Odds for a royal flush. In a standard 5-card poker hand for 1 deck: Calculate P(Flush) Flush Hands Calculate Total 5 Card hands Choose 5 cards from 52 cards. Odds for a royal flush

 
 In a standard 5-card poker hand for 1 deck: Calculate P(Flush) Flush Hands Calculate Total 5 Card hands Choose 5 cards from 52 cardsOdds for a royal flush The chances of a royal flush and quad aces in the same hand: 1 in 2,700,000,000

The Royal Flush is a five card hand having all in the same suit with the following card values: an Ace a King a Queen a Jack, and a 10 The number of Royal Flushes is exactly four, since there are one in each. Bottom line: In stud poker, the probability of an ordinary flush is 0. 000154% in the Pre-Flop round. thatguy6793 Legend. Note that you would break up a flush, a straight, or a high pair when you're missing only one card in a royal flush. 0032%. 0000) 3 of a kind (4. You can pick either player and then permute them to get the same result. But notice I said "average," meaning you could hit more than one royal or even no royals. Overall the straight flush only contributes 0. 00001539 = 1 in 64,974. 96. That means we don't talk about the odds here. 000002%. For simplicity’s sake, we’ll call that 2%. The following table shows the return table based on a breakeven meter of 20536. 000154% chance of making a royal flush. 000022: 45,836. The royal flush is a case of the straight flush. Usually, when you are drawing cards, you want to know your odds you need to use something called hypergeometric distribution, i. 4- heart 3- heart 2- heart a is a straight flush, but its top card is the five, not the ace. So, if you’re looking to hit this elusive hand, your best bet is to play often and hope for the best!Odds of you specifically losing with a straight flush to a royal flush are 77260583400:1, but the AK vs 98 situation is only 1 of 8 SF over SF situations so the odds drop to 9657572925:1. So we need to divvy up one of the 40 possible straight flushes so that 2 of the 5 cards get dealt to player and the other 3 appear on the board. 000154% Straight Flush 36 0. A royal flush is the best hand in poker, consisting of a 10, jack, queen, king, and. Yes. 001% = 1 / 108,290 royal flop in Omaha . 000031: Straight flush: J-7: 4,140: 0. Royal hole card draw chance = 8% (higher than I thought it would be) Now need exactly one board to make the royal on the flop combin(48,3) = 17,296 Flop a royal = 0. Many people have misconceptions about odds as TV presenters love to. 01%), and one-way straight flush hands (0. The top win is for a royal flush using at least one hole card, which I call a "hidden royal flush. As mentioned in the OP, this is a job for the Principle of Inclusion/Exclusion (although the probability of more than one royal flush is small). 0032%. What is the probability of being dealt a royal flush? A royal flush (which is what you would want to be dealt!) is a ten, jack, queen, king and ace, all of the same suit. The order of the deal does not matter. This is a ratio, not a fraction. In essence, the chance of being dealt a Royal Flush in a standard 5-card poker game is infrequent, making it one of the most coveted and exciting moments in poker. Jacks or Better – you will hit on average every 40 390 hands. Expressed in odds form, the odds of being dealt a Royal Flush in Video Poker are 649,739-to-1 among most US online casinos. With this five-card hand, all the cards must be of the same suit, which is why the probability of earning a royal flush is so low. So, ÷1081 for each of the two hands, = 1 in 3,594,493,636. Statistics and Probability; Statistics and Probability questions and answers; What is the denominator of the reduced fraction representing the probability of being dealt a royal flush in five-card, no-draw poker?Apparently the odds of flopping a flush draw are 10. If you draw five cards randomly from a 52-card deck, the probability of making a royal flush is 0. 4 May 2012. I did not check the probability of getting AKQJ10 of a suite, but I believe it is 4*4*4*4*4/52*51*50*49*48 = 1,081901057093 * 10^ (-4), so the probability is close to 1 in 163 million. The odds of the deck the be stacked in the perfect way according to how many players there are to give you the royal flush on the flop seem to be. Every poker player strives to be. The odds of hitting a royal flush will change also depending on the hands that you are initially dealt. If you play live holdem at 40 hands per hour, you'll get 1 on average for every 1000 hours of play. well, im not an expert in probability or statistics but if the odds of getting a royal flush in a 7-cards game like Texas holdem (where you make the best 5-card hand. The Play bet may be up to three times. The world's most trusted Seven Card Stud poker odds calculator. 