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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.
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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?
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How do you make a s out of six lines?
by hands
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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?
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Why is poker hand 2 5 the worst hand in Texas poker?
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Why are bridge cards narrower than poker cards?
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What are those things called you put on your bike that make noise when you were a kid?
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Is Chinese poker the same as poker?
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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?
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