Odds Of Winning Hands In Texas Holdem



Eight-Player Power Ratings in Texas Hold ’Em Introduction. The following table ranks the top hands in an 8-player game. This table assumes that all players stay in until the end. Explanation of column headings. Cards: Initial two-card hand. Probability of win: Probability that this hand will win, or tie for the win.

For example: To calculate your hand odds in a Texas Hold'em game when 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 can expect to hit your flush one of those times. Pocket pairs are a favourite type hand for many players. Pocket pairs from 22 right up to AA can be played profitably with the right strategy, even if hands like AA and KK are a lot more exciting to play. Use the pocket pairs table below to find out the odds of being dealt different ranges of pocket pairs during a game of Texas Holdem. The poker odds calculators on CardPlayer.com let you run any scenario that you see at the poker table, see your odds and outs, and cover the math of winning and losing poker hands. Texas Hold'em Omaha.

Martin HarrisMo Nuwwarah

Table Of Contents

In this series we are offering various strategy advice for short deck hold'em, also sometimes called six plus hold'em (or 6+ hold'em), including sharing tips from some of the pros who have found the game a fun and challenging poker variant to play.

Before we delve any further into strategy, with this article we're going to highlight some of the more interesting and notable odds and probabilities in short deck hold'em. In particular, we'll point out how those odds and probabilities differ from what you encounter in regular, full deck hold'em, which in turn creates some important differences when it comes to strategy.

Short Deck Hold'em (Six Plus Hold'em): Rules and Hand Rankings

As discussed last week, short deck hold'em tosses out all of the fives, fours, threes, and twos, creating a 36-card deck with which to play. The game is played just like regular hold'em, with players being dealt two hole cards and making hands with the five community cards dealt as a flop, turn, and river. Also, as in regular hold'em the ace can be high or low, meaning in short deck A-6-7-8-9 makes a straight.

The big change from regular hold'em comes from the hand rankings being altered. In short deck, flushes rank above full houses, and depending on the game it is sometimes the case that three of a kind beats straights.

Regular hold'emShort deck (straights beat trips)Short deck (trips beat straights)
Royal FlushRoyal FlushRoyal Flush
Straight FlushStraight FlushStraight Flush
Four of a KindFour of a KindFour of a Kind
Full HouseFlushFlush
FlushFull HouseFull House
StraightStraightThree of a Kind
Three of a KindThree of a KindStraight
Two PairTwo PairTwo Pair
One PairOne PairOne Pair
High CardHigh CardHigh Card

The reason for these changes has to do with the fact that in short deck the probabilities of making certain hands are different. In short deck, it is actually easier to make a full house than a flush, which is why flushes rank higher than full houses. (The opposite is true in regular hold'em.) It is also easier to make a straight than to make trips in short deck, which is why some rank three of a kind higher than a straight.

While some short deck games use small and big blinds just like in regular hold'em (with or without antes), others have introduced another twist by removing the blinds and having all players ante, with the button putting in a double-ante and play beginning before the flop with the player left of the button having an option to call, fold, or raise.

Short Deck Hold'em (Six Plus Hold'em): Preflop Probabilities

If you're a regular hold'em player, you're probably well acquainted with probabilities related to starting hands, and therefore know the chances of getting dealt pocket aces (1 in 221), a pocket pair (1 in 17), or two cards of the same suit (1 in 4.25). But what happens to those preflop probabilities after the fives through deuces are removed from the deck?

As you might imagine, reducing the deck from 52 cards down to 36 cards also reduces the number of different starting hand combinations there are.

Whereas in regular hold'em there are 1,326 distinct starting hands, in short deck hold'em there are only 630 distinct starting hands — less than half (about 47.5 percent). That's counting suits as distinct, which isn't generally done when valuing starting hand strength.

