table, which in case, there are 9 spades left in the deck.
When calculating outs, it's also important not to overcount your odds. An example would be a flush draw in addition to an open straight draw.
Example: You hold
and the board shows
. A Nine or Ace gives you a straight (8 outs), while any diamond gives you the flush (9 outs). However, there is an Ace of diamonds and Nine of diamonds, so you don't want to count these twice toward your straight draw and flush draw. The true number of outs is actually 15 (8 outs + 9 outs - 2 outs) instead of 17 (8 outs + 9 outs)
In addition to this, sometimes an out for you really isn't a true out. An example would be chasing an open ended straight draw when two of another suit are on the table. In this regard, where you would normally have 8 total outs to hit your straight, 2 of those outs will result in three to a suit on the table. This makes a possible flush for your opponents. As a result, you really only have 6 outs for a nut straight draw. Another more complex situation is as follows:
Example: You hold J8o and the flop comes 9TJ rainbow (all of a different suit). To make a straight, you need a Queen or 7 to drop, giving you 4 outs each or a total of 8 outs. But, you have to look at the situation if a Queen drops, because the board will then show 9TJQ. This means that anyone holding a King will have made a King high straight, while you hold the dominated Queen high straight.
So, the only card that can really help you is the 7, which gives you 4 outs, or the equivalent of a gut shot draw. While it's true that someone might not be holding the King (especially in a short or heads-up game), in a big game, it's a very scary position to be in.
How to calculate hand odds (the longer way):
Once you know how to correctly count the number of outs you have on a hand, you can use that to calculate what percent of the time you will hit your hand by the river. Probability can be calculated easily for a single event, like the flipping of the River card from the Turn. This would simply be: Total Outs / Remaining Cards. For two cards however, like from the Flop to the River, it's a bit more tricky. This is calculated by figuring the probability of your cards not hitting twice in a row. This can be calculated as shown below:
Flop to River % = 1 - [ ((47 - Outs) / 47) * ((46 - Outs) / 46) ]
Turn to River % = 1 - [ (46 - Outs) / 46 ]
The number 47 represents the remaining cards left in the deck after the flop (52 total cards, minus 2 in our hand and 3 on the flop = 47 remaining cards). Even though there might not technically be 47 cards remaining, we do calculations assuming we are the only players in the game. To illustrate, here is a two overcard draw, which has 3 outs for each overcard, giving a total of 6 outs for a top pair draw:
Two Overcard Draw = 1 - [ (47 - 6) / 47 * (46 - 6) / 46 ]
= 1 - [ (41/47) * (40/46) ]
= 1 - [ 0.87 * 0.87 ]
= 1 - 0.76
= 0.24
= 24% Chance to Draw Overcards from Flop to River
However, most of the time we want to see this in hand odds, which will be explained after you read about pot odds. To change a percent to odds, the formula is:
Odds = ( 1 / Percentage ) - 1
Thus, to change the 24% draw into an odd we can use, we do the following:
Odds = ( 1 / 24% Two Overcard Draw ) - 1
= ( 1 / 0.24 ) - 1
= 4.17 - 1
= 3.17 or approx 3.2
How to calculate hand odds (the shorter way):
Now that you've learned the proper way of calculating hand odds in texas hold'em, there is a shortcut that will makes it much easier to calculate odds. The shortcut is, after you find the number of outs you have, multiply by 4 and you will get a close estimate to the percentage of hitting that hand from the Flop. Multiply by 2 instead to get a percentage estimate from the Turn. You can see these figures for yourself below:
Sample Outs and Percentages from Above Chart
4 17% 9% 5 10 Gut Shot, Two Pair -> Full House
5 20% 11% 4 8 One Pair -> Two Pair or Set, Gut+Backdoor
6 24% 13% 3.2 6.7 Two Overcard Draw, Open Straight w/Flush Threat
7 28% 15% 2.6 5.6 Set -> Full House
As you can see, this is a much easier method of finding your percentage odds. But what about ratio odds? This is still done using the formula:
Odds = ( 1 / Percentage ) - 1
However, we can rephrase this math equation so that your brain might process it a bit easier:
Odds = (100 / Whole Percentage) - 1
Using 100 divided by the whole percentage number, such as 24%, we can easily see that 100/24 is equal to about 4. We minus 1 from that and get a rough estimate of our odds at about 3:1. Let's try this all the way through with an example:
You hold:
Flop is:
Total Outs: Queen Gut Shot (4) + Ace Overcard (3) - Q or A Diamond (2) = 5
Percentage for Draw = 5 Outs * 4 = 20%
Odds = (100 / 20) - 1
= 5 - 1
= 4:1
Again, 4:1 odds means that you will make your draw 1 out of every 5 times. If the 1 out of 5 doesn't make a ton of sense to you, think about the 1:1 odds of flipping heads or tails on a coin. You'll flip heads 50% of the time, so 1 out of every 2 times it'll come heads.
