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There are 20 unique 5-card hands.
Solution:
First break apart the player card combinations.
You can either use player card 1, player card 2, or both player cards 1 and 2 with the hand. Therefore, you are taking 5 cards, 3 at a time, when playing with both player cards, and 5 cards, 4 at a time, when playing with 1 player card.
Mathematically, this can be expressed using the Binomial coefficient
2 x ( 5 choose 4 ) + ( 5 choose 3 ) = Number of possible 5-card hands.
5 choose 4 = 5 : This represents the combinations between 1 player card and 5 table cards, 4 at a time. (http://www.wolframalpha.com/input/?i=5+choose+4)
5 choose 3 = 10 : This represents the combinations between 2 player cards, and 5 table cards, 3 at a time. (http://www.wolframalpha.com/input/?i=5+choose+3)
Thus, 2 x ( 5 ) + ( 10 ) = 20 .
Further Information:
All possible hand combinations are listed below.
A and B are the two player cards.
0 through 5 are the five table cards.
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A 1 2 3 4
A 2 3 4 5
A 3 4 5 1
A 4 5 1 2
A 5 1 2 3
B 1 2 3 4
B 2 3 4 5
B 3 4 5 1
B 4 5 1 2
B 5 1 2 3
A B 2 3 4
A B 3 4 5
A B 1 2 3
A B 4 5 1
A B 5 1 2
A B 4 5 2
A B 4 1 2
A B 5 1 3
A B 5 2 3
A B 1 3 5
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Does a flush plus pair or a fullhouse win?
You use your best five cards to make your poker hand. A full house (three of a kind + a pair) beats a flush (five non-sequential cards of the same suit). - Bdx
Odds of four aces in a hand?
Assuming 5 cards are drawn, the probability is 1.84689 * 10-5. The odds are 1 time in 54145 times. This can be expressed as a decimal, 0.0000184689 or as a percentage, 0.00184689% . Also, I checked these numbers against Wikipedia poker probability. They give the probability of 0.0240%, but this is for any four of a kind. For the ace four of a kind, we have to divide by 13, and get 0.001846%. The difference of 0.00000089% is due to roundoff. Explanation: There are 52 cards in a deck. A draw of 5 cards means the number of combinations is: 52!/(5! x 47!) = 2598960 different hands (order of cards doesn't make a difference) Four of a kind = only one combination can form a four of a kind, but since we have 5 cards, one card is anything but an ace (one of 48 cards). So there are 48 combinations that form a 4 of a kind. 48/ 2598960 = 1.84689 * 10-5 I used excel in solving this. The combinations can easily be solved by +fact(52)/(fact(47)*fact(5)) Of course, in poker you can exchange cards which I have not included in the calculations.
Does three aces and two eights beat 4 eights?
If you are referring to Poker, the first thing to consider is not the specific cards, but the special combinations they make. For example, two pairs beats one pair - no matter what cards the pairs are made of. Or in this case, 4 of a kind beats full house (3 + 2), no matter what cards. Only if two or more players have the same combinations will the highest cards in each combination be compared.
How many cards are needed for a 20 story house of cards?
The amount of cards needed to make a 20 story house of cards will vary depending on how big the diameter is. Hundreds of cards are probably needed.
How do you make a s out of six lines?
by hands
Is it possible for poker to be a board game?
No, poker can not possibly be made into a board game unless you changed almost every rule, such as not using cards, or having pairs, straights, flushes and so on. It would be a whole new game. ___________ There are solitaire games that use poker rules for hands, where you lay your cards out on a flat surface as they come and then total each row and column to see what the best poker hands are. You could make that game into a board game fairly easily.
What is a poker run?
A poker run is when you have to go to different places to collect cards to make your hand. It is not played in a casino, it is mostly played by motorcycle clubs, snowmobilers, and off-road vehicle enthusiasts.
Why is poker hand 2 5 the worst hand in Texas poker?
Actually, 2 7 unsuited is called the worst starting hand, or hole cards in Texas Holdem poker because it is the two lowest ranking cards that cannot make a straight or flush using both cards.
Why are bridge cards narrower than poker cards?
Each player receives 13 cards at the beginning of a bridge hand, so bridge cards are narrow to make it easier for a player to hold the cards in their hand.
Is Chinese poker the same as poker?
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What are those things called you put on your bike that make noise when you were a kid?
poker cards and clothes pins
How many different relationships does Hallmark make cards for?
they make cards for 40 different relationships
Can you have three pair in Texan Hold'em?
No, there is no three pair in poker. You can only use five cards to make your hand, three pair would require six cards.
What does river mean in poker?
The last card to be flipped in poker. Community cards (which everyone share) consists of 5 cards (in most poker games) The first three are called the flop, followed by the turn (or fourth street) and finally the river (or fifth street).
How do you lean on a small stacked poker player?
Constantly raise when he's in hands. Force him to make the choice of all-in/fold. Make him fold his blinds, etc.
What does the joker stand for in Pai-Gow Poker?
The traditional Asian game of Pai Gow is played with tiles that look like dominoes. To make it easier to understand an American version was introduced using standard playing cards and the ranking of hands were fashioned after poker hands.The joker can be used as an ace or a wild card to complete a straight, a flush or straight flush only.Please note that this rule can vary. House rules often apply in these kinds of poker games.
How many possible hands are there for only getting 4 cards that make a straight?
2,560
