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Poker Hands Two Pair Tie

2021年3月12日

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Become a better poker player in double-quick time thanks to PokerStars fast-paced poker format, Zoom poker. Once you fold in a Zoom game, you’ll instantly be dealt a new hand against new opponents. Play more hands, learn new strategies and interact with more play money users every second with Zoom. Two Pair (5s-5c-4c-4h-Jc) One Pair (9s-9c-Ah-8d-2c) High Card (Ah-Qs-7h-5s-3s) If the players have the same ranking hand at showdown, the highest kicker is used as a tie-breaker. For example, if there are two players remaining and each has a Pair of Nines, the player who also has Ace-Eight-Deuce will beat the player who also has King-Queen-Jack.
*Poker Hand Rankings - Texas Holdem Starting Hands Chart At the bottom of this page is a comprehensive listing of Texas Hold’em starting hands based on their EV (expected value). Expected value is the average number of big blinds this hand will make or lose.
*Since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. Eliminating identical hands that ignore relative suit values leaves 6,009,159 distinct 7-card hands. The number of distinct 5-card poker hands that are possible from 7.
*A Two Pair is ranked based on the value of the highest pair in the hand. For example, J-J-2-2-5 beats 10-10-9-9-A. In case two or more players have the same high pair, the tie is broken by the.
What happens when two or more players have the same poker hand? How do you determine who wins? This page will guide you through all the poker hands and show you how to determine the winner, or when to declare a tie. This article assumes you already know about how poker hands are ranked. If you don’t, please read our poker hand ranking page before going any further.kicker
A “kicker” is often used to determine the winning poker hand. For example, let’s say two players both have a pair of aces. Play one has A-A-K-8-3 and player two has A-A-j-3-2. The kicker is the highest card excluding the pair of aces. In other words, the kicker for player one is a king, and for player two it’s a jack. Since a king is better than a jack, player one has the best hand even if both players made a pair of aces. If the kicker also was tied, then you compare the next higest card. For example, if player one has A-A-K-4-2 and player two has A-A-K-5-4, you can take out the aces and kings from both hands. You are left with comparing a 4-2 with a 5-4. Player two has the highest card (a five) thus has the best hand. This is how you use kicker cards to determine the winning hand.Poker HandsRoyal FlushPoker Hands Two Pair Tiers
Since all suits are equal, all royal flushes are equal. The probability of seeing two royal flushes played on the same hand are likely comparable to the probability of getting struck by lightning so don’t expect to encounter this situation!Straight Flush
If there are two straight flushes, the one with the higher top card is the best. The suit of the flush does not count in determining the wining hand as all suits are considered equal. If two flushes are ranked in the same sequence, then it’s a tie.Four of a Kind
If two people have fours of a kind, the player with the higher ranking set of four cards has the winning hand. Thus, the player with four jacks has a better hand than the player with four tens. Kickers are not used so the fifth card is irrelevant.Full House
A hand with three cards of the same rank and two cards of another rank. An example is A-A-A-2-2 (called Aces full of 2s). If two players have full houses, the one with the higher ranking three cards is the winner. For example, tens full of 3s (10-10-10-3-3) beats fours full of Aces (4-4-4-A-A). Someone will always have the better Full House hand and kickers are not used.Flush
If two players have flushes, the highest card determines which is the winning poker hand. If the highest cards are equal then the second highest card is used to determine the winner, and so one. In other words, use the kickers to determine the winner. For example: 2-4-5-8-9 all in spades beats 2-3-5-6-7 all in clubs because you compare the highest card (9 vs 7). All suits are equal.
Best Flush Example:
*10-3-8-K-A (suited) beats 9-4-J-Q-K (suited) – Highest card is A vs K.
*Q-10-9-5-2 (suited) beats Q-10-3-6-5 (suited) – since the two top cards are the same in both hands, the third card determiens the winner. In this example, 9 beats 6.Straight
When comparing two straights, the one with the highest ranking top card is better. An Ace can ONLY count high or low in a straight. For example, A-2-3-4-5 does not beat 10-J-Q-K-A. Also, Q-K-A-2-3 does not count as a straight because the ace doesn’t count as either the low card or the high card. A tie can occur when two players make the exact same straight based on the card ranks, and card suit is irrelevent. Unless of course it results in a straight flush explained earlier.
Best Straight Example
*2-3-4-5-6 beats A-2-3-4-5
*10-J-Q-K-A beats 9-10-J-Q-K
*4-5-6-7-8 ties 4-5-6-7-8Three of a kind
The highest three of a kind when comparing two hands is ranked better. For example the hand 8-8-8-3-2 beats 5-5-5-A-Q. Unless wild cards are used, a tie cannot occur. Someone will always have the better Three of a Kind hand.Two pair
If both players have two pairs, the hand with the highest pair has the winning poker hand and the smaller pair is irrelevant. For example, Q-Q-5-5-3 beats 10-10-7-7-A because the queens beat the tens. If the higher pairs are the same then the smaller pair is used to determine the higher ranking hand. Q-Q-10-10-4 would beat Q-Q-9-9-K. If both pairs are the same then kicker cards are compared.
Best Two Pair Example
*A-A-3-3-5 beats K-K-J-J-9
*K-K-3-3-5 beats K-K-2-2-A
*K-K-3-3-5 beats K-K-3-3-2Pair
The higher pair determines the best hand. If two players have the same pair then the highest card is used. If this card is the same, then the second highest card is compared and finally the third if it comes down to it.
Best Pair Hand
*8-8-3-2-5 wins over 5-5-A-K-J
*10-10-A-2-5 wins over 10-10-K-Q-10
*J-J-K-10-5 wins over J-J-K-9-8High Card
If two players have none of the hands above, then the highest card wins. If the highest cards are the same then the second highest are compared and so on. Use the kicker rules.
Best High Card Example
*A-8-3-2-5 beats K-Q-J-10-3
*A-K-3-2-5 beats A-Q-J-9-5Related Entries
Related posts:
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
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.
___________________________________________________________________________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.
___________________________________________________________________________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.Poker Hands Two Pair Ties
Definitions of Poker HandsPoker HandDefinition1Royal FlushA, K, Q, J, 10, all in the same suit2Straight FlushFive consecutive cards,all in the same suit3Four of a KindFour cards of the same rank,one card of another rank4Full HouseThree of a kind with a pair5FlushFive cards of the same suit,not in consecutive order6StraightFive consecutive cards,not of the same suit7Three of a KindThree cards of the same rank,2 cards of two other ranks8Two PairTwo cards of the same rank,two cards of another rank,one card of a third rank9One PairThree cards of the same rank,3 cards of three other ranks10High CardIf no one has any of the above hands,the player with the highest card wins
___________________________________________________________________________Counting Poker Hands
Straight FlushCounting 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 KindThere 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 HouseLet’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?
FlushThere 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.
StraightThere 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 KindThere 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 PairThese two are left as exercises.
High CardThe 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 HandsPoker HandCountProbability2Straight Flush400.00001543Four of a Kind6240.00024014Full House3,7440.00144065Flush5,1080.00196546Straight10,2000.00392467Three of a Kind54,9120.02112858Two Pair123,5520.04753909One Pair1,098,2400.422569010High Card1,302,5400.5011774Total2,598,9601.0000000How To Break A Two Pair Tie In Poker
___________________________________________________________________________ 2017 – Dan Ma
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2021年3月12日

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