If we don't consider suits as distinct, in regular hold'em there are just 169 combinations of starting hands (13 pocket pairs, 78 non-paired suited hands, and 78 non-paired unsuited hands). Meanwhile when not considering suits as distinct, in short deck hold'em there are just 81 combinations of hands (9 pocket pairs, 36 non-paired suited hands, and 36 non-paired unsuited hands) — again, less than half as many in short deck versus regular hold'em (about 47.9 percent).

Fewer starting hand combos obviously affects the frequency with which you are dealt specific hands. For example, when it comes to being dealt pocket aces, that happens about twice as often in short deck hold'em — once every 105 hands (just under one percent of the time).

Pocket pairs come around more frequently in short deck, too — once every 11.66 hands (about 8.6 percent of the time). That's almost 1.5-times as often as in regular hold'em.

Meanwhile in short deck you're dealt suited hands at just about the same frequency as in regular hold'em — once every 4.375 hands (or about 22.8 percent of the time).

Here is all of that in table form, with a couple more comparisons of probabilities added to the list:

Regular hold'emShort deck (Six Plus) hold'em
Number of cards used5236
Distinct starting hands1,326630
Distinct non-equivalent starting hands16981
Probability of being dealt pocket aces0.45% (1 in 221)0.95% (1 in 105)
Probability of being dealt any pocket pair5.9% (1 in 17)8.6% (1 in 11.66)
Probability of being dealt any suited hand23.5% (1 in 4.25)22.9% (1 in 4.4)
Probability of being dealt connectors15.7% (1 in 6.4)22.9% (1 in 4.4)
Probability of being dealt ace-king1.2% (1 in 83)2.5% (1 in 39)
Probability of being dealt two Broadway cards14.3% (1 in 7)30.2% (1 in 3.3)

It’s obvious players have to adjust their thinking when it comes to starting hands and their value in short deck hold’em. Hand values go up in short deck, so what might seem like a decent starting hand in regular hold’em is going to be average or worse in short deck.

Another preflop issue to keep in mind — with fewer starting hands overall, that means the gap in equities between starting hands is narrower as well. For example, in a preflop all-in situation, is about a 78 percent favorite to beat in regular hold'em, but in short deck hold'em the aces are only about 63-67 percent to win depending on the rules being used. Search online for 'short deck hold'em calculator' or 'six plus hold'em calculator' if you're curious to test out some hand comparisons using some recently-built equity calculators.

We’ll talk more about preflop strategy in the next installment.

Short Deck Hold'em (Six Plus Hold'em): Postflop Odds

Postflop is where short deck hold'em introduces some surprises to new players, since the odds and probabilities can be quite different from regular hold'em.

Of course, if you just take a moment to think about it, it's obvious that when drawing to a certain number of outs, the chance of hitting your needed card changes when there are fewer cards left in the deck.

Let's say you hold and the flop comes to give you an open-ended straight draw. You have eight outs (the kings and the eights) to fill your straight, but instead of there being 47 unseen cards (as in regular hold'em), there are only 31 unseen cards in short deck. Whereas in regular hold'em you'd have an 8 in 47 chance of filling your straight on the turn (about 17 percent), in short deck hold'em your odds of turning the straight are 8 in 31 (nearly 26 percent).

I have seen discussions of short deck hold'em outs recommending players replace the 'Rule of 2 and 4' from regular hold'em with a new 'Rule of 3 and 6' for short deck. In regular hold'em, if you flop an open-ended straight draw with eight outs, you can roughly estimate your chance of filling the straight by multiplying those eight outs by two for the turn (~16 percent) and by four for the turn and river (~32 percent).

In short deck you can do something similar, multiplying your eight outs by three for the turn (~24 percent, which is close to the actual 25.8 percent) and by six for the turn and river (~48 percent, which is also close to the actual 45.6 percent).

