Register here: http://gg.gg/ozu6y
Sanderson M. Smith
How many different starting hands are there in poker? There is a total of 169 non-equivalent starting poker hands in Texas Hold’em, which is composed of 13 pocket pairs, 78 suited hands and 78. There are 52 cards in a standard deck, as you know I’m sure. There are, therefore, 52 different possibilities for drawing the first card of your ’hand’. Starting Hand Combinations There are 52 cards in a deck, 13 of each suit, and 4 of each rank. This means there are: 16 possible hand combinations of every unpaired hand. However, even though the hands are not identical from that perspective, they still form equivalent poker hands because each hand is an A-Q-8-7-3 high card hand. There are 7,462 distinct poker hands. There are 7,462 distinct poker hands.Home | About Sanderson Smith | Writings and Reflections | Algebra 2 | AP Statistics | Statistics/Finance | ForumHow Many Different Poker Starting Hands Are There Every
Poker Bankroll Challenge: Stage 2 Stakes: $0.02/$0.04 Buy In: $3 (75 x BB) Starting Bankroll: $28 Target: $6 (2 x Buy In) Finishing Bankroll: $34 Estimated Sessions: 2 Use this exercise to continue to get used to the starting hand chart and knowing what position you are in, but also start thinking about each starting hand you play in terms of what category of hand it is and what you are.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 is52C5 = 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 1A K Q J 10K Q J 10 9Q J 10 9 8J 10 9 8 710 9 8 7 69 8 7 658 7 6 547 6 5 4 36 5 4 3 25 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.TABLE 2How Many Different Poker Starting Hands Are There BadHAND
N = NUMBER OF WAYS listed by McGerveyComputations and commentsProbability of HANDN/(2,598,960) and approximate odds.
Straight flush40
There are four suits (spades, hearts, diamond, clubs). Using TABLE 1,4(10) = 40.0.0000151 in 64,974
Four of a kind624
(13C1)(48C1) = 624.
Choose 1 of 13 denominations to get four cards and combine with 1 card from the remaining 48.0.000241 in 4,165
Full house3,744
(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.0.001441 in 694
Flush5,108
(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 = 5,108.0.0019651 in 509
Straight10,200
(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 = 10,200.0.003921 in 255
Three of a kind54,912
(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 = 54,912.0.02111 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.0.03251 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.0.0006091 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 | ForumHow Many Different Poker Starting Hands Are There Now
Previous Page | Print This PageHow Many Different Poker Starting Hands Are There People
Copyright © 2003-2009 Sanderson Smith
Register here: http://gg.gg/ozu6y
https://diarynote-jp.indered.space
Sanderson M. Smith
How many different starting hands are there in poker? There is a total of 169 non-equivalent starting poker hands in Texas Hold’em, which is composed of 13 pocket pairs, 78 suited hands and 78. There are 52 cards in a standard deck, as you know I’m sure. There are, therefore, 52 different possibilities for drawing the first card of your ’hand’. Starting Hand Combinations There are 52 cards in a deck, 13 of each suit, and 4 of each rank. This means there are: 16 possible hand combinations of every unpaired hand. However, even though the hands are not identical from that perspective, they still form equivalent poker hands because each hand is an A-Q-8-7-3 high card hand. There are 7,462 distinct poker hands. There are 7,462 distinct poker hands.Home | About Sanderson Smith | Writings and Reflections | Algebra 2 | AP Statistics | Statistics/Finance | ForumHow Many Different Poker Starting Hands Are There Every
Poker Bankroll Challenge: Stage 2 Stakes: $0.02/$0.04 Buy In: $3 (75 x BB) Starting Bankroll: $28 Target: $6 (2 x Buy In) Finishing Bankroll: $34 Estimated Sessions: 2 Use this exercise to continue to get used to the starting hand chart and knowing what position you are in, but also start thinking about each starting hand you play in terms of what category of hand it is and what you are.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 is52C5 = 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 1A K Q J 10K Q J 10 9Q J 10 9 8J 10 9 8 710 9 8 7 69 8 7 658 7 6 547 6 5 4 36 5 4 3 25 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.TABLE 2How Many Different Poker Starting Hands Are There BadHAND
N = NUMBER OF WAYS listed by McGerveyComputations and commentsProbability of HANDN/(2,598,960) and approximate odds.
Straight flush40
There are four suits (spades, hearts, diamond, clubs). Using TABLE 1,4(10) = 40.0.0000151 in 64,974
Four of a kind624
(13C1)(48C1) = 624.
Choose 1 of 13 denominations to get four cards and combine with 1 card from the remaining 48.0.000241 in 4,165
Full house3,744
(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.0.001441 in 694
Flush5,108
(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 = 5,108.0.0019651 in 509
Straight10,200
(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 = 10,200.0.003921 in 255
Three of a kind54,912
(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 = 54,912.0.02111 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.0.03251 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.0.0006091 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 | ForumHow Many Different Poker Starting Hands Are There Now
Previous Page | Print This PageHow Many Different Poker Starting Hands Are There People
Copyright © 2003-2009 Sanderson Smith
Register here: http://gg.gg/ozu6y
https://diarynote-jp.indered.space
コメント