What are the odds of a royal flush. It is important to understand that these odds represent an overall probability and not an individual event, as poker is a game of chance and each hand is distinct. What are the odds of a royal flush

 
 It is important to understand that these odds represent an overall probability and not an individual event, as poker is a game of chance and each hand is distinctWhat are the odds of a royal flush  The other ten cards are placed back in the deck

3025) Dealt straight (4. What are the odds of getting a royal flush? Hitting a royal flush is even harder than a straight flush. You just need to have two hole cards that can make a royal, i. 00015% of being dealt or forming a Royal Flush hand. The lower right cell shows a house edge of 2. # straight flushes = 9 4C1 = 9·4 = 36 Subtracting the number of royal flushes and dividing by the number of possible hands gives the probability: € P(straight. 000154%. It just so happens that we also refer to an ace-high straight flush as a royal flush. Drawing to a Royal. butlercups. 1 Answer. 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. 41% ending in bust. 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. In summary, the conversation discusses the statistical chances. e. Here's the answer for "Like the odds of getting dealt a royal flush Crossword Clue", The SLIM is the answer for Like the odds of getting dealt a royal flush NYT Crossword Clue. How about 6 players combined, assuming no one would ever fold two suited broadway cards? texas-hold-em. 04754A royal flush consists of an ace, king, queen, jack, and 10 all in the same suit. Flush. 39 x 10^-7 or close to 1 in 4. This leads. If. What is the probability that she is never dealt a royal straight flush dealt? b. Let’s compare that to the odds of making other hands in the poker hand rankings: Royal Flush – 0. Algorithm is 100% random can guarantee you. Search for crossword clues found in the Daily Celebrity, NY Times, Daily Mirror, Telegraph and major publications. The exact odds of hitting a royal flush in video poker depend on the game. 0002%. so 1:1,000,000 hands (roughly). This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. A royal flush is actually a type of straight-flush, but it beats all. A royal flush is an exceptionally rare poker hand. The Probability of a Royal Flush (fraction) constant defines the probability of drawing a Royal Flush and represent the probability as a fraction. The Odds of getting royal flush. This means that there are 5148 – 40 = 5108 flushes that are not of a higher rank. 00002 Four-of-a-Kind 624 0. It is important to understand that these odds represent an overall probability and not an individual event, as poker is a game of chance and each hand is distinct. Your chances of hitting it are 0. . As the game goes on the chances increase with each new card dealt on the table. We must make sure not to double count these hands. 9USD: 2: free texas holdem headsup: 84482: 927516318: free texas holdem headsup: $12. Here is the information the is needed The probability of a Straight Flush occurring is 0. Royal flush: 6,000-1: 0. 00164604 = 0. Five-Card Stud (Natural) Probabilities Hand Number Probability Straight Flush 2 40 0. If the player makes a max coin bet of 10 coins per line, then he will activate the Ultimate X feature. 003232% chances for. The general odds of making a Royal Flush with all 7 cards in play (2 hole cards and 5 community cards) are approximately 1 in 30,940 in a game of Texas Hold. 4% * 17. How to Maximise a Royal Flush Hand. The odds of being dealt the Royal Flush on the flop is only the tip of the iceberg. For example if the player had 3 to a royal and 4 to a flush the correct play is to keep three to the royal, discarding the fourth suited card. It means that you will have 0. Three suited cards in a row except 2-3-4, and ace-2-3. As mentioned earlier, this interprets to a 0. The royal flush odds you learned from Hold’Em work pretty much the same way in Omaha and Omaha Hi-Lo. A royal flush is the hardest hand to make in standard real money Texas Hold’em games. 999908^9 = 0. The highest paying hand is Royal Flush, which is a combination of a Ten, a Jack, a Queen, a King, and an Ace of the same suit. 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 four, since there are one in each suit in a standard deck. I saw the All 6 side bet at The Point casino in Washington on July 21, 2023. 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 out of 7 total cards) is 1:30,000 (roughly). Quad aces + royal flush. So many comments for the real odds, Idk what is correct. 0000000060747, or about 1 in 165 million. ago. A royal flush is actually the best possible version of a straight flush. So the highest ranking straight flush consists of a nine, ten, jack, queen and king of the same suit. It takes about 100 hours of single-hand video poker to play 40,000 hands, or about 25 hours if you're playing four-handed. 