X:1 Hand Odds = You'll hit 1 out of every X+1 times
Pot Odds and Poker Odds:
Now that you know how to calculate poker odds in terms of hand odds, you're probably wondering what you're going to need it for? That's a good question. This is where pot odds come into play.
Pot odds is simply a ratio of the amount of money in the pot compared with how much money it takes to call. If there is $100 in the pot and it takes $10 to call, your pot odds are 100:10, or 10:1. If there is $50 in the pot and it takes $10 to call, then your pot odds are 50:10 or 5:1. The higher the ratio, the better your pot odds are.
X:1 Pot Odds = You must win this hand 1 out of X+1 times to break even
Pot odds ratios are a very useful tool to see how often you need to win the hand to break even. If there is $100 in the pot and it takes $10 to call, you must win this hand 1 out of 11 times in order to break even. The thinking goes along the lines of: If you play 11 times, it'll cost you $110, but when you win, you get $110 ($100 + your $10 call).
The usefulness of hand odds and pot odds becomes very apparent when you start comparing the two. As we know now, in a flush draw, your hand odds for making your flush are 1.9 to 1. Let's say you're in a hand with a nut flush draw and it's $5 to you on the flop to call. Do you call? Your answer should be: What are my pot odds?
If there is $15 in the pot plus a $5 bet from an opponent, then you are getting 20:5 or 4:1 pot odds. This means that in order to break even, you must win 1 out of every 5 times. However, with your flush draw, your odds of winning are 1 out of every 3 times! You should quickly realize that not only are you breaking even, but you're making a nice profit on this too. Let's calculate the profit margin on this by theoretically playing this hand 100 times from the flop, when is then checked to the river.
Net Cost to Play = 100 hands * $5 to call = -$500
Pot Value = $15 + $5 bet + $5 call
Odds to Win = 1.9:1 or 35% (From the flop)
Total Hands Won = 100 * Odds to Win (35%) = 35 wins
Net Profit = Net Cost to Play + (Total Times Won * Pot Value)
= -$500 + (35 * $25)
= -$500 + $875
= $375 Profit
As you can see, you have a great reason to play this flush draw, because you'll be making money in the long run according to your hand odds and pot odds. The most fundamental point to take from this is:
If your Pot Odds > Hand Odds, then you are making a profit
So, even though you may be faced with a gut shot straight draw at times, which is a terrible draw at 5 to 1 hand odds, it can be worth it to call if you are getting pot odds greater than 5 to 1. Othertimes, if you have an excellent draw such as the flush draw, but someone has just raised a large amount so your pot odds are 1:1 for instance, then you obviously should not continue trying to draw to a flush, as you will lose money in the long run. In this situation, a fold or semi-bluff is your only solution, unless you know there will be callers behind you that improve your pot odds to better than break even.
Your ability to memorize or calculate your hand odds and figure out your pot odds will lead you to make many of the right decisions in the future. Just be sure to remember that fundamental principle of playing drawing hands when your pot odds are greater than your hand odds.
Poker Odds from the Flop to Turn and Turn to River
An important note I have to make is that many players who understand Hold'em odds tend to forget is that much of the theoretical odds calculations from the flop to the river assume there is no betting on the turn. So while it's true that for a flush draw, the odds are 1.9 to 1 that the flush will complete, you can only call a 1.9 to 1 pot on the flop if your opponent will let you see both the turn and river cards for one call. Unfortunately, most of the time, this will not be the case, so you should not calculate pot odds from the flop to the river and instead calculate them one card at a time.
