Hand Odds
Does Your Hand Need Improvement?
Before digging into the hand odds of the post-flop era you must establish whether your hand needs improvement or not. This is the most difficult aspect of poker strategy because you can't know your opponent's exact hand. You can, however, make an educated guess based on the available clues.
How many opponents are seated at the table?
How many opponents are remaining in the hand?
What hand do you have?
What are the community cards?
How did your opponent act pre-flop?
What is the current betting behaviour of your opponent?
What is the general playing style of your opponent?
There are two basic scenarios to consider:
Full table multi-way pot: 9-10 players at the table and more than two players chasing the pot post-flop.
Short-handed table heads-up pot: 6 or fewer players at the table and only two players chasing the pot post-flop
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Only the full table multi-way pot scenario is relevant to beginners seeing as that is where a tight and simple style of play works best.
Full Table Multi-way Pot Scenario
You will need a top pair to win at the very least. Whether a top pair is enough to win or not depends on the community cards and the current betting behaviour of your opponents. When you have top pair or over pair you need to pay careful attention to the community cards and your opponent's betting behaviour because these are two frequently beaten hands.
Unfavourable community cards:
►2 community cards of the same rank. Your opponent could have a trips.
►3 community cards of the same rank. Your opponent could have a full house. Even if you have full house you will need a high pocket pair to ascertain that the hand odds are on your side. Preferably an over pair.
►2 pairs among the community cards. Your opponent could have a full house. Even if you have a full house you will need the higher trips to ascertain that the hand odds are on your side.
►3 coordinated community cards that can form a straight with 2 connected pocket cards of medium or high rank. Your opponent could have a straight. Even if you have a straight you need it to be the nut straight to ascertain that the hand odds are on your side.
►4 coordinated community cards that can form a straight with a medium or high pocket card. Your opponent could have a straight. Even if you have a straight you need it to be the nut straight to ascertain that the hand odds are on your side.
►3-4 suited community cards. Your opponent could have a flush. Even if you have a flush you will need a high pocket card of that suit to ascertain that the hand odds are on your side.
Unfavourable betting behaviour exhibited by your opponent:
►Betting & raising. |
The clues within the scenario above will usually point you in the right direction. Unfavourable community cards, relative to your current hand ranking, in combination with unfavourable actions taken by your opponent or opponents mean that your hand needs improvement. If your hand needs improvement you must evaluate your hand odds. If your hand does not need improvement you must evaluate your opponent's hand odds instead.
Example 1
You are at a full table in a multi-way pot. It is currently the flop. Your pocket cards are 9h-9c. The community cards are Qh-Qc-8d. There are two community cards of matching rank which also happen to outrank your pocket pair. The community cards are in other words very unfavourable. Your opponent has just placed the first bet of the round. You have one opponent acting after you as well. This opponent raised pre-flop. Your opponents' betting behaviour is unfavourable. The clues tell you that the circumstances as a whole are extremely unfavourable. Your hand needs improvement. You must evaluate your hand odds.
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Example 2
You are at a full table in a multi-way pot. It is currently the flop. Your pocket cards are Th-Tc. The community cards are 5c-2d-9h. The community cards are favourable. Your two opponent have just checked. Their betting behaviour is favourable. The clues tell you that the circumstances as a whole are favourable. Your hand likely does not need improvement to win. You only need to worry about your opponents' hand odds which should be pretty awful judging from the community cards.
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We won't go into any details on how to read your opponent in the complex short-handed heads-up pot scenario for this is beyond the scope of our school. We teach the basics and we don't recommend beginners to play at short-handed tables in the first place. We will still give a basic presentation of the scenario just to give you the general idea.
Short-handed Table Heads-up Pot Scenario
Here you must weigh your actions carefully against the community cards, your opponent's pre-flop actions, current actions and general playing style. Your hand is secondary. Should you have a top pair or higher you have little to worry about but a hand below a top pair is not necessarily in need of improvement. It depends on what your opponent is up to.
Unfavourable community cards:
►3 or more community cards that rank higher than your pocket cards. Your opponent could have a top pair.
►4 connected community cards that you are not forming a straight with. Your opponent could have a straight.
►4 suited community cards that you are not forming a flush with. Your opponent could have a flush.
