Poker hands & online poker hands :) : poker research with tips & hints - Part 2 of 2

Other poker hands

Since I'm such a nice guy, I'll let you figure out how I came up with these numbers (see the previous long post).
Straight: 5 cards in a row. The suits don't matter.
Number of card combinations: 9.
Number of suit combinations: 1,024
Total: 9,216Probability: 0.35%
Note: Some argue that the number combinations are actually 10 since the ace can be either low or high. I would argue that it must be one or the other (can't have it both ways).

Flush: 5 cards from the same suit. The cards don't matter.
Number of card combinations: 1,287
Number of suit combinations: 4
Total: 5148
Probability: 0.2%
Note: Some argue that the total should subtract 36 from the total of 5148 since they consider the straight flush a completely different hand than the flush.

Straight flush: 5 cards in a row from the same suit.
Number of card combinations: 9
Number of suit combinations: 4
Total: 36
Probability: you figure it out

And now! The most popular hand in all of spaghetti western movie history!
Royal flush: The 10, jack, queen, king and ace from the same suit.
Number of card combinations: 1
Number of suit combinations: 4
Total: 4
Probability: is it in the real world or Hollywood?

Well done.
Having got through all these thrilling estimates, just do not tell me that you won't win an online poker tournament!
Get a Feeling of Poker with us and be happy!

Yours etc.,
Alex Cup

Poker hands, online poker hands: poker research with tips and hints

Poker hands: basics
Poker is a game played with a standard 52 playing card deck. There are 4 suits: spades, clubs, diamonds and hearts. Each suit has the same 13 cards. There are 9 numbered cards: 2 through 10, and 4 face cards: jack, queen, king and ace.
Each poker player is dealt 5 cards from the deck. The object is to get a 5- card combination (known as a poker hand) that is more valuable than everyone else's. The harder it is to get a particular poker hand, the more valuable it is.
Here are the poker hands in order from least importance to most:

• none the same;
• pair;
• two pair;
• three of a kind;
• full house;
• four of a kind.

Poker hands: what and how we research

What we are actually doing in this fun exercise is figure out the different ways of getting these hands.
For starters, the total number of poker hands is { 52; 5} = 2,598,960. Well, poker is generous enough...
The method I will use to figure out the number of ways of getting the above hands I call the choose/choose method.
I call it that because what I will do first is choose from the 13 cards (also known as faces) common to each suit, and then choose the suit for each group of cards that have the same face. The method for choosing is exactly the same as the elevator problem.

Studying major poker hands

None the same: First we choose 5 faces from the 13. We have {13; 5} = 1,258 choices there. Then, for each face, we have 4 suits to choose 1 suit from. So, the number of suit choices is 4x4x4x4x4 = 1,024. The total number of hands where none of the cards match is 1,287 x 1,024 = 1,317,888. The probability of getting this hand is 50.7%.
Pair: First we choose the face for the pair. There are 13 choices for that. Now we have 12 faces from which to choose the remaining 3 which works out to be {12; 3} = 220 combinations. So, the total number of face choices for this case is 13 x 220 = 2,860.In choosing the suits, for the pair we have {4; 2} = 6 choices and for the rest of the cards, once again we have 4. So, the number of suit choices in this case is 6x4x4x4 = 384. Ergo, (there's some Latin for you) the total number of hands with one pair is 2,860 x 384 = 1,098,240. The probability of getting this hand is 42.3%.THAT MEANS THE TOTAL PROBABILITY OF GETTING AT BEST A PAIR IS A WHOPPING 93%!!! Makes you wonder how people won at poker in those old spaghetti western movies, doesn't it?
Two pair: We have to choose 2 faces, one for each pair. We have {13; 2} = 78 choices there. Then, we have 11 faces left to choose from for the last card. So, the number of face choices for this case is 78 x 11 = 858As far as the suit choices go, just like the last case, we have 6 choices for the first pair, 6 for the second pair, and 4 for the single card. The number of suit choices is 6x6x4 = 144. The total number of hands with two pair is 858 x 144 = 123,552. The probability of getting this hand is 4.8%
Three of a kind: The smarter ones among you should be able to do this one in your sleep:{13; 1} = 13 choices for the 3 cards that are the same{12; 2} = 66 choices for the other 2 cardsSo there are 13 x 66 = 858 card choices in this case.To choose the suits, we have for the 3 of kind cards and 4 choices for each of the other 2 cards. The total number of suit choices is 4x4x4 = 64. So, the total number of hands for this case is 858 x 64 = 54,912. The probability of getting this hand is 2.1%
Full house: Do you think point form will do?{13; 1} = 13 choices for the 3 cards that are the same{12; 1} = 12 choices for the 2 cards that are the sameTotal number of card choices: 13 x 12 = 156{4; 3} = 4 suit choices for the 3 of a kind cards{4; 2} = 6 choices for the 2 of a kind cardsTotal number of suit choices: 4 x 6 = 24.Total number of hands that are a full house: 156 x 24 = 3,744.Probability of getting this hand for real: 0.144%.Probability of getting this hand in a spaghetti western: happens all the time.
Four of a kind: Deja vu, anyone?{13; 1} = 13 choices for the 4 cards that are the same{12; 1} = 12 choices for the 1 card left.Total number of card choices: 13 x 12 = 156{4; 4} = 1 suit choices for the 4 of a kind cards{4; 1} = 4 choices for the last card.Total number of suit choices: 4Total number of hands that have 4 of a kind: 156 x 4 = 624Probability of getting this hand for real: 0.024%Believe it or not, this is not the most popular hand in gambling movies. More on this later.Anyway, if you add all these numbers up, they add up to 2,598,960.

Interested? To be followed...

Alex Cup.