To calculate your odds one card at a time, simply use the same odds that you have going from the turn to the river. So for example, your odds of hitting a flush from the turn to river is 4 to 1, which means your odds of hitting a flush from the flop to the turn is 4 to 1 as well.
To help illustrate even further, we will use the flush calculation example that shows the often incorrect way of thinking.
Example of Incorrect Pot Odds Math
You Hold: Flush Draw
Flop: $10 Pot + $10 Bet
You Call: $10 (getting 2 to 1 odds)
Turn: $30 Pot + $10 Bet
You Call: $10 (getting 4 to 1 odds)
Long-Term Results Over 100 Hands
Cost to Play = 100 Hands * ($10 Flop Call + $10 Turn Call) = $2,000
Total Won = 100 Hands * 35% Chance to Win * $50 Pot = $1,750
Total Net = $1,750 (Won) - $2,000 (Cost)
= -$250 Profit
= -$2.5/Hand
Example of Correct Pot Odds Math
You Hold: Flush Draw
Flop: $30 Pot + $10 Bet
You Call: $10 (getting 4 to 1 odds)
Turn: $50 Pot + $16 Bet
You Call: $16 (getting about 4 to 1 odds)
Long-Term Results Over 100 Hands
Cost to Play = 100 Hands * ($10 Flop Call + $16 Turn Call) = $2,600
Total Won = 100 Hands * 35% Chance to Win * $82 Pot = $2,870
Total Net = $2,870 (Won) - $2,600 (Cost)
= $270 Profit
= $2.7/Hand
As you can see from these example calculations, calling a flush draw with 2 to 1 pot odds on the flop can lead to a long term loss, if there is additional betting past the flop. Most of the time however, there is a concept called Implied Value (which we'll get to next) that is able to help flush draws and open-ended straight draws still remain profitable even with seemingly 'bad' odds. The draws that you want to worry about the most are your long shot draws: overcards, gutshots and two outers (hoping to make a set with your pocket pair). If you draw these hands using incorrect odds (such as flop to river odds), you will be severely punished in the long run.
Implied Value
Implied Value is a pretty cool concept that takes into account future betting. Like the above section, where you have to worry about your opponent betting on the turn, implied value most often is used to anticipate your opponent calling on the river. So for example, let's say you have yet another flush draw and are being offered a 3 to 1 pot odds on the turn. Knowing that you need 4 to 1 pot odds to make this a profitable call, you decide to fold.
Aha, but wait! Here is where implied value comes into play. So, even though you're getting 3 to 1 pot odds on the turn, you can likely anticipate your opponent calling you on the river if you do hit your flush draw. This means that even though you're only getting 3 to 1 pot odds, since you anticipate your opponent calling a bet on the river, you are anticipating 4 to 1 pot odds - so you are able to make this call on the turn.
So in the most practical standpoint, implied value usually means that you can minus one bet off your drawing odds on the turn, as it anticipate your opponents calling at least one bet. In some more advanced areas, you can use implied odds as a means of making some draws that might not be profitable for a majority of the time, but stand to make big payouts when they do hit. Some examples of this would be having a tight image and drawing to a gutshot vs another tight player. Even though this is a horribly bad play (and hopefully you don't have to pay much for it), it can possibly be a positive play if you know your opponent will pay you off if you hit your draw - namely because he won't believe you played a gutshot draw. For many reasons, I do not recommend fancy implied odds plays like these, but mentioned it more so that you can recognize some players who pull these 'tricky' plays on you as well.
Conclusion - Poker Odds
Knowing how to figure your odds in texas hold'em is going to be one of the most fundamental points in becoming a solid poker player. If this poker odds page was a bit difficult to understand, don't worry. Keep playing, bookmark this page and come back when you need another touch up reminder on how to properly apply odds. It takes awhile to learn how to do them properly and to memorize them as well.
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