000154% (649,739-to-1. Therefore, the probability of being dealt a straight flush (P. The best hand (because of the low probability that it will occur) is the royal flush, which consists of 10, J, Q, K, A of the same suit. Say a hand has "Property i i " if it includes a royal flush of suit i i, for i = 1. Here's the poker hand rankings in the order of best to worst: Royal flush - Where A, K, Q, J, 10 are of the same suit. If a royal flush pays in both directions (10-J-Q-K-A and A-K-Q-J-10) it is known as a reversible royal. 000,015,39 (40/2,598,960) Use the table below to calculate the probabilities of all poker. To fill the royal flush, you only have 1 card out of 47 which can fill your hand. 41% ending in bust. That's less than a 0. Deuces Royal Flush — Same as the Royal Flush, but with one card being a deuce; Four Deuces — Four deuces; Natural Royal Flush — a 10, Jack, Queen, King, and Ace of the same suit; Deuces Wild Odds. 6 So the event that you will have pocket aces that will turn to quads and lose will happen 1 in (221 122. We present the probabilities for a 5 card deal here, and then concentrate on how to calculate these numbers. Probability Odds Against; Royal Flush: 4,324: 0. If one of these three cards is an ace, two other cards must match that ace. While there is no one definitive answer, estimates suggest that the odds of hitting a royal flush in a card gamr range from 1 in 649,740 to 1 in 2. There are many different odds and combinations that you can make with a royal. Everyone knows that the odds are always in the house’s favor when it comes to gambling. The odds of landing a Straight-Flush on the Flop alone are 1 in 72,193 (excluding a Royal Flush); AND THEN, Villain (enforser) also had the Nut Flush! The chances of both of the above happening in this same hand are a staggeringly unlikely 1 in 5,574,332, or 0. The expected value will be calculated of each, and the player is given the best one as his hand on the deal. 1 / 40,000. Translated into percentages, there is a 0. That calculation equates to an 0. 01E-12 (very weak) So the probability for player winning with royal flush should be near 4/ 2,598,960 because the coincidence is weak: 1. Hold any combination of four cards to a straight flush. A royal flush is the best possible straight flush - Ace, King, Queen, Jack, and Ten of the same suit - e. 00000153907 = 0. 5 to 1 for a straight. Looking to win at poker, not sure how to choose or hire a poker coach? Read our complete guide on how to find and evaluate the best poker training site and poker coaching that best suits you. Poker Tools; Hold'em. A typical flush might be the king, jack, eight, five, and three of hearts. Fortunately, there’s a basic strategy to diminish the learning curve dramatically. For comparison, the odds of getting a royal flush are 0. When you play a basic video poker game with 52 cards, the odds of getting a Royal Flush during the initial draw are 1 in 649,740. That calculation equates to an 0. Criss Cross Poker tutorial with rules, pay table, strategy, combinations, and odds of wins and returns with full expected value table. Poker 4 aces vs royal flush, is sports gambling real, casino sharm sheikh,. 88%, with that rate dropping. There are separate line items for a six-card royal flush and six-card royal flush in diamonds. We just discussed how players can receive certain parts of a royal flush and improve their opportunities of getting video poker's best hand. In a 52-card deck there are only 4 possible royal flush combinations and they are all ranked equally. For more on odds, including the probability of winning any given hand on the. net. These statistics also vary between video poker types and depend on some other factors that we’ll get into below. I am completely unfamiliar with poker, and just learning the principles of probability. These Are the Odds of Getting a Royal Flush in Video Poker. As in a regular straight, you can have an ace either high (A-K-Q-J-T) or low (5-4-3-2-1). ShinjukuAce • 8 yr. There are 4 of them, one for each of the four suits. " Taking this to be your intention, i. Again, assuming the deck is. You can assume that all hands are valid (no invalid characters or repeated cards), each player's. 00024 Full House 3744 0. 0213 or Odds of catching the gutshot Royal Flush on the river 1/46 = 0. Let's do this two ways. The royal flush is the strongest hand you can get in poker. The probability is. 2. 961472. 