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Can You Go J Q K A 2 In Poker

4/5/2022
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You start the standard game with 4 players and the deck of cards is a standard deck with all cards 2-8 being removed, leaving 24 cards. The people seated across from each other are partners. The dealer starts dealing to their left, typically in sets of 2-3 cards, dispersing 5 cards in 2 passes, this leaves 4 down or 'buried' cards.

Sanderson M. Smith

  1. No this is not a bug. In this situation you would need a 10 J in your hand for a straight. A 2 3 4 5 is a straight because you can count the A also as '1'. Round-the-Corner-Straights (in this case J-Q-K-A-2) are not allowed in Poker.
  2. The highest card in Poker is the Ace and it would be the end of a straight, 10, J, Q, K, A. The Ace can also be used low, as a one.
  3. IF YOU MEAN TO EXCLUDE STRAIGHT FLUSHES AND ROYAL FLUSHES (SEE BELOW), the number of such hands is 10.4-choose-1^5 - 36 - 4 = 10200, with probability 0.00392465 A FLUSH Here all 5 cards are from the same suit (they may also be a straight).
  4. Under high rules, an ace can rank either high (as in A ♥ K ♥ Q ♥ J ♥ 10 ♥, an ace-high straight flush) or low (as in 5 ♦ 4 ♦ 3 ♦ 2 ♦ A ♦, a five-high straight flush), but cannot simultaneously rank both high and low (so Q ♣ K ♣ A ♣ 2 ♣ 3 ♣ is an ace-high flush).

Home About Sanderson Smith Writings and Reflections Algebra 2 AP Statistics Statistics/Finance Forum

POKER PROBABILITIES (FIVECARD HANDS)

In many forms of poker, one is dealt 5 cards from astandard deck of 52 cards. The number of different 5 -card pokerhands is

52C5 = 2,598,960

A wonderful exercise involves having students verify probabilitiesthat appear in books relating to gambling. For instance, inProbabilities in Everyday Life, by John D. McGervey, one findsmany interesting tables containing probabilities for poker and othergames of chance.

This article and the tables below assume the reader is familiarwith the names for various poker hands. In the NUMBER OF WAYS columnof TABLE 2 are the numbers as they appear on page 132 in McGervey'sbook. I have done computations to verify McGervey's figures. Thiscould be an excellent exercise for students who are studyingprobability.

There are 13 denominations (A,K,Q,J,10,9,8,7,6,5,4,3,2) in thedeck. One can think of J as 11, Q as 12, and K as 13. Since an acecan be 'high' or 'low', it can be thought of as 14 or 1. With this inmind, there are 10 five-card sequences of consecutive dominations.These are displayed in TABLE 1.

TABLE 1
A K Q J 10
K Q J 10 9
Q J 10 9 8
J 10 9 8 7
10 9 8 7 6
9 8 7 65
8 7 6 54
7 6 5 4 3
6 5 4 3 2
5 4 3 2 A
Can You Go J Q K A 2 In Poker

The following table displays computations to verify McGervey'snumbers. There are, of course , many other possible poker handcombinations. Those in the table are specifically listed inMcGervey's book. The computations I have indicated in the table doyield values that are in agreement with those that appear in thebook.

TABLE 2
HAND

N = NUMBER OF WAYS listed by McGervey

Computations and comments
Probability of HAND
N/(2,598,960)
and approximate odds.

Straight flush

40

There are four suits (spades, hearts, diamond, clubs). Using TABLE 1,4(10) = 40.

0.000015
1 in 64,974

Four of a kind

624

(13C1)(48C1) = 624.

Choose 1 of 13 denominations to get four cards and combine with 1 card from the remaining 48.

0.00024
1 in 4,165

Full house

3,744

(13C1)(4C3)(12C1)(4C2) = 3,744.

Choose 1 denominaiton, pick 3 of 4 from it, choose a second denomination, pick 2 of 4 from it.

0.00144
1 in 694

Flush

5,108

(4C1)(13C5) = 5,148.

Choose 1 suit, then choose 5 of the 13 cards in the suit. This figure includes all flushes. McGervey's figure does not include straight flushes (listed above). Note that 5,148 - 40 = 5,108.

0.001965
1 in 509

Straight

10,200

(4C1)5(10) = 45(10) = 10,240

Using TABLE 1, there are 10 possible sequences. Each denomination card can be 1 of 4 in the denomination. This figure includes all straights. McGervey's figure does not include straight flushes (listed above). Note that 10,240 - 40 = 10,200.

0.00392
1 in 255

Three of a kind

54,912

(13C1)(4C3)(48C2) = 58,656.

Choose 1 of 13 denominations, pick 3 of the four cards from it, then combine with 2 of the remaining 48 cards. This figure includes all full houses. McGervey's figure does not include full houses (listed above). Note that 54,912 - 3,744 = 54,912.

0.0211
1 in 47

Exactly one pair, with the pair being aces.

84,480

(4C2)(48C1)(44C1)(40C1)/3! = 84,480.

Choose 2 of the four aces, pick 1 card from remaining 48 (and remove from consider other cards in that denomination), choose 1 card from remaining 44 (and remove other cards from that denomination), then chose 1 card from the remaining 40. The division by 3! = 6 is necessary to remove duplication in the choice of the last 3 cards. For instance, the process would allow for KQJ, but also KJQ, QKJ, QJK, JQK, and JKQ. These are the same sets of three cards, just chosen in a different order.