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Establishing whether a hand needs improvement or not is not enough. There is no point to continue playing a hand if the hand you are drawing to is weaker than the hand currently held by your opponent. Even if your hand improves you lose. This is known as drawing dead. An out caught when drawing dead is called a dead card. Furthermore, you can not only consider your own hand odds even if the hand your are drawing to is stronger than your opponent's current hand. Your opponent's hand can also improve and you could be sharing outs with him. When sharing outs which will make his hand stronger than yours, you must adjust your hand odds by removing those outs from the equation. Such outs are known as counterfeit outs.
Dead Card: This is a worthless out that will improve your hand to a weaker hand than your opponent's current hand.
Counterfeit Out: This is a worthless out that will improve your opponent's hand to a stronger hand than it will improve your hand to. |
Dead Card Example:
For the sake of argument we will define both your cards and your opponent's cards. It is currently the turn. Your pocket cards are 9d-Tc. The community cards are 6c-Ts-Jc-Qd. Your opponent's pocket cards are As-Kd. You have a pair and an OESD with either K or Q as top card. Your opponent already has a straight with the top card A. This means that all 8 outs you have are dead cards. Even if your hand improves you lose.
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Counterfeit Outs Example:
For the sake of argument we will define both your cards and your opponent's cards. It is currently the flop. Your pocket cards are 9c-9d. The community cards are Ts-Jd-Qh . Your opponent's pocket cards are As-Ad. You have a pair and an OESD with either K or Q as top card. Your hand needs improvement to win. You have 2 outs for a trips. These 2 outs won't improve your opponent's hand so they are legitimate. Your OESD has 8 outs but 4 of these outs, the Kings, are counterfeit outs because they will improve your opponent's hand to a higher straight than yours. This means that you have a total of 2+4=6 outs instead of the 2+8=10 outs suggested only by your cards and the community cards.
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The take home message is that an out is not always a legitimate out. It depends on what cards your opponents are holding. You can not see their cards but there are clues that can help you make an educated guess. These are the very same clues that should help you decide whether your hand needs improvement or not in the first place. You can in other words never know your exact number of outs but you don't have to know the exact number to profit from poker. Your opponents won't know the exact number of outs either and chances are most of them don't even know what outs are to begin with. Therefore a general estimate of outs will suffice and give you the edge you need to profit from poker. Just remember to keep it real. Don't be too optimistic or too pessimistic when estimating your number of outs - just be realistic. Focus on what you do know and assume as little as possible.
Before you move on we would like to remind you that the number of players in the hand affect the hand odds considerably. The fewer the players at the table, the better your odds of winning the showdown. With only one other player seated at the table (heads-up game) you can afford a very loose play all the way from the pre-flop to the showdown. The odds are roughly 9 times better than at a full table (with 8-9 opponents). This means that full tables and short-handed tables facilitate totally different strategies.
►A full or nearly full table facilitates a tight/mathematical strategy. To profit you must focus on your cards.
►A short-handed table facilitates a loose/psychological strategy. To profit you must read and bluff your opponents.
There is a popular proverb on this theme that you would do well to remember:
At a full table you are playing your cards. At a short-handed table you are playing your opponents.
Hand Odds Charts
Once you have established whether it is your hand or your opponent's hand that needs to improve is time to start looking at the actual hand odds. There are three different hand odds to consider:
Turn hand odds: The hand odds of hitting a made hand on the turn when you are on the flop
River hand odds: The hand odds of hitting a made hand on the river when you are on the turn.
Turn & River hand odds: The hand odds of hitting a made hand over the turn AND river combined when you are on the flop. |
Normally you should only consider the hand odds for one community card at the time. The one exception is when you must go all-in on the flop in which case you must consider the combined hand odds of turn and river.
| When to consider combined hand odds: When you are on the flop and face an all-in decision. |
Please observe that you should not calculate the hand odds on the fly when playing. It is far more efficient to simply memorize the most important hand odds. It is very important to learn the hand odds on the basis of outs rather than the name of the drawing hand because you do not always have the same number of outs. You can have several draws at the same time and you can also have counterfeit outs and/or dead cards.
In the chart below you can see the hand odds and chance of improving for different number of outs on the Turn, River and Turn & River. We recommend that you learn the hand odds on the basis of odds rather than chance because odds are more practical.
