This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities

The dead man’s hand is a slang term used in poker for a two pair of black aces and black eights, although its meaning has changed over time.The story goes that lawman and gambler “Wild Bill. The most important thing to understand is that you should take these poker hand orders only as a starter guide to poker hand strength. Every hand can be a winner or loser, depending on the circumstances.

Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog – multiplication principle, permutation and combination (also covered here). There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise.

• Poker Starting Hands Percentages - Learn good starting hand ranges for online poker. Play the right hands and win more pots. Over $200k in freerolls every year! Poker Starting Hands Percentage.
• Every poker hand’s strength decreases against more players These hand rankings reinforce the concept that you want to isolate opponents with your premium hands that win much less often against more players. Interestingly, but not surprisingly, every hand wins dramatically less when it is played against more opponents.

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Preliminary Calculation

Usually the order in which the cards are dealt is not important (except in the case of stud poker). Thus the following three examples point to the same poker hand. The only difference is the order in which the cards are dealt.

These are the same hand. Order is not important.

The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects. The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards.

The notation is called the binomial coefficient and is pronounced “n choose r”, which is identical to the number of -element subsets of a set with objects. Other notations for are , and . Many calculators have a function for . Of course the calculation can also be done by definition by first calculating factorials.

Thus the probability of obtaining a specific hand (say, 2, 6, 10, K, A, all diamond) would be 1 in 2,598,960. If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of all diamond cards? It is

This is definitely a very rare event (less than 0.05% chance of happening). The numerator 1,287 is the number of hands consisting of all diamond cards, which is obtained by the following calculation.

The reasoning for the above calculation is that to draw a 5-card hand consisting of all diamond, we are drawing 5 cards from the 13 diamond cards and drawing zero cards from the other 39 cards. Since (there is only one way to draw nothing), is the number of hands with all diamonds.

If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of cards in one suit? The probability of getting all 5 cards in another suit (say heart) would also be 1287/2598960. So we have the following derivation.

Thus getting a hand with all cards in one suit is 4 times more likely than getting one with all diamond, but is still a rare event (with about a 0.2% chance of happening). Some of the higher ranked poker hands are in one suit but with additional strict requirements. They will be further discussed below.

Another example. What is the probability of obtaining a hand that has 3 diamonds and 2 hearts? The answer is 22308/2598960 = 0.008583433. The number of “3 diamond, 2 heart” hands is calculated as follows:

One theme that emerges is that the multiplication principle is behind the numerator of a poker hand probability. For example, we can think of the process to get a 5-card hand with 3 diamonds and 2 hearts in three steps. The first is to draw 3 cards from the 13 diamond cards, the second is to draw 2 cards from the 13 heart cards, and the third is to draw zero from the remaining 26 cards. The third step can be omitted since the number of ways of choosing zero is 1. In any case, the number of possible ways to carry out that 2-step (or 3-step) process is to multiply all the possibilities together.

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The Poker Hands

Here’s a ranking chart of the Poker hands.

The chart lists the rankings with an example for each ranking. The examples are a good reminder of the definitions. The highest ranking of them all is the royal flush, which consists of 5 consecutive cards in one suit with the highest card being Ace. There is only one such hand in each suit. Thus the chance for getting a royal flush is 4 in 2,598,960.

Royal flush is a specific example of a straight flush, which consists of 5 consecutive cards in one suit. There are 10 such hands in one suit. So there are 40 hands for straight flush in total. A flush is a hand with 5 cards in the same suit but not in consecutive order (or not in sequence). Thus the requirement for flush is considerably more relaxed than a straight flush. A straight is like a straight flush in that the 5 cards are in sequence but the 5 cards in a straight are not of the same suit. For a more in depth discussion on Poker hands, see the Wikipedia entry on Poker hands.

The counting for some of these hands is done in the next section. The definition of the hands can be inferred from the above chart. For the sake of completeness, the following table lists out the definition.

Definitions of Poker Hands

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Counting Poker Hands

Straight Flush
Counting from A-K-Q-J-10, K-Q-J-10-9, Q-J-10-9-8, …, 6-5-4-3-2 to 5-4-3-2-A, there are 10 hands that are in sequence in a given suit. So there are 40 straight flush hands all together.

Four of a Kind
There is only one way to have a four of a kind for a given rank. The fifth card can be any one of the remaining 48 cards. Thus there are 48 possibilities of a four of a kind in one rank. Thus there are 13 x 48 = 624 many four of a kind in total.