36. In this game, players are dealt 7 cards throughout the. The following pay table can be found at Internet casinos using Gtech software. For example, an ace, king, queen, jack and 10 of hearts. Royal Flush. Your chances of a royal flush on the deal are 1 in 649,740. In a. The top win is for a royal flush using at least one hole card, which I call a "hidden royal flush. The odds of winning the Mega Millions jackpot is 1 in 302. 00016927: Five Aces: 140,000-1: 0. Likewise, a two card Royal Flush with no Ace or ten may initially seem less valuable than some of the hands listed beneath it. As the game goes on the chances increase with each new card dealt on the table. 0. The odds of being dealt a Royal Flush on the flop in a random 5-card hand are 1 in 649,740. James King on 06/12/2023 Discover the precise analysis of the odds of achieving a Royal Flush in Texas Hold'em poker. We need only seek the probability for obtaining 2 of 13 cards in 1 from 4 suits, when selecting 2 from 52 cards. In any event, don’t expect to be dealt a royal flush in your poker career. Paul Phua says that to start with, you will have to play 30,940 poker hands before you get dealt a Royal Flush. Royal Flush (five credit bet) 800. The odds of being dealt the Royal Flush on the flop is only the tip of the iceberg. 1). Design detection in this example is easy because the category royal flush was already defined (aka prespecified) by the rules of the game. Because players going all-in for a flush draw after the flop usually have near the nuts, this 3. Fact-3) Odds that you will lose to royal flush = 88/nchoosek(48,5)= 1/19458 Fact-4) Adding other 116 possible straight flushes, Odds that you lose = (88+116)/nchoosek(48,5) = 1/8393. What is a flush and what happens if two players have a royal flush? Who Wins If Two Players Have A Royal Flush In Poker? June 09, 2023. That's 2. A royal flush usually appears about once in every 40,000 hands when a player uses optimal strategy. In Cajun stud, a five-card player hand is revealed gradually. Of all possible hole cards combinations, 23. 03% of the time, the player wins 44. 0. The probability that one hand is a royal flush is 0. It can be formed 4 ways (one for each suit),. as a royal flush. Patience will reap rewards against overly-aggressive players. 34042552) 2 to a royal flush, queen highest 5 (0. That means we don't talk about the odds here. Full House - A full house is when you have three of a kind with a pair. 3. 7922%: 1:1 A "bug" is a card (typically a Joker) that can be used to fill a straight or flush, but is otherwise just an Ace. 144% Flush 5,108 0. 112%. The top prize is a royal flush, which pays out 250x. 00139% Four of a Kind 624 0. We now carry out the division and see that a royal flush is rare indeed. To find the odds, we divide the number of Royal Flush possibilities (4) by the number of poker hands (2,598,960). 003232% 30,939:1: Straight Flush: 37,260: Any paying hand (tens or better, three of a kind) Any three to a royal flush. 00000000025. The probability of filling the royal flush is about 2%. 0002%: 1:649,739: The board allows for a royal flush: 1. The fifth card is called the side card. For a traditional video poker game (9-6 Jacks or Better), you’ve got a 1 in 40,391 chance of hitting a royal. The condition for a straight is for your five cards to have adjacent ranks, such that no two cards have the same rank. That's equivalent to throwing a quarter and having land on heads about 50 times in a row. 0000153908. Find out about Odds in Pai Gow Poker. The odds against a royal flush, for example, are nearly 31,000-to-1, making it the rarest and strongest hand in poker. A royal flush is an exceptionally rare poker hand. This is the strongest possible hand in poker and can never be beaten. Naturally, a nine-high straight flush would beat a six-high straight flush, for example. Determining the Probability of Forming the Royal Flush. If your starting hand is suited, such as two spades or two diamonds, the probability of getting a flush on the flop is 0. Odds of Drawing to a Royal Flush in Video PokerThere are 4,234 ways to make a Royal Flush from any seven cards (1,081 ways in each suite; There are five essential cards that must be part of a Royal Flush: Ten, Jack, Queen, King, Ace. In a seven-card game like Omaha or Texas Hold’em, the odds of drawing a flush are much better. The return table below is based on a $5 bet, which equates to. A straight flush can be any five cards in order, such as A-2-3-4-5 or 3-4-5-6-7. In , when it comes to the battle between 5 of a kind and a royal flush, it’s all about probability. The odds of getting any royal flush in 5-card poker are 1 in 649,740. 1 Answer. It is made when we have the Ace-high straight while holding cards all of the same suit. 1. Play Instantly. 