Here's a table showing how your odds of hitting a certain number of outs change from regular hold'em to short deck:

Regular Hold’em OutsTurnTurn+RiverShort Deck Hold’em OutsTurnTurn+River
12.1%4.3%13.2%6.5%
24.3%8.4%26.5%12.7%
36.4%12.5%39.7%18.7%
48.5%16.5%412.9%24.5%
510.6%20.4%516.1%30.1%
612.8%24.1%619.4%35.5%
714.9%27.8%722.6%40.6%
817.0%31.5%825.8%45.6%
919.1%35.0%929.0%50.3%
1225.5%38.4%1238.7%63.2%
1531.9%54.1%1548.4%74.2%

By the way, don’t forget when you are drawing to a flush that there are fewer outs available to you in short deck than in regular hold'em. If you flop a flush draw in regular hold’em you have nine outs, but in short deck you only have five.

Short Deck Poker Strategy

As already noted, hand values tend to be higher in short deck hold’em, which means one-pair hands aren’t going to be as strong postflop in short deck as they are in regular hold’em. And thanks to the increased chance of players filling draws, those one-pair hands and other modest “made hands” are going to be more vulnerable, too.

Speaking of pairs, it's important to remember that pocket pairs in short deck should be valued drastically differently. Aces and kings are obviously strong hands in regular hold'em, and that stays true in short deck, except the difference between the two is even more pronounced.

Things change quickly after that as pairs below kings are unexciting holdings in short deck. The reason for this will be familiar to any pot-limit Omaha player of decent experience level: similar to PLO, the only easily dominated hands in short deck are pocket pairs.

Where traditional 'dominated' spots in hold'em — like ace-queen against queens — are much closer in equity in short deck, holding a pair versus a higher pair is still a pretty rough spot. And medium pairs are actually a slight dog against overcards, in contrast to regular hold'em. Pairing hole cards happens much more often in short deck, and it's far easier for connecting cards to make straights.

Because equities run much closer in short deck, it's important to maximize opportunities for high-equity spots like holding bigger pairs while minimizing the times you're on the wrong side of that.

A few other items related to postflop probabilities in short deck:

  • with suited cards you flop flush draws less often in short deck, and complete flushes less often as well
  • with connectors and one-gappers you flop straight draws more often in short deck, and complete them more often, too
  • with a pocket pair, you flop a set more often in short deck (about 17 percent of the time vs. 12 percent in regular hold’em

We'll be exploring postflop strategy in more detail going forward in the series as well. Blockers, bluffing opportunities and more will be examined in the coming weeks.

Meanwhile, take a look at the video below and listen to Tom Dwan, Patrik Antonius, Daniel Cates, Kane Kalas, Jason Koon, Phil Ivey, Wai Kin Yong, and Gabe Patgorski offer some general advice about how to approach short deck hold’em strategy.

  • Tags

    cash game strategytournament strategyshort deck hold’emsix plus hold’emoddsprobabilitiespreflop strategypostflop strategydrawing handsstarting hand selection

Is poker a game of skill or chance? This question has been discussed and
argued in many places and is the center of the arguments for and against
legalizing Texas holdem and other forms of poker in many places, including
online.

The answer to this question boils down to the mathematics behind the game. If
the math shows one player can win more often than another based on the
mathematical and statistical truths about Texas holdem then the game is one of
skill.

Let’s look at a few facts before moving on.

  • Fact 1

    Texas holdem is played with a deck of 52 playing cards, consisting of
    the same four suits, and 13 ranks in every deck. You know each deck has an
    ace of spades, and ace of hearts, an ace of clubs, and an ace of diamonds.
    The same is true for kings, queens, and all of the ranks down through twos.

  • Fact 2

    Over a long period of time each player will play from each position at
    the table an equal number of times. In other words, each player will play in
    the small blind, the big blind, under the gun, on the button, etc. an equal
    number of times as other players. If you take two individual players it
    might not be 100% the same, but it’ll be close. When you take thousands of
    players and average their times played in each position mathematically they
    each play the different positions an equal number of times.