Full House
Let’s fix two ranks, say 2 and 8. How many ways can we have three of 2 and two of 8? We are choosing 3 cards out of the four 2’s and choosing 2 cards out of the four 8’s. That would be = 4 x 6 = 24. But the two ranks can be other ranks too. How many ways can we pick two ranks out of 13? That would be 13 x 12 = 156. So the total number of possibilities for Full House is

Note that the multiplication principle is at work here. When we pick two ranks, the number of ways is 13 x 12 = 156. Why did we not use = 78?

Flush
There are = 1,287 possible hands with all cards in the same suit. Recall that there are only 10 straight flush on a given suit. Thus of all the 5-card hands with all cards in a given suit, there are 1,287-10 = 1,277 hands that are not straight flush. Thus the total number of flush hands is 4 x 1277 = 5,108.

Straight
There are 10 five-consecutive sequences in 13 cards (as shown in the explanation for straight flush in this section). In each such sequence, there are 4 choices for each card (one for each suit). Thus the number of 5-card hands with 5 cards in sequence is . Then we need to subtract the number of straight flushes (40) from this number. Thus the number of straight is 10240 – 10 = 10,200.

Three of a Kind
There are 13 ranks (from A, K, …, to 2). We choose one of them to have 3 cards in that rank and two other ranks to have one card in each of those ranks. The following derivation reflects all the choosing in this process.

Two Pair and One Pair
These two are left as exercises.

High Card
The count is the complement that makes up 2,598,960.

The following table gives the counts of all the poker hands. The probability is the fraction of the 2,598,960 hands that meet the requirement of the type of hands in question. Note that royal flush is not listed. This is because it is included in the count for straight flush. Royal flush is omitted so that he counts add up to 2,598,960.

Probabilities of Poker Hands

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2017 – Dan Ma

When two players appear to have the same hand in poker, deciding who is the winner is not always easy. I’ve played for over 10 years and will show you how to determine whether there is a winner or if there it is a tie.

What happens if you have the same hand in poker? If two or more players have the same hand the high card determines the winner. For straights or flushes, the highest top card is declared the winner. For one pair and two pair hands, the highest kicker wins. If players have the same 5-card hand, it is a tie and the pot is split equally.

Sometimes the basics are not enough and further explanation is needed. Let’s go through all the possible hands and show how a tiebreaker is handled for each and every possible situation in poker.

Poker Tiebreaker Rules

Having a tie in poker is actually a fairly rare thing. For the purposes of this article we will focus on ties in Texas Hold’em. However, the methodology works for any form of poker.

Who Wins If No One Has a Pair? High Card Tiebreaker Rules

The easy way to determine who wins if no one has even a pair is for everyone to put their hands in order from high to low. Then, simply start at the top and work your way down until the tie is broken. The highest non-tie card wins.

High-Card Tiebreaker Examples:

• AJT85 beats AJT82
• T8542 Beats T7653
• 85432 Beats 76542
• K6542 Beats K6532

What Happens If Two Players Have the Same One-pair Hand?

If two or more players have the same pair, you use the same methodology as you do for high-card hands. The next highest non-tie card determines the winner.

One-Pair Tiebreaker Examples:

• KKT75 beats KK942
• 88652 Beats 88642
• AAK83 Beats AAK82

Who Wins in Poker If Both Players Have 2 Pair? Two-Pair Tiebreaker Rules

Two pair winners are really easy to determine, the player with the higher pair wins. For example, JJ22 beats TT99.

If both players have the same two pair, it is also easy to figure out the winner since there is only one kicker. Whichever kicker is higher wins.

Two-Pair Tiebreaker Examples:

• 7733A beats 55442
• JJTT8 beats JJTT5
• 8822A beats 8822K

Three of a Kind Tiebreaker Rules

The person with the highest three of a kind wins. If two players have the same three of a kind, then the kickers are used to determine the tiebreaker.

Three of a Kind Tiebreaker Examples:Which Hand Is Best in High-Low Poker?

• TTT92 beats 77743
• QQQT2 beats QQQ76

What Happens If Two Players Have a Straight or Flush?

If two or more players have a straight or flush, whoever has the top card wins.

Straight & Flush Tiebreaker Examples:

• 76543 beats 5432A (Ace is a one in this case)
• J♠ 9♠ 5♠ 3♠ 2♠ beats T♠ 8♠ 7♠ 6♠ 4♠

What If Two Players Have a Full House?

To break a tie with a full house, whoever has the highest “trips” parts of their hand wins. The “pair” part of the hand does not matter except as a tiebreaker. If the pairs are the same as well, then the hand is a tie and the pot is split.