33% outcome means the pot odds calculation depends on how high your flush is. 39 x 10^-7 or close to 1 in 4. What Are The Odds of Flopping a Royal Flush? The odds of being dealt a royal flush under the conditions you stipulate are 1 in 649,740. (What they can do is change the payout. My local casino has a jackpot for hitting a royal flush on the flop in a cash game. We now carry out the division and see that a royal flush is rare indeed. 000154%. Getting a royal straight flush post-flop increases the. 000154%. The Royal Flush is a five card hand having all in the same suit with these card values: an Ace a King a Queen a Jack, and a 10 The number of Royal Flushes is exactly. The odds of flopping a royal flush plummet to a probability of 0. Poker-hand rankings: from strongest to weakest. Royal Flush. By Henry Tamburin. If you drew five random cards from a 52-card deck, you’d have an 0. Keep this in mind. 11 to 1 for a full house. Understand the rarity and value of this unbeatable hand,. In a standard 5-card poker hand for 1 deck: Calculate P(Flush) Flush Hands Calculate Total 5 Card hands Choose 5 cards from 52 cards. How about 6 players combined, assuming no one would ever fold two suited broadway cards? texas-hold-em. Full House, Four of a Kind, Straight Flush and Royal Flush. probability of the royal ush bonus occurring is n/64,974. com The royal flush is a case of the straight flush. royal flush is P (A)*P (B)*P (C) = 1. 1. We would like to show you a description here but the site won’t allow us. The chances of a royal flush and quad aces in the same hand: 1 in 2,700,000,000. Royal flush A, K, Q, J, 10, all the same suit. It follows the same pay table as the 6 Card Bonus above. That's a lot of zeros. Best of luck in and out of the casinos, John. Needless to say I lost the hand. And the odds of making a royal flush is 649,739 to 1. 00323% probability of hitting the other three cards and completing a royal flush by the river. Probability of a flush = Possible flushes :I want to calculate the chance of a straight flush. If you get 2 cards in the flop your odds improve to about 4% to get a Royal flush and reduce to 2% if you miss it on the turn. But since you can draw one time your odds increase. Each flush is ranked by its highest card, then by the rank of its second-highest card and so on. At three decision points along the way, the player may either raise his Ante bet by one to three times or fold. b) A straight-flush (excluding royal flush) is all cards the same suit and showing consecutive numbers (but not the highest 5 consecutive numbers). 005% chance of flopping a royal flush. 000154%. 000154% and odds of 649,739 : 1. Since the values. The odds of hitting a royal flush is roughly 1-in-40,000 hands. Royal Flush: A royal flush is the highest possible straight flush. 0032% and 30,939:1 chances of appearing. Players should be aware in Texas hold’em of the “nut. While 5 of a kind is a rare and impressive hand to have, it still falls short against the unbeatable royal flush. 33% chance of completing the flush on the turn and seeing another flush card on the river. The odds of hitting a sequential, left to right, royal is 1-in-120 Royals. Keep in Mind the Odds: However, it’s best to keep in mind that the odds of successfully completing these hands are incredibly low - a royal flush has less than 0. The Odds of Making a Straight Flush in Poker. The standard deviation, relative to the Ante. Here's the poker hand rankings in the order of best to worst: Royal flush - Where A, K, Q, J, 10 are of the same suit. There are only 4 ways of getting such a hand (because there are 4 suits), so the probability of being dealt a royal flush is `4/(2,598,960)=0. Poker Fast Facts. 3925%, and a high hand 50. Statistics and Probability; Statistics and Probability questions and answers; Five cards are selected from a 52-card deck for a poker hand. You can expect to hit a Full House a little over 2% of the time, but the payout is just 8 to 1. For Jacks-or-better, the royal flush cycle is 40,391 hands, whereas a full-pay Deuces Wild game it's. 0240% Full House 3,744 0. 1. Hand Payoff Combinations Probability Return; Natural royal flush: 800: 440202756: 0. Four of a kind. A♣K♣Q♣8♣2♣. e. $4^5 imes 9/inom{52}{13}$. 