0.0325
1 in 31

Two pairs, with the pairs being 3's and 2's.

1,584

McGervey's figure excludes a full house with 3's and 2's.

(4C2)(4C1)(44C1) = 1,584.

Choose 2 of the 4 threes, 2 of the 4 twos, and one card from the 44 cards that are not 2's or 3's.

0.000609
1 in 1,641

'I must complain the cards are ill shuffled 'til Ihave a good hand.'

-Swift, Thoughts on Various Subjects

Home About Sanderson Smith Writings and Reflections Algebra 2 AP Statistics Statistics/Finance Forum

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Copyright © 2003-2009 Sanderson Smith

Sanderson M. Smith

Home About Sanderson Smith Writings and Reflections Algebra 2 AP Statistics Statistics/Finance Forum

POKER PROBABILITIES (FIVECARD HANDS)

In many forms of poker, one is dealt 5 cards from astandard deck of 52 cards. The number of different 5 -card pokerhands is

Poker
52C5 = 2,598,960

A wonderful exercise involves having students verify probabilitiesthat appear in books relating to gambling. For instance, inProbabilities in Everyday Life, by John D. McGervey, one findsmany interesting tables containing probabilities for poker and othergames of chance.

This article and the tables below assume the reader is familiarwith the names for various poker hands. In the NUMBER OF WAYS columnof TABLE 2 are the numbers as they appear on page 132 in McGervey'sbook. I have done computations to verify McGervey's figures. Thiscould be an excellent exercise for students who are studyingprobability.

There are 13 denominations (A,K,Q,J,10,9,8,7,6,5,4,3,2) in thedeck. One can think of J as 11, Q as 12, and K as 13. Since an acecan be 'high' or 'low', it can be thought of as 14 or 1. With this inmind, there are 10 five-card sequences of consecutive dominations.These are displayed in TABLE 1.

TABLE 1
A K Q J 10
K Q J 10 9
Q J 10 9 8
J 10 9 8 7
10 9 8 7 6
9 8 7 65
8 7 6 54
7 6 5 4 3
6 5 4 3 2
5 4 3 2 A

The following table displays computations to verify McGervey'snumbers. There are, of course , many other possible poker handcombinations. Those in the table are specifically listed inMcGervey's book. The computations I have indicated in the table doyield values that are in agreement with those that appear in thebook.

Poker
TABLE 2
HAND

N = NUMBER OF WAYS listed by McGervey

Computations and comments
Probability of HAND
N/(2,598,960)
and approximate odds.

Straight flush

40

There are four suits (spades, hearts, diamond, clubs). Using TABLE 1,4(10) = 40.

0.000015
1 in 64,974

Four of a kind

624

(13C1)(48C1) = 624.

Choose 1 of 13 denominations to get four cards and combine with 1 card from the remaining 48.

0.00024
1 in 4,165

Full house

3,744

(13C1)(4C3)(12C1)(4C2) = 3,744.

Choose 1 denominaiton, pick 3 of 4 from it, choose a second denomination, pick 2 of 4 from it.

0.00144
1 in 694

Flush

5,108

(4C1)(13C5) = 5,148.

Choose 1 suit, then choose 5 of the 13 cards in the suit. This figure includes all flushes. McGervey's figure does not include straight flushes (listed above). Note that 5,148 - 40 = 5,108.

0.001965
1 in 509

Straight

10,200

(4C1)5(10) = 45(10) = 10,240

Using TABLE 1, there are 10 possible sequences. Each denomination card can be 1 of 4 in the denomination. This figure includes all straights. McGervey's figure does not include straight flushes (listed above). Note that 10,240 - 40 = 10,200.

0.00392
1 in 255

Three of a kind

54,912

(13C1)(4C3)(48C2) = 58,656.

Choose 1 of 13 denominations, pick 3 of the four cards from it, then combine with 2 of the remaining 48 cards. This figure includes all full houses. McGervey's figure does not include full houses (listed above). Note that 54,912 - 3,744 = 54,912.

0.0211
1 in 47

Exactly one pair, with the pair being aces.

84,480

(4C2)(48C1)(44C1)(40C1)/3! = 84,480.

Choose 2 of the four aces, pick 1 card from remaining 48 (and remove from consider other cards in that denomination), choose 1 card from remaining 44 (and remove other cards from that denomination), then chose 1 card from the remaining 40. The division by 3! = 6 is necessary to remove duplication in the choice of the last 3 cards. For instance, the process would allow for KQJ, but also KJQ, QKJ, QJK, JQK, and JKQ. These are the same sets of three cards, just chosen in a different order.

0.0325
1 in 31

Two pairs, with the pairs being 3's and 2's.

1,584

McGervey's figure excludes a full house with 3's and 2's.

(4C2)(4C1)(44C1) = 1,584.

Choose 2 of the 4 threes, 2 of the 4 twos, and one card from the 44 cards that are not 2's or 3's.

0.000609
1 in 1,641

Can You Go J Q K A 2 In Poker Tournaments

'I must complain the cards are ill shuffled 'til Ihave a good hand.'

-Swift, Thoughts on Various Subjects

Home About Sanderson Smith Writings and Reflections Algebra 2 AP Statistics Statistics/Finance Forum

Previous Page Print This Page

Can You Go J Q K A 2 In Poker Room

Copyright © 2003-2009 Sanderson Smith