Although we present the full range of outs you should never count on drawing hands with less than 4 outs. It must also be stressed that when the chance of improving is higher than 50%, which is unlikely but fully possible, the hand odds will always outweigh the pot odds, saving you the trouble of having to weigh the odds against eachother. We will elabourate on this in the next chapter.
Click here for printable version of the complete hand odds handout (including the chart below).
| Outs |
Turn |
River |
Turn & River |
| 21 |
1.24:1 (44.7%) |
1.19:1 (45.7%) |
70.0% |
| 20 |
1.35:1 (42.6%) |
1.30:1 (43.5%) |
67.5% |
| 19 |
1.47:1 (40.4%) |
1.42:1 (41.3%) |
65.0% |
| 18 |
1.61:1 (38.3%) |
1.56:1 (39.1%) |
62.4% |
| 17 |
1.76:1 (36.1%) |
1.71:1 (37.0%) |
59.8% |
| 16 |
1.94:1 (34.0%) |
1.88:1 (34.8%) |
57.0% |
| 15 |
2.13:1 (31.9%) |
2.07:1 (32.6%) |
54.1% |
| 14 |
2.36:1 (29.8%) |
2.29:1 (30.4%) |
51.1% |
| 13 |
2.62:1 (27.7%) |
2.54:1 (28.3%) |
1.08:1 (48.1%) |
| 12 |
2.92:1 (25.5%) |
2.83:1 (26.1%) |
1.22:1 (45.0%) |
| 11 |
3.27:1 (23.4%) |
3.18:1 (23.9%) |
1.39:1 (41.7%) |
| 10 |
3.70:1 (21.3%) |
3.60:1 (21.7%) |
1.60:1 (38.4%) |
| 9 |
4.22:1 (19.1%) |
4.11:1 (19.6%) |
1.86:1 (35.0%) |
| 8 |
4.88:1 (17.0%) |
4.75:1 (17.4%) |
2.17:1 (31.5%) |
| 7 |
5.71:1 (14.9%) |
5.57:1 (15.2%) |
2.59:1 (27.8%) |
| 6 |
6.83:1 (12.8%) |
6.67:1 (13.0%) |
3.14:1 (24.1%) |
| 5 |
8.40:1 (10.6%) |
8.20:1 (10.9%) |
3.91:1 (20.4%) |
| 4 |
10.8:1 (8.51%) |
10.5:1 (8.70%) |
5.07:1 (16.5%) |
| 3 |
14.7:1 (6.38%) |
14.3:1 (6.52%) |
7.01:1 (12.5%) |
| 2 |
22.5:1 (4.26%) |
22.0:1 (4.35%) |
10.9:1 (8.42%) |
| 1 |
46.0:1 (2.12%) |
45.0:1 (2.17%) |
22.5:1 (4.26%) |
To help illustrate the table above we will also present the number of outs for a number of drawing hands (assuming they need improvement to win):
| Drawing Hand |
Improved Hand |
Outs |
| OESFD |
Straight, Flush or Straight Flush |
15 |
| ISFD |
Straight, Flush or Straight Flush |
12 |
| Trips (Turn) |
Full House or Quads (River) |
10 |
| FD |
Flush |
9 |
| OESD |
Straight |
8 |
| Double ISD |
Straight |
8 |
| Trips (Flop) |
Full House or Quads (Turn) |
7 |
| Over Cards |
Top Pair |
6 |
| Two Pairs |
Full House |
6 |
| ISD |
Straight |
4 |
| Pair |
Trips |
2 |
| OESFD |
Straight Flush |
2 |
| ISFD |
Straight Flush |
1 |
| Trips |
Quads |
1 |
Single Draw Hand Odds Examples
►It is currently the river. There are no more cards to come which means that your hand can't improve. Outs and associated hand odds do not apply here.
►It is currently the flop. Your pocket cards are JhQh and the community cards are Kh-Th-5c. You have an OESFD with 15 outs. There are two cards to come but you are not standing before an all-in decision so it is only your hand odds over the next card that need to be considered. Your hand odds on the turn are 2.13:1 against.
►It is currently the turn. Your pocket cards are Jc-Qh and the community cards are Kc-Td-5s-2d. You have an OESD with 8 outs. There is only one card to come - the river. Your hand odds on the river are 4.75:1 against.