7/5. Getting your royal flush cards at the very beginning can give you incentive to go all-in or to double down on your bets. 0020 f) Royal Flush There are only 4. Getting dealt a royal flush not on the flop is less rare, but still makes the poker royal flush difficult to obtain. When we speak of odds in probability it has a very specific meaning. Four singletons. ) What Are the Odds?1 Answer Sorted by: 2 Wild cards are typically a "house rule" sort of thing. You can pick either player and then permute them to get the same result. But this. Both cars are fast and impressive, but the Ferrari. However, if we want to know the chance of flopping a. The reason for 239 is to keep the win under $1200, thus avoiding a W2-G form, for a. But not all flushes are created equal. Following is my intermediate strategy. 24%; When you hold four cards and throw away one, there is a good chance you will receive a. A royal flush is a combination of a straight and a flush, with the added stipulation of being a high straight. Moreover, the data on the odds of hitting a royal came from Dan Paymar’s book, Video Poker – Optimum Play (second edition) . The trouble is, the odds of getting that perfect poker hand is often a lot lower than you might think. An A-5 is a five-high straight flush, which is lower than an Ace-high straight flush. Unlike normal poker, a 3, 4 or 5 card straight/flush/straight flush can be played. This crossword clue might have a different answer every time it appears on a new New York Times Puzzle, please read all the answers until you find the one that solves your clue. The odds of winning the Mega Millions jackpot is 1 in 302. 100% (1 rating) (1) (i) "Royal Flush": All te 5 cards are of the same suit and are of the sequence: 10 - J - Q - K - A. The odds of hitting a royal flush are about 1 in 40,000. 1% chance to hit your flush on the turn. In a third version there is a separate pay for a suited blackjack as follows. Level Contributor . 93: 0. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. 00001540898529 The probability of a Royal Flush occurring is 0. 4 to an inside straight with 3-4 high cards: Go for the straight flush; 2 T J Q A — 2 to a royal flush (both high) vs. The next pay table is a short pay version of true 10/7 double bonus. What is the probability of the second player receiving a royal flush? c. 6) = 227. A royal flush is a rare, but not impossible, occurrence in poker. 2 million. From here, the odds of a royal flush are 649,739 : 1, the odds of four of a kind are 4,164 : 1. 1 Answer. Therefore, the chance of hitting the royal flush when you hold a four-card royal flush and draw one card, is 1 in 47. Royal Flush: The unbeatable hand – the hand all players dream of getting – a Royal Flush is the best possible hand in Texas Hold ‘Em poker, and cannot be beaten. Payouts in the Aces and Faces video poker start with a pair of jacks, while a royal flush is the game’s jackpot. The number of hands in a royal flush cycle varies slightly from game to game. Royal Flush - Ace, King, Queen, Jack, 10 all of the same suit Odds Royal Flush( ) ≈ ( ) 52,5 P Royal Flush C = ( ) 2,598,960 P Royal Flush = 4 ≈ 0. Some of these flushes have already been counted as higher ranked hands. This is of course correct if we calculate the probability of being dealt two cards to a royal flush and then flopping the three cards we need to complete the hand. All of a,b,c are 4/2598960=0. Today's NY Times Crossword, featured prominently on. 7184%: 1:36: Witnessing a royal flush over 2500 hands at a full ring table: 49. Then, to obtain a royal flush in, say, spades, you can choose any five cards from A, K, Q, J, 10 and the four wild cards. For example, here are a couple hands you shouldn't play because they are not listed. Four of a Kind - All the four cards are of the same rank. Royal Flush. This means you’ll pick up suited hole cards roughly once every four hands in Texas Hold’em. and there is absolutely no reason to ever lower your odds of winning when you can always consult the chart. The probability of no royal flush in one hand is: 1 − 1 649740 = 649739 649740 1 − 1 649740 = 649739 649740. 000000. In a 52-card deck, there are 5,108 possible Flush hand combinations and 1,277 distinct ranks of Flushes. The odds for getting a specific royal flush in 5-card poker would be 1 in. The bet amount is $1, nd there is no Envy Bonus. Now let us compute this conditional. Those odds are 20/52 * 4/51 or about 3%. the streets of Las Vegas did their best to remove him. 923825. But in the most common variations, the odds are known and players can use them in order to pick the best game or to make informed decisions. Probability of getting a flush (and so excluding straight and royal flushes) =5108/2598960~=. If all four cards in the players hand are the same suit, this is a called a flush and scores 4 points. The precise odds depend on game and playing strategy. In a standard 5-card poker hand for 1 deck: Calculate P(Flush) Flush Hands Calculate Total 5 Card hands Choose 5 cards from 52 cards. If the cards are dealt one at a time to each player in turn, what is the probability of the first player receiving a royal flush? I know that the probability of a royal flush is $dfrac{1}{649740}$, because of ${_{52}}C_5=2598960$, and $dfrac{4}{2598960} = dfrac{1. However, those three top hands all pay the same as a 5-card royal flush at 1000. A "bug" is. This means that the odds of hitting a royal flush with your initial five cards will differ from a royal flush after discarding 4, 3, 2 or 1 card. So for a given pocket. 