Full House Tiebreaker Examples:

• TTT22 beats 777AA
• 555JJ beats 444KK
• QQQ33 beats QQQ22

Four of a Kind, Straight Flushes, and Royal Flushes

Unless the hand is on the board, it is extremely rare for there to be two players with the same ultra-premium hand like four of a kind, a straight flush, or a royal flush. However, it is easy to decide who is the winner.

• Four of a kind – The highest four of a kind hand wins
• Straight flush– Usually when this happens, one player will have the top of the straight flush and the other the bottom. The top wins.
• Royal flush– The only time it is possible for two players to have a royal flush is if it is on the board. Even if it was possible, two royal flushes is always a tie. Contrary to what some people believe, one suit does not beat another suit unless a specific local rule dictates it.

What Happens If Players Have the Same Hand Even After a Tiebreaker?

Can there be a tie in poker? In poker, if no winner can be determined with a tiebreaker, then the hand is declared a tie and the tied players split the pot. The most frequent time there is a tie in poker is where the board is paired twice and two or more players each have the same high card.

Examples of tied hands:

• One player has AK and the other has AQ and the board is J2255. Each player has A2255 and for a tie.
• One player has A8 and another has A6. The final board is AQJJ9. Both players have a pair of Aces with kickers of QJJ9. They would split the pot.
• One player has 98 and the other has 92. The final board is AKQT5. Both players have the high card hand AKQT9. The pot is once again split between them.

What If the Best Hand Is on the Board?

If no part of anyone’s hand can break the tie, then the pot is split equally among the players with live cards. This commonly happens when there is a straight or a flush on the board. This is known as “playing the board.”

How Do We Split up the Pot?

The easiest method to split up a pot in poker is to start with the highest chip color and work your way down. If there is an uneven number of a color, you pull in enough from the next lowest amount to even it up. Then start the process again with the next highest color available.

What If There Is an Uneven Amount in the Pot?

If there is an extra chip left over after the pot has been split, then the first player seated clockwise from the dealer gets it. In heads-up, the player who was the Big Blind gets the extra chip.

Which Hand Is Best in High-Lo Poker?

There are a few variations of poker, namely Omaha Hi-Lo where the low hand wins half of the pot. In this case, whoever can make the lowest possible hand that isn’t a straight wins. 5-4-3-2-A is known as the “nut low.” and is a really strong hand in Hi-Lo games.

In order to qualify for a low hand, the highest card has to be 8 or lower. 86532 qualifies but 95432 does not.

What Are Common Tie-Breaker Mistakes?

In pub poker or home games, I see people scoop a pot quite frequently when it was supposed to be a tie. The most common time this happens is when someone is dominated and then their kicker is counterfeited at some point during the hand.

Here are some examples:

AQ vs. A2– Board runs out A588K, which means they both are holding two pair Aces and eights with a King kicker. I have witnessed the pot be pushed to the AQ guy and the next hand be about to start before anyone notices.

66 vs. 44– Board runs out KTT7K, which means they both are playing the board with two-pair, Kings over Tens with a seve kicker. I swear, I wish the guy with 66 would notice the counterfeiting just one time. I’ve seen supposedly “experienced” players not even understand that 66 and 44 are tied here.

AA vs. AK– Board runs out 97568, with a straight on the board it’s a split pot. Yet you’d be surprised how often the guy with AA will try to drag in the entire pot.

Remind Me, What Is the Hand Ranking Order Again?

Ranked from best hand to worst:

Every Poker Hand Odds

• Royal Flush
• Straight Flush
• Four of a Kind
• Full House
• Flush
• Straight
• Three of a Kind
• Two-Pair
• One-Pair
• High Card

Final Thoughts

Now you know how to break any possible tie in poker if two players seem to have the same hand. If you want to learn the basics of poker strategy, you might want to check out my complete poker tutorial. Thanks for reading!

Related Questions

Can you have two hands in poker? You are required to always play your highest hand possible in Texas hold’em or other poker games. However, if you verbally announce a weaker version of your hand then you actually have, the dealer may actually force you to play the weaker hand.

Which is higher straight or flush? According to the hand ranking rules of poker, a flush always beats a straight.

Chances Of Every Poker Hand

Is JQKA2 a straight? AThis is know as an around-the-corner straight and is only used as a special rule in some home games. In games that follow the exact rules of poker, JQKA2 is not considered a straight and is just an Ace-high high-card hand.