No Limit Hold Em Odds
After the flop, your play will depend on many factors, including information gathered pre-flop, what you know of your opponents and how they play, and the probabilities of having or making the best hand. If you have hit top pair with a strong kicker on the flop, then you have a strong hand and should bet at the pot. But the more difficult scenario is when you have flopped a flush draw or a straight draw, or perhaps an inside straight draw with two over cards. If someone bets, should you make the call?
At this point, it is important to first surmise what your opponent’s hand is. Then, you must calculate the number of outs you have to make your hand the winning hand. The final step is to then understand the probabilities of hitting one of your outs, giving you the winning hand. These are all crucial steps in the decision making process.
For example, let’s say I am holding JT offsuit.
The question is: what are the odds of a set-over-set situation occurring at a Hold'em table? The odds of flopping a set when holding a pocket pair is approximately 12%. The odds of flopping a set when holding a pocket pair AND somebody else flopping a set while holding a pocket pair is roughly 1% (the actual number is a bit over 1%).
The flop comes A 8 9 – rainbow.
The pot is current at $8.00, and Player1 bets $2.00. Everyone else folds.
Should I make the call?
- Mar 13, 2017 He is the author of hundreds of articles and two books, Winning 7-Card Stud (Kensington 2003) and Winning No-Limit Hold'em (Lighthouse 2012). He is also the host of poker radio show House of Cards.
- Mar 21, 2019 This unbeatable hand is rare, though, with the odds of making a royal flush just 1 in 30,939 or 0.0032 percent using 7 cards. These odds apply to the game of Texas Hold’em where you build your hand using 5 cards, but still have 7 cards to choose from, namely 2 pocket cards and 5 on the board.
- NL Hold’em Starting Hand Charts. One aspect of the game of No-Limit Hold’em that causes beginning players much grief is deciding which hands to play and which hands to dump. NL Hold’em is much more difficult than Limit Hold’em.
- Texas Hold'em Odds and Probabilities answers all of these questions and more. Every single decision you make at the poker table is in some way related to odds and probabilities. Whether you are deciding to bet, call, fold, raise, or even bluff, odds and probabilities are an integral part of the decision-making process.
Well, first I should think about what he may be holding. Let’s say there was no pre-flop raise and Player1 is in early position. He may have a pair of Aces with no kicker, or maybe a pair of 9’s.
So, if I put him on a pair of Ace’s, then I would need either a 7 or a Q to complete my straight and win the hand. Therefore, I have 8 outs – the four 7’s in the deck plus the four Q’s in the deck.
Now, if I have 8 outs, here is the calculation of hitting one of my cards on the turn or river:
There are 47 cards left unseen (I’m holding 2, there are 3 on the board, 52-5= 47). 47 – 8 outs = 39.
My calculation becomes: 1 – 39/47 (turn) * 38/46 (46 cards unseen prior to river):
1 – 39/47 * 38/46 = 31.5%
I have a 31.5% chance to hit my hand over the turn and river.
Now back to our scenario, I have to call a $2.00 bet to win what will be a $12.00 pot. Since my bet is only about 17% of the pot, yet I have a 31.5% chance of winning (across the turn & river card!), the “pot odds” justify making the call.
Now let’s say Player1 bets $12 instead of $2. I would have to call $12 to win what will be a $32 pot. My bet is 37.5% of the pot, greater than my odds of hitting one of my outs, and therefore I should fold (we will get to implied odds further down).
The above scenarios are important to grasp. Picture yourself on the flip side now. Let’s say you have a pair of Aces, and you do not want to allow someone to out draw you. You should do exactly what was outlined above – bet more than their odds would justify. If you bet the amount of the pot, then those chasing the straight (or the flush for that matter) are not getting proper pot odds to call, so you either force them to fold, or you force them to play incorrectly and chase a hand when they are betting against the odds. Your bet can help cause your opponents to make mistakes and incorrectly play their flush draw or straight draw.
So, how are you supposed to calculate your probabilities on the fly in the heat of battle… without a calculator? You don’t. See the chart below! You can right click and save the chart on your computer and even print it off to look at whenever you need!
Memorize these figures (particularly the first chart), they will help you justify your calls. Now, the above scenarios were pretty simplified. There are other, more advanced, factors to potentially consider. For example, if you do not hit your card on the turn, can you assume Player1 will bet again and how much? If you know this information, this should also be included in your calculation of the bet vs. pot amounts.
Let’s say you know Player1 will probably bet another $4 on the turn. So really, you are looking at calling $6.00 against a pot of $16.00. The percentage now is 37.5% (6/16) as opposed to our earlier example where it was 17%. In this case, the call isn’t as clear and the current pot odds don’t quite justify the call because 37.5% is greater than our 31.5%. However, there are implied odds to consider, and these odds may justify making this call.
This is the last factor that is important to consider; implied odds. In the game of No-Limit Hold’em, you potentially could win a much larger pot than the current pot you are calculating your odds against. If you do hit your hand, could you then bet the entire pot amount and assume Player1 will call? How much of a bankroll does Player1 have and is it possible to take it all on this hand? These are interesting questions and also can affect your decision. The total pot size at the very end of the hand, could easily justify making the call in the hopes of winning that pot. This is called “implied odds” and should also be considered.
Now go play and try incorporating this knowledge. I would say good luck, but luck is the enemy of a good player. Better yet, good pot odds!
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In this lesson we’re going to run through a number of heads-up match-ups that will help give you an idea of where you stand in a variety of pre-flop situations when playing hold’em. Be aware that we’re only going to focus on individual hand match-ups. When playing hold’em it’s essential that you put your opponent on a range of hands, rather than specific holdings. However, knowing the odds of common pre-flop match-ups is a good starting point. Pick out and study what will help you. While it’s not essential that these statistics be committed to memory, it won’t hurt you if you do.
Let’s start by looking at hand match-ups when holding a pair:
Pair vs. Pair
The higher pair is an 80 percent favourite. We can get very technical and highlight the fact that if the underpair didn’t have any clean suits and/or the maximum number of straight outs then the high pair’s equity would increases by one or two percent.
Pair vs. Overcards
This is the classic coin flip hand that you’ll see many times late in tournaments with one player being all-in. The term coin flip indicates an even money situation which is really a 55 to 45 percent situation, as the pair is a slight favourite.
Texas Hold Em No Limit
Pair vs. Undercards
In this situation the pair is normally about a 5-to-1 favourite and can vary depending on whether the two undercards are suited and/or connectors.
Pair vs. Overcard and an undercard
The pair is about a 70 percent favourite. Another example of this holding would be J-J against A-9. The underdog non-paired hand has three outs while the favourite has redraws.
Pair vs. Overcard and one of that pair
The classic example of this situation is the confrontation between a pair of cowboys and big slick. The A-K has three outs and it becomes a 70-30 percent situation or a 2.3-to-1 dog for the cowboys. This is a far cry from the next situation where even though one of the pair is matched the other card is lower.
Pair vs. Undercard and one of that pair
The non pair has to hit its undercard twice or make a straight or flush to prevail. The pair is better than a 90 percent favourite or slightly better than 10-to-1 odds. I’ll take those odds anytime.
Pair vs. Lower suited connectors
You see this match-up late in tournaments when a player is getting desperate and pushes all-in with middle suited connectors. A hand such as Q-Q against 7-6 suited would be a prime example. The pair is a strong favourite to win.
Pair vs. Higher suited connectors
Here is the real coin flip situation. A pair of eights heads-up against a suited Q-J is a fifty-fifty proposition. The higher suited cards would have an edge against a lower pair, such as 2’s or 3’s, since the board itself can sometimes destroy little pairs.
Common Pre-Flop Match-Ups (Non Pairs)
The following heads-up confrontations contain no pairs.
Two high cards vs. Two undercards
The two higher cards are usually a 65% favourite to win, but it can vary depending on whether any of the cards are suited and/or connectors.
High card, low card vs. Two middle cards
In this match-up the high card gives it the edge. But it’s only a marginal winner, approximately 57% to the hand containing the high card.
High card, middle card vs. Second highest, low card
The edge is increased by around 5% when the low card becomes the third highest card, as shown in this example, which gives approx 62% to 38% for high card/middle card combination.
High card, same card vs. Same card, low card
In this example the A-J is in a very strong position. If we discount any flush or straight possibilities, it only leaves the player holding J-8 with three outs (the three remaining 8’s).
Same high card, high kicker vs. Same card, low kicker
The high kicker gives this hand a fairly big edge. It’s very common for A-K run into A-Q, A-J, and lower, and it’s why Ace-King is such a powerful hand, particularly at the business end of no-limit hold’em tournaments when people move all-in with any sort of Ace.
Statistical Variations
For any math maniacs reading this who do not find these odds precise enough, I acknowledge that the math is rounded and for the most part does not take into account the possibilities of ties and back door straights and flushes. What players need to be equipped with is the general statistical match-up – not the fact that in the example of a pair of eights against a suited Q-J the percents are exactly 50.61 for the eights to 48.99 for the suited connectors with the balance going to potential ties. I call that a fifty-fifty proposition.
Of greater importance than quibbling over tenths of a percent is the fact that in most heads-up confrontations you can never be a prohibitive underdog. That is one reason why poker is so challenging and fun. Of course, while true, I’m not attempting to embolden the reader to ignore the odds and become a maniac. Math is the underpinning of poker and if you regularly get your money into the middle with the worst of it you will go broke.
One statistic that hasn’t been mentioned, and it’s one that I particularly like is this – the odds of both players being dealt Aces when playing heads up (one on one) is 270,724-to-1. It’s my favourite statistic because it provides me with almost total confidence when I’m playing heads up and receive pocket Aces that I’m the boss! That confident feeling lasts right up to the river when my Aces get cracked by some rotten piece of cheese which my opponent elected to play. As mentioned already, rarely are you a prohibitive underdog – so remember that to keep those losing hands in perspective.
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By Tom 'TIME' Leonard
Tom has been writing about poker since 1994 and has played across the USA for over 40 years, playing every game in almost every card room in Atlantic City, California and Las Vegas.