  • Fact 3

    The rules in each game are the same for every player at the table.

  • Fact 4

    The player that starts the hand with a better two card starting hand
    wins the hand more often than the player with a worse hand. This has been
    proven by computer simulations that run millions of hands and consider every
    possible outcome.

Why Is This Important?

The reason all of this is important to Texas holdem players is that you can
use all of this math to help you win.

Though there are thousands of possibilities on every hand of Texas holdem,
you can use the fact that everything is based on a set of 52 cards to predict
outcomes and possibilities at every stage for every hand.

Here’s an Example

If you start the hand with two aces as your hole cards, you know that the
remaining 50 cards in the deck only have two aces. The remaining 48 cards
consist of four of each rank below the aces. At the beginning of the hand you
don’t know where any of the other cards are located, but as the hand progresses
you learn where some of them are located.

Continuing with the example, if the flop has an ace and two fours, you hold a
full house. You also know the only hand at this time that can beat you is four
fours. Because two fours are on the flop, the number of times a single opponent
has the other two fours is 1 in 1,326 hands. This is such a small percentage of
the time that you always play the full house in this example as if it’s the best
hand.

How do we know the number of times the opponent has the other two fours?

Because two fours are on the flop, let’s say the four of hearts and the four
of diamonds, so you know that your opponent has to have the four of clubs and
the four of spades. The chances of the first card in their hand being one of
these two cards are two out of 52. If they get one of them as the first card
that leaves the single other card they need out of 51 unseen cards, or one out
of 51.

You multiply two over 52 times one over 51 and this gives us the 1 out of
1,326 hands.

Basic Texas Holdem Math

Some of the math we discuss on this page can be complicated and the truth is
some players won’t be able to use it all. But that doesn’t mean they can’t be
winning Texas holdem players. The math covered in this section forms the
building blocks for the advanced math covered lower on the page.

Every Texas holdem player can use the basic math included in this section,
and if you aren’t using it yet you need to start right away.

Starting Hands

At the most basic level of Texas holdem everything starts with your starting
hand. As we mentioned above, mathematically the player who stars the hand with
the better starting hand wins more than the player with the inferior hand.

This means the first math lesson you need to learn and start using is to play
better starting hand on average than your opponents. While this can get
complicated, especially in games with many multi way pots, you still need to
learn how to play better starting hands.

Probability Of Winning Hands In Texas Holdem

If you take nothing else from this page, if you simply tighten up your
starting hand selection it’ll immediately improve your results.

Position

It’s difficult to directly relate position to mathematics, but the main thin
to know is the later your position, the better your chances to play in a
positive expectation situation. We’ll discuss expectation in a later section,
but it’s important to understand that having position on an opponent is a strong
advantage that equates to a mathematical advantage over the long run.

Outs

One of the most important skills Texas holdem players need to develop is the
ability to determine the number of outs, or cards remaining in the deck that can
complete the hand they’re drawing to. You use this information to determine your
chances of winning the hand as well as to determine the pot odds. Pot odds are
discussed in the next section, but they show you whether or not a call is
profitable in the long run when an opponent makes a bet.

We can determine how many outs you have because we know what’s in the deck
and what we need to improve our hand. If you have a king, queen, jack, and 10
after the turn you know any of the four aces or four nines complete your
straight.

This means you have eight outs. You’ve seen six cards, so the deck has 46
cards remaining in it. Don’t make the mistake of thinking about the cards that
have been folded or your opponent holds. You haven’t seen these cards so any
unseen card is still considered a possible river card.

In other words, on average, if you play this situation 46 times you’re going
to complete your straight eight times and not complete it 38 times.

You should always consider how many outs you have in every situation while
playing. B knowing your outs you have another piece of information that can help
you make profitable decisions throughout the hand.

Pot Odds

The next question many players ask after they learn how to determine their
out sis how they can use this information to make more money at the table. This
is where pot odds come into play.

