In Texas Hold'em, there are a total of 2,598,960 different five card poker hands. This includes the four royal flushes (Diamonds, Spades, Clubs and Hearts). So - the odds of hitting a royal flush would be 4/2,598,960, which would work out to 1/649,740. So, you should hit a royal flush every 650,000 hands that you play or so.

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Texas Hold'em Odds Of Hitting A Flush

Introduction

Texas Hold'em Odds 'Outs' are unseen cards that will make any hand you expect will win the pot if they come off on the turn or river. There are 47 unseen cards on the flop. To determine your odds of making your hand, you divide your number of outs by the remaining unseen cards (that will not help your hand). An outside straight draw has 8 outs.
This week's What are the Odds?article #6 looks at the odds of being dealt a Royal Flush poker hand in comparison to winning a lottery at Lottoland. Everyone knows that a Royal Flush is the best possible hand that a player can be dealt in poker, getting a straight flush.
This leaves 9 cards of your suit, and 38 of a different suit; your odds of completing your flush on the turn are thus 9/47, or 19.14%. If the turn hasn't completed your flush, your odds of completing it on the river are 9/46, or 19.5%.

Rules

A single 52-card deck is used. All cards count as its poker value. Aces may be high or low.
One player is designated as the dealer, usually with a laminated marker. This person does not have to physically deal the game. However it is important that a symbolic dealer position rotate around the table.
The player to the dealer's left must make a 'small blind' bet. The player to the left of the small blind must make a 'big blind' bet. The amounts of both blinds should be specified in advance. The purpose of the blinds is to get the ball rolling with some money in the pot.
Two cards shall be dealt down to each player, starting with the person to the dealer's left.
The player to the left of the big blind must either call or raise the big blind bet. The play in turn will go around the table according to normal poker rules, which I assume the reader already knows. Table rules will specify any limits on the size or number of allowed raises.
The small blind may also raise the big blind. If nobody raises the big blind the player making the big blind has the option to raise his own bet. The term for this is the 'big blind option.'
Three community cards will be dealt face up in the center of the table. This is called the 'flop.'
Another round of betting will ensue, starting with the player to the dealer's left.
A fourth community card will be dealt face up in the center of the table. This card is called the 'turn.'
Another round of betting will ensue, starting with the player to the dealer's left. Generally the minimum bet is double the first two rounds of betting.
A fifth and final community card will be dealt face up in the center of the table. This card is called the 'river.'
Another round of betting will ensue, starting with the player to the dealer's left. The minimum bet is generally the same as the previous round.
Each player still in the game at the end will determine the highest poker value among his own two cards and the five community cards. It is NOT a requirement that the player use both of his own cards. The player with the hand of highest poker value shall win. Following are the hand rankings.
1. Straight flush: Five consecutive and suited cards. For example 5, 6, 7, 8, 9.
2. Four of a kind: Four cards of the same rank, plus any fifth card. For example Q, Q, Q, Q ,4.
3. Full house: Three of a kind and a pair. For example 6, 6, 6, J , J.
4. Flush: Any five cards of the same suit, except for a higher ranking straight flush. For example A, Q, 8, 4 , 3.
5. Straight: Five consecutive cards, except for a higher ranking straight flush. For example 8, 9, 10, J, Q.
6. Three of a kind: Three cards of the same rank, plus any other two cards. For example 5, 5, 5, Q ,2 .
7. Two pair: Two pairs, plus any fifth card. For example 8, 8, 2, 2 ,Q .
8. Pair: A pair and any other three cards. For example 7, 7, 2, 5 ,A .
9. ? High: Any five cards that do not form any higher poker hand. A king high hand for example might be K, Q, 7, 5 ,4 .
If two or more players have poker values of the same rank then the individual cards will be used to break the tie. If necessary all five cards will be considered.
I get asked a lot whether the two unused cards in a player's hand are used to break a tie. The answer is a firm NO. The two unused cards do not matter.
If a new player arrives at the table he should either wait for the big blind position or put up an amount equal to the big blind, amounting to a call of the big blind.
If a bet is made after another player runs out of money, then a separate pot is created. The player that ran out of money is not eligible to win the second pot. If more than one player runs out of money then multiple separate pots can be created.
In formal games players may not bet with cash or buy chips with cash in the middle of a hand.
There are numerous rules of etiquette, which I won't get into.
There house may set the betting rules. There are three main types. A 'structured' game features raises of specified amounts. For example a '3/6 game' would mean that raises after the deal and flop are $3, and after the turn and river are $6. There is usually a limit to the number of raises a player may make, typically three. A 'pot limit' game has structured minimum raises but the maximum raise may be anything up to the amount in the pot at the time the raise is made. A 'no limit' game also has structured minimum raises but there is no maximum raise.

Examples

Example 1

Board: A, 2, 4, 5, 6
Player 1: J, 6
Player 2: 7, Q 3d sphinx slot machine.

Player 1 wins. Both have an ace high flush, so the second highest card is considered. Player 1's jack beats player 2's 7. The only way to have a flush tie is if the flush is entirely on the board and no hole cards are higher than the lowest card on the board in the same suit.

Example 2

Board: J, A, 7, 5, 6
Player 1: 2, J
Player 2: 10, J

Player 2 wins. Both have a pair of jacks so the singletons are considered. High highet singleton in both hands is an ace so the second highest singleton is considered. Player 1's second highest singleton is a 7, compared to player 2's 10. A 10 beats a 7 so player 2 wins.

Example 3

Board: A, A, K, Q, J
Player 1: Q, J
Player 2: Q, 2

Tie. Both have a two pair of aces and queens, with a king singleton. Some people incorrectly believe that in such cases the unused cards are considered, in this case player 1's pair of jacks beating player 2's jack/2. Only the top five cards matter. The jacks and deuce are irrelevant.

One of the most important aspects of Texas Hold'em is the value of each two-card hand before the flop. The decision of how to play your first two cards is something you face every hand, and the value of your first two cards is highly correlated to your probability of winning.

The following table shows my power rating for each initial 2-card hand in a 10-player game. The numbers are on a 0 to 40 scale. Basically, you should only play hands that are dark green, blue, or purple. Of course you should be more be more liberal in late position and picky in early position. If forced I would say you should need 10 points in late position and 19 points in early position to call the big blind. If your table is loose, as if often the case online, you can play a bit lo

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