►It is currently the flop. Your pocket cards are 6h-7c and the community cards are 9c-Th-2s. You have an ISD with 4 outs. There are two cards to come and you are standing before an all-in decision. Your hand odds over turn and river combined are 5.07:1 against.
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You can also have several draws at the same time and then the outs must be added together.
Multiple Draws Hand Odds Examples
►It is currently the flop. Your pocket cards are Ah-Kc and the community cards are 7c-Th-Qs. You have an ISD and Over Cards at the same time. You have a total of 4+6=10 outs. There are two cards to come and you are standing before an all-in decision. Your hand odds over turn and river combined are 1.6:1 against.
►It is currently the flop. Your pocket cards are Js-Qs and the community cards are 9s-Ts-4d. You have an OESFD and Over Cards at the same time. You have a total of 15+6=21 outs. There are two cards to come and you are standing before an all-in decision. The chance of improving over the turn AND river is 70%. This translates to hand odds of 2.33:1 for. When the hand odds are higher for than against (chance of winning higher than 50%) it means you always have a profitable hand. Having a draw with such hand odds is basically the same thing as having the strongest hand in so far as how you should act.
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The examples above are very simple and reality is not that simple. You also have your opponent's cards to consider. We have already established that your opponent's pocket cards have a huge impact on your outs and associated hand odds. Unfortunately your opponent's pocket cards are hidden from your view and therefore you can't know your exact number of outs and hand odds. We will illustrate this point by revealing your opponent's pocket cards in the examples below.
Real Hand Odds Examples
►It is currently the flop. Your pocket cards are Jc-Qd and the community cards are 9s-Ts-4d. Your opponent's pocket cards are AcAd. Your pocket cards and the community cards tell you that you have an OESD and Over Cards with a total of 8+6=14 outs. This is, however, no longer true when taking your opponent's over pair into consideration. The 6 outs of your over cards are dead cards because a top pair is not enough to win this hand. This leaves you with only 8 outs. Fortunately none of these 8 outs are counterfeits. There are two cards to come but you are not standing before an all-in decision. Your hand odds on the turn are 4.88:1 against.
►It is currently the turn. Your pocket cards are Td-Tc and the community cards are 7d-8s-Jc-Ks. Your opponent's pocket cards are Kd-Js. You have a pair and an ISD. Your opponent has two pairs. If your hand improves to a straight or trips you will win. You have 2 outs for the trips (Th-Ts) and the ISD has 4 outs (9c-9d-9h-9s). None of these outs are counterfeits. You have a total of 2+4=6 outs. There is only one card to come. Your hand odds on the river are 6.83:1 against.
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There are also the draws that need to catch two outs. They are never worth considering but we will still present them just to add some perspective:
| Drawing Hand (Flop) |
Outs |
Improved Hand (River) |
Chance |
Hand Odds |
| Backdoor FD |
10 |
Flush |
4.2% |
23:1 against |
| Backdoor OESD |
9 |
Straight |
3.7%-4.4% |
21.7-26:1 against |
Although the hand odds of starting hands are not important enough to memorize, we will still present them just to add some perspective. Below are the improvement odds for two general pre-flop starting hands over the flop:
| Starting Hand (Pre-flop) |
Improved Hand (Flop) |
Chance |
Hand Odds |
| 2 cards of different rank |
Pair |
32% |
2:1 against |
| 2 cards of different rank |
The higher pair |
17% |
4.8:1 against |
| Pocket Pair |
Set |
12% |
7.5:1 against |
To further enhance the perspective we will also present the hand odds for these two hands over the flop, turn and river combined:
| Starting Hand (Pre-flop) |
Improved Hand (River) |
Chance |
Hand Odds |
| 2 cards of different rank |
Pair |
49% |
1.1:1 against |
| 2 cards of different rank |
The higher pair |
28% |
2.6:1 against |
| Pocket Pair |
Set |
19% |
4.2:1 against |
As you can see, the chance to hit a pair on the river is roughly 50% regardless of starting hand and this is the reason why low pocket cards are essentially worthless even if they are suited, connected or a pair. The chance to hit a pair is much higher than the chance to hit a higher hand and if your pocket cards are low you will most of the time end up with a low pair or worse which won’t stand a chance against the higher pairs or cards held by other players. The take home message is that you need decent pocket cards before you should even think about any hand odds.
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