3 to 1 for a 3 of a kind. Is it: chance to flop a royal flush (or any 5 exact cards) = 1/52 * 1/51 * 1/50 * 1/49 * 1/48 ? = 0. 00018469. A royal flush is defined as an ace-high straight flush. 045 units. Return rate. A royal flush consists of AKQJT of the same suit. e. So overall the probability of flopping a royal flush is (40/1326) * (1/19600) = 40 / 25,989,600 = 1 / 649,740. General Strategy. , 10♣J♣Q♣K♣A♣. There are 52c5 = 2,598,960 combinations of 5 cards, so the probability of flopping a royal flush is 4 / 2,598,960 = 1 / 649,740. g. 000510204 = 0. The chances of picking up a royal flush are 1 in 30,940 hands or 0. This hand is simply a straight flush kind of thing. They are ranked by high card, from Ace-High (AKQJT) down to five-high (5432A). 001980792317 - 0. But what are the odds of that happening, and when can you expect it? Typically, your odds of hitting a five-card royal flush is 1 in 649 740, but the chances of a four-card flush are once in every 2777 hands. Question 4: What is the probability of being dealt a royal flush from the first 5 cards in a deck? The number of al possible 5-card hand is ({52choose 5} = 2,598,960) A royal flush is ace, king, queen,. Instant Win ALL IN Prize Structure. For an ace high straight flush (a royal flush), the wild card can be any of the five cards: A,K,Q,J,T and there are four suits, so there are 20 ways this can happen. Compare this to the overall probability of the royal being 1 in 30,940. 91%. It is the best hand in most forms of poker (also the rarest), including Texas Hold'em. Search for crossword clues found in the Daily Celebrity, NY Times, Daily Mirror, Telegraph and major publications. After the player makes a bet, the dealer will deal the player and himself seven cards each. So knowing nothing about your holding, the probability of receiving 2 cards that can participate in a royal flush and then having the flop be the other 3 royal flush cards is 4/2598960, or 1/649740. 547%. Two to a royal flush, ace high, with no deuces. ABC poker will work against bad players. 6 million, according to the Mega Millions site. These numbers are ON AVERAGE and vary based on the game you play, but are good benchmarks with which to set your expectations as you play: Jackpot Frequencies. Always go for the Royal: If you have a good chance of making a royal flush, always go for it, as the Jacks or Better poker strategy instructs. Except the sub is called "Never tell me the odds. Of the remaining 47 cards, any two others can be selected, so the frequency of all Royal Flushes is 4 C 1 × 47 C 2 = 4,324). some casinos will pay less than 4,000 coins for a royal flush. 011%. The minimum bet is $5. 🔥 The royal flush is undoubtedly one of the most desirable poker hands in a game of poker. Thus, the math is the same. $egingroup$ Agreed. 33851373) 2 to a royal flush, king highest, no penaltycards 6 (0. Any paying hand (tens or better, three of a kind) Any three to a royal flush. 906%. A casino that deals 10-handed hold’em games expects to have to pay the royal ush bonus about once every 6,500 hands. So 32 different seven-card straight flushes are possible. In 9-6 Jacks or Better, your royal chances are about 1 in 40,391, while in 9-6 Double Double Bonus Poker they're 1 in 40,799 and in 9-7-5. 01E-12 = 1. However, this number depends on the number of Players sitting at the table. 555%. Odds. The odds against making a royal flush are 649,739-to-1. During my first (around) 1000 hands I got 2 royal flushes and 2 straight flushes which then led me to believe they were pretty common. 00000153907 which is computed as 4 possible royal flush hands divided by 52C5 total cases as you pointed out. This excludes the royal flush and straight flush. So the probability of being dealt a Royal flush is 4 in 2,598,960 - or 1 in 649,740. Poker Hand Number of Ways to Get This Probability of This Hand Royal Flush 4 0. There are 2,598,960 unique poker hands. Show Probability [P( ext{Royal Flush Hand})=frac{1}{649740}approx 0. You have your odds wrong, 649 740 is the odds of getting a royal flush on the flop (or being dealt a royal flush in 5 card stud).