00003232 Other straight flush 37,260 0. If the board were, say, a K-high straight flush, a player with the ace in his hand would win with a royal. Odds of making a Flush. So really, this is the same as asking the probability of a Royal Flush when you are dealt five cards from a deck of fifty-two. We would like to show you a description here but the site won’t allow us. Does it go to a tie-breaker or is the pot split? Get ₹3000. m. It appeared along with the Emperor's Challenge side bet. 6) = 227. 39 The odds of this happening exactly twice are: (30,938/30,939) 98 x (1/30,939) 2 x C (100,2) =. royal flush: [noun] a straight flush having an ace as the highest card — see poker illustration. The game is an optional feature to 3-play, 5-play, and 10-play video poker. 1 Answer. . They only take into account the odds and probabilities of making ranked hands from your initial seven cards. P(Royal Flush) = 4 * 47c2 / 52c7 = 1/30940. of 40-hour weeks. Odds of hitting a royal are roughly 650000-1 Hitting them twice in a certain amount of times is a bit lower of course. 000154% according to Upswing Poker . Electrical Engineering questions and answers. The odds of hitting a royal flush will change also depending on the hands that you are initially dealt. So 32 different seven-card straight flushes are possible. Odds of Making a Royal Flush on the Flop. Dividing by the number of possible hands gives the probability: or 1 in 649,740. 6 million playable five-card hands in Texas Hold’em, and just four of those hands are royal flushes. A royal flush is the highest-ranking Poker hand and consists of a sequence of a 10, Jack, Queen, King, and Ace, all of which with the same suit. 000020; Payout: 4000 coins; Joker Poker games all have one thing in common that sets them apart from other video poker variants – the presence of the joker card. A Royal Flush is the highest possible hand in Poker and the odds are 649,739 : 1. Calculate Total 5 Card hands To calculate the probability of hitting by the river, we’ll employ the trick of calculating the chance of hitting and then subtracting from 100%. The Probability of a Royal Flush (percentage) constant defines the probability of being dealt a Royal Flush and represent the probability as a fractional percentage. Royal Flush (Straight Flush) A royal flush is essentially the best possible hand that you can get in poker, but it’s still just a straight flush. 7922%: 1:1 Version 2 mostly uses the same pay table as version 1 but adds a $100,000 win for a "6-Card Super Royal," which is a suited 9-A straight flush. In this game, players are dealt 7 cards throughout the. royal flush b. One out of 60 royal flushes is sequential. Naturally, a nine-high straight flush would beat a six-high straight flush, for example. Royal flush - using wild cards. 000154%. There are four different Royal Flush hands, one for each suit. With your example, you just multiply 48,048 X 48,048 and the odds of hitting back-to-back royals are 2,308,610,304 to 1. "The odds of hitting a royal flush in Texas Hold’em are 639,739:1, or about once in every 650K hands. The odds of drawing a royal flush in Texas Hold’em are roughly 650,000 to 1, which means you have a better chance of hitting a hole in one or matching five numbers in the lottery. In a third version there is a separate pay for a suited blackjack as follows. Conversely, the odds against hitting a Royal Flush are 649,739 in 1. A "reversible royal" is one that pays a premium for a sequential royal flush in EITHER direction. 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). A royal flush is the highest-ranking hand in the game, consisting of the ten, jack, queen, king, and ace of the same suit. According to gambling experts, out of more than 2. 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. Let’s assume you play for 8 hour at a speed of 400 hands per hour, or 3200 hands total. 000515486% or approximately 1 in 194,000. Since it is the highest possible hand. 000831. The odds of hitting a royal flush is roughly 1-in-40,000 hands. This probability can also be expressed as. 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. Now we intuition we see that. 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. Before somebody mentions it, this assumes that each hand is dealt from a separate deck. 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. A typical flush might be the king, jack, eight, five, and three of hearts. That calculation equates to an 0. This is because there is only a 0. 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. In high. 2 to a royal flush: Go for the straight flush; 2 9 J Q K — 3 to a straight flush (type 1) vs. Speaking of odds, a few weