Poker Odds, Outs And Math To Improve Your Game

poker odds outs math

Poker Math And Outs You Should Know

You can find hundreds of different numbers referring to poker odds, but not all of those are important. However, understanding crucial numbers will let you use your poker stats more efficiently and make better decisions in Texas Holdem poker games. Therefore, I created this guide and included key poker odds that you must know. Just follow these few tables, and you will learn how to count poker outs, use poker math to your advantage and find probabilities of hitting or improving your hand in Texas Hold ’em.

Probability to hit your hand
The name of the drawOutsProbability to hit on next cardProbability to hit till river (Both on the Turn Or River)
Four of a kind12.1%4.3%
three of a kind24.3%8.4%
High pair36.4%12.5%
Insight straight draw48.5%16.5%
Two pair or three of a kind510.6%20.3%
Any pair with your holding612.8%24.1%
Insight straight or high pair714.9%27.8%
Open-ended straight draw817%31.5%
Flush draw919.2%35%
Inside straight or a pair1021.3%38.4%
Open-ended straight or high pair1123.4%41.7%
Flush or high pair1225.5%45%
1327.7%48.1%
Open-ended straight or a pair1429.8%51.1%
Flush or open-ended straight1531.9%54.1%
1634%57%
1736.2%59.8%
Flush, inside straight or a pair1838.3%62.4%
1940.4%65%
2042.6%67.5%
Flush, open-ended straight or pair2144.7%70%

It could take some time to remember all of the information above regarding poker odds and outs. However, you have a shortcut to apply correct poker math on the go and quickly calculate the probability of hitting your hand while playing. Therefore, I will explain a simple rule, which will help you a lot with Texas Holdem odds.

There is quite an easy way to get the answer very fast and we can call it “the rule of 2 and 4”.

If you are on the flop just multiply your outs by 4 and you will get an approximate percentage how likely you are to improve your hand till the river by seeing both cards. Similarly, by multiplying your outs by 2, you will get a number showing how likely you are to improve your hand on the coming street. This could be used on the turn as well to get the estimate about your probability to improve on the river. So all you have to know is how many outs you have, and you can easily calculate your poker odds with this rule.

Few quick examples to highlight the rule of 2 and how likely you are to improve your hand on the next street:

  • You have a flush draw on the flop with 9 outs. You will improve it on the turn: 9*2=18% and real poker odds are around 19%
  • You have a straight draw on the flop with 8 outs. You will improve it on the turn: 8*2=16% and real poker odds are around 17%
  • You have two over cards on the turn with 6 outs. You will improve it on the river: 6*2=12% and real poker odds are around 13%

How the rule of 4 works and how often you will improve your hand from flop till river (assuming you will see both cards):

  • You have a flush draw on the flop with 9 outs. You will improve it on the turn or river: 9*4=36% and real poker odds are around 35%
  • You have a straight draw on the flop with 8 outs. You will improve it on the turn or river: 8*4=32% and real poker odds are around 31%
  • You have two over cards on the turn with 6 outs. You will improve it on the turn or river: 6*4=24% and real poker odds are around 24%

As you see, these estimates are very close to real values and you will not go wrong by following this simple rule. Moreover, it will save you a lot of time when making a decision in the game and quickly show your actual poker odds.

You should be aware, that when you have a lot of poker outs to improve your hand, the rule of 4 will not be exact. For example, if you have open-ended straight or flush draw, you will have 15 outs, but will only improve your hand 54% of the time (not 60% like “the rule of 4” would suggest). Therefore, when having many outs to improve, your poker odds should be reduced a little bit when using this rule, but it can still give you a good estimate of the strength of your hand and probability to improve it. Furthermore, with so many outs, you will be ahead of your opponent’s range and can call no matter how much he bets.

I think it is the easiest and fastest way to get a good estimate of your poker odds and actual probabilities to improve your hand and applying it will help you make the best decision when you have some doubts.

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Benefits Of Knowing Poker Outs And Probabilities

When you know how many outs you have to improve your hand and most importantly probability of that happening, you can and should compare that to the pot odds you are getting and work out the best decision. This is pretty easy, yet critical concept to understand and implement in your game. I will give you an example so you could see it in practice:

You face 1/2 Pot Size all-in bet on the flop while holding a flush draw and having 9 outs to improve. Using our “rule of 4” we multiply our outs and see that you have around 36% probability to improve to a flush and make a winning hand till the river. (Remember, you are guaranteed to see both Turn and River because your opponent is already all-in)

Now you need to know what pot odds you are getting and can easily make the right decision knowing if calling is profitable or not. Let us say the pot is 1000 chips and your opponent is shoving for another 500 chips. This means you have to call 500 to win 2000 chips pot (initial 1000, 500 that your opponent is betting and 500 which you call). This comes up to simple math 500/2000=0.25 which equals to 25% pot odds.

So in this example, you have a higher probability of improving your hand (36%) compared to the price you are paying (25%). Therefore, it is extremely profitable call and folding in this spot would be a huge mistake.

To make your life much easier I created a table, giving you poker odds of the most common situation when facing a bet from your opponent.

Calling Pot Odds
The Size Of The Bet You FacePot Odds, %
2x Pot Bet40%
1.5x Pot Bet38%
Pot Size Bet33%
2/3 Pot Bet29%
1/2 Pot Bet25%
1/3 Pot Bet20%

While in the first example we covered a situation where your opponent is all-in on the flop, and you are guaranteed to see both cards, do not make a mistake of assuming that it is always the case. If your opponent bets the same amount but is not all in, then you can only compare those odds with your probability to improve with the next card. So in above example, you still have 9 outs, but can only multiply it by 2, getting the probability of 18% to improve your hand on the turn.

So you can’t be calling in a vacuum. However, in most cases, you will have implied odds (meaning you can win more when improved) and can still justify a call. Moreover, if you have an overcard to the board, it can give additional outs to draw to a winning hand and even give you direct odds to make that call.

Poker Probability Of Hitting The Hand On The Flop

Poker Odds Of Hitting A Hand On The Flop
Hand that you might flopPoker Odds, %
One pair (hitting one of your hole cards)32%
Set (hitting three of a kind with pocket pair)11.8%
Two pair hand (both of your hole cards)2%
Straight (with two connected cards like)1.3%
A flush0.8%

Just taking a glance at the table you can see how unlikely you are to hit a strong hand on the flop. Moreover, keep in mind, that your opponent will likely miss as well and the probability of him having strong poker hand is quite low.

Therefore, you should not be afraid to bet as a bluff and learn how to continue putting a lot of pressure on your opponents. You can learn a bit more in my continuation bet article and will see that bluffing is often a good idea. Moreover, if you want to improve your chances of hitting a strong hand you need to know, which ranges you should play from different positions and I can help you our with free poker hands cheat sheet!

Texas Holdem Odds For Winning With Different Hands

Common situationsHandsPoker Odds, %
Pocket pair vs other pocket pairAA vs 8880.5% vs 19.5%
Pair vs two suited over cards55 vs QJs49.1% vs 50.9%
Pair vs two off-suit over cards55 vs QJo51.6% vs 48.4%
Pair vs undercardsKK vs 65o81.3% vs 18.7%
Pair vs one over cardsQQ vs A770.8% vs 29.2%
Two higher cards vs two lower cardsAK vs JT62.7% vs 37.3%
High and low card vs two in the middleA5 vs T954.7% vs 45.3%
Same card with high and low kickerAK vs AT73% vs 27%

Understanding how likely you are to win confrontation preflop can help you make more educated decisions. Moreover, you will understand when you should let go of weaker hand when not having right poker odds to continue. Therefore, knowing these probabilities and improving your poker math will make you a better player.

Learn these texas holdem odds of different confrontations and step up with your game.

Poker Odds Of Hitting Over Card While Having A Pair

Probability to see an over card for your pocket pair
The handOn The FlopTill The River
AA0%0%
KK23%35%
QQ41%60%
JJ57%76%
TT70%87%
9979%93%
8887%97%
7792%99%
6696%99%
5598%99%
4499%99%
3399%99%
22100%100%

As you see from the table, you should not be surprised to see over cards even when holding premium pairs. The probability of that happening is reasonably high and you will see and over card to pocket jack on the flop around 57% of the time.

That does not mean that you should be afraid when you see one. However, simple poker math suggests that you should not be looking to play such hand passively and let many opponents see the flop. Instead, deny chances of hitting their poker outs by raising preflop and force them to make mistakes by continuing with weaker hands.

Summary Of Poker Math Advantages

Following these tips, you can make better decisions and most importantly base it on poker math and not just be guessing around. Obviously, there are many other topics which you should master, such as poker bankroll management, GTO poker strategy, poker tells, big blind play and many more. Obviously, you have to learn poker in the right way as well and only then you will take full advantage of understanding poker math and implementing poker odds to gain the best possible results.

That being said, you can always join my free poker training and start improving your game! Do that, learn in the right way and see you on the tables!

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