Pot odds are simply a ratio or comparison between the money in the pot and
the chances you have of completing your hand. You use this ratio to determine if
a call or fold is the best play based on the information you currently have.

Odds Of Each Hand In Texas Holdem

If you consider the example in the last section concerning the straight draw,
you know that the deck holds eight cards that complete your straight and 38
cards that don’t. This creates a ratio of 38 to 8, which reduces to 4.75 to 1.
You reduce by dividing 38 by 8.

The way you use this ratio is by comparing it to the amount of money in the
pot and how much you have to put into the pot. If the pot odds are in your favor
it’s profitable to call and if not you should fold.

Example

If the pot has $100 in it and you have to make a $10 call the pot is offering
10 to 1 odds. You determine this the same way as above, by dividing $100 by $10.

If you’re in the situation described above of drawing to a straight on the
river you can see that a call is correct because the pot is offering 10 to 1 and
you have a 4.75 to 1 chance of winning.

On the other hand of the pot has $100 in it and you have to put $40 in to see
the river the pot is only offering 2.5 to 1 odds and your chances of hitting
your straight are still 4.75 to 1 so you should fold.

Pot odds can get complicated, especially when you start considering how they
work when you’re determining the correct play with both the turn and river to
come.

Fortunately charts are available to quickly check the odds of hitting your
hand based on how many outs you have. We’ve included one next so all you have to
do is determine your outs and compute the odds the pot is offering. Then compare
the two to see if it’s profitable to call or fold.

Number of OutsTurn & River CombinedRiver Only
122.26 to 145 to 1
210.9 to 122 to 1
37 to 114.33 to 1
45.06 to 110.5 to 1
53.93 to 18.2 to 1
63.15 to 16.67 to 1
72.6 to 15.57 to 1
82.17 to 14.75 to 1
91.86 to 14.11 to 1
101.6 to 13.6 to 1
111.4 to 13.18 to 1
121.22 to 12.83 to 1
131.08 to 12.54 to 1
140.95 to 12.29 to 1
150.85 to 12.07 to 1
160.75 to 11.88 to 1
170.67 to 11.71 to 1
180.6 to 11.56 to 1
190.54 to 11.42 to 1
200.48 to 11.3 to 1

Expand | Shrink

When you’re determining your pot odds for the turn and river you determine
them on the turn and then if you don’t hit your draw you determine them again on
the river. This often happens, especially in limit Texas holdem. But if an
opponent moves all in on the turn you simply use the turn and river combined
odds in your decision.

Advanced Texas Holdem Math

Many beginning Texas holdem players look at a discussion about expectation
and instantly decide it’s too hard and ignore it. When they do this they
severely hurt their long term chances at being a profitable player.

We’ve broken down how to look at situations while playing poker in a simple
manner that almost any player can use below. Do yourself a favor and go into
this with an open mind. Once you understand it at a simple level you can learn
more as you gain experience. You may be surprised at just how easy it gets to
determine positive and negative expectation with a little practice.

Texas

Expectation

Expectation is what the average outcome will be if you play the same
situation hundreds or thousands of times. Once you determine the expectation you
know if a situation offers positive or negative results on average.

Your goal as a Texas holdem player is to play in as many positive expectation
situations as possible and avoid as many negative expectation situations as
possible.

You need to understand that expectation is something that can be applied to
almost any situation in poker, but it’s also subjective in many areas.

  • If you play at a table where every opponent is better than you in the long
    run you’re going to lose money. This is a negative expectation situation.
  • If you play at a table where every opponent is a worse
    player than you it’s a positive expectation situation because you’re going to
    win in the long run.

The problem is determining whether a situation is positive or negative
expectation when you sit down at a table with some players who are better than
you and some who are worse.

