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Hardest math question ever?

If you go here:

http://en.wikipedia.org/wiki/Poker_probability

And scroll down about a fourth way and you will see this:

"Flush — The flush contains any five of the thirteen ranks, all of which belong to one of the four suits, minus the 40 straight flushes. Thus, the total number of flushes is:
(image of formula)"

On the formula I need to replace the variables 13 with 15, the number 4 with 3, & the 40 with 36 ....and get the new answer.

Okay a little details of they 'why' I need this: I'm creating a card game with 16 levels of cards and 3 suits (verses 13 levels of cards and 4 suits in a standard poker deck)
I've calculated all other formulas needed but I can't seem to understand how they got 5108 for their answer.

If someone out there can help me then I will never doubt yahoo answers ever again! :)

ok,

probability of flush in normal poker is:
5108/2598960 = .00197 chance

the 5108 is the number of ways you can get a flush. This is the number of combinations.

In your game:

(16 nCr 5)*(3 nCr 1) - (12 nCr 1)*(3 nCr 1)
=13068

total of 1712304 different hands:

13068/1712304
=0.0076318224
=0.763%

How To Play Poker - Learn In 8 Steps

1. Become familiar with poker hand rankings. The person who wins is the person with the highest-valued hand. You can't win if you don't know which hands will take the pot. If two players have hands with the same value (e.g. two full houses) or no one has a winning hand, then the player with the highest value card in their hand wins (Ace is highest). Print out a ranking of the poker hands and memorize the hands.

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2. Chip in. Place an "ante" (pronounced ant-ee) or "token bet" (pronounced token bet) into the pot (usually a spot at the center of the table, although you can use a pot if you wish). Every player places an equal amount of whatever your currency (poker chips, nickels, bills, car keys...). Whoever wins takes it all.

3. Deal or be dealt with. After shuffling (showing off) the dealer distributes the cards face down starting with the player to his or her immediate left and continuing clockwise, one card at a time, until everyone has five cards. The deck is placed in the middle of the table.

4. Look at your cards while everyone else looks at theirs. This is the time to evaluate how strong your hand is. Beginner players usually end up showing how strong their hand is with what is known as a tell. Some tells include; shallow breathing, lack of or too much eye contact, facial muscle flexes, etc. Trying to reduce these tells will give you a better chance. Keep your "poker face".

5. Take turns. The first person to make a call is usually the player on the dealer's left (who was dealt the first card). That player can open (place the first bet) or check (pass the decision onto the next player). Once the pot is opened, meaning that a player bets a certain amount (e.g. places a nickel in the pot), all of the people who already has their turns have two options:

a) See or call - Stay in the game by putting the equivalent amount in the pot.

b) Fold - Quit the game by putting your cards face down on the table; whatever you put in the pot stays in the pot.

After they've made their choices, everyone who still has a turn will have those options, plus an additional one:

Raise - Stay in the game by putting more than the last person put in the pot.

If someone raises, then everyone who already had a turn must see or fold again. Then the next person has their turn.

6. Draw. Once everyone has had a turn (even if everyone checked) get rid of up to three cards you don't want and have them replaced. This is done in turns, again beginning with the player on the dealer's left and going clockwise. Choose the cards that you don't think will help you gain a winning hand. You might get rid of three cards, or you might keep them all. If you do get rid of cards, put them face down on the table so no one sees what you had.

7. Go through another around of betting. As before, the first player can either open or check, and the checking can continue until someone opens, after which players can see, raise or fold. More people will start to fold once they realize their weak hand isn't worth the bet.

8. Expose your cards. Everyone turns their cards over to see who has the winning hand. Winner takes all.

Roulette Beginner's Guide here

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