Odds of each hand in texas holdem

You can find many situations where it’s easier to determine expectation
mathematically, and we’ll teach you how to do this now. While this may seem
overly complicated at first, especially to do at the table while playing, you
don’t need to know exactly how negative or positive a situation is, you only
need to know if it’s positive or negative.

Once you determine if a situation is positive expectation or negative
expectation you simply remember the next time you’re in a similar situation.
Once you start determining expectation you’ll find that you learn mist
situations quickly and only have to think through an occasional situation at the
table.

The best way to see how to determine expectation is by running through a
couple examples.

Example 1

You’re facing a bet after the turn and you have four to a flush.
The pot had $400 in it and your opponent bet $100. You’re certain that if you
miss your flush draw you’ll lose and when you hit your flush draw you’ll win.

In order to see the river you have to call the $100 bet. When you lose you
lose $100, and when you win you get back $600. You get your $100 back plus the
$400 that was in the pot plus the $100 bet your opponent made.

Many players claim that part of the money already in the pot is theirs, but
once you put money into the pot it isn’t yours. The only way to get it back is
to win the pot. So you can’t consider it in any other way when determining
expectation.

The way to see if it’s positive or negative to call is to determine what will
happen on average if you play the same situation many times. Most players find
it easiest to determine by pretending to play the hand 100 times.

In this example you’re going to hit your flush 9 out of 46 times. This means
19.56% of the time you’re going to win and 80.44% of the time you’re going to
lose. To make this simple we’ll round these numbers off to 20% and 80%.

If you have to put $100 in the pot 100 times your total investment is
$10,000. The 80 times you lose you get nothing back. The 20 times you win you
get $600. 20 times $600 is $12,000. When you take the $12,000 you win and
subtract the $10,000 you lose when you play the situation 100 times, you see
that you win $2,000 overall.

To determine how much you win on average per hand simply divide the $2,000 by
100 to get a positive expectation of $20 per hand. This means that every time
you’re in this situation you’ll win on average $20.

The truth is you may win a little more because we’re ignoring the river.
Because you know you can’t win if you miss your flush, you always need to fold on
the river when you miss your draw. Every once in a while you may be able to
extract a small bet from your opponent on the river when you hit your flush,
increasing your average expectation. Sometimes it’s even correct for your
opponent to call on the river in this situation. See the next example to see
why.

Example 2

Let’s say you’re playing the same hand as above but you have a
straight and your opponent appears to be drawing to a flush. You’re on the
river, the pot has $600 in it, and the board has the third suited card hit on the
river.

If your opponent was drawing to the flush, they completed it and you’re going
to lose the hand. In this situation your opponent bets $20.

In this situation you clearly have to call.

The reason you have to call is because you can’t know for certain your
opponent was drawing to the flush. They may be bluffing or have two pair or any
other number of hands that aren’t as good as your straight.

Let’s look at the math behind this decision.

If you play the situation 100 times your total investment is $20 times 100,
or $2,000.

When you win you get $640, consisting of the original $600 pot, your
opponent’s $20 bet, and your $20 call. If you win three hands you get back
$1,920 for a loss of $80, or 80 cents per hand.

If you win at least four times you’re in a positive expectation situation.
Four wins nets $2,560 for an overall win of $560, or $5.60 per hand.

What this means is if your opponent is bluffing or has a weaker hand just
four times out of 100 or more, calling is a positive expectation situation. Four
times out of 100 is only 4%. You’ll win at least 4% of the time in this
situation.

The numbers get closer the more your opponent bets on the river, and the
closer the numbers get the more you’re going to need to use what you know about
your opponent to determine if a situation is positive or not.

Start looking at every decision you make at the Texas holdem tables in terms
of positive and negative expectation.It’s hard at first, but the more you
practice the better you’ll get at predicting if a situation offers positive
expectation.

Summary

Texas holdem math is often the only thing that separates winning and losing
players. Take the time to learn the basics now so you can improve your game in
every way possible as you gain experience. This guide is the perfect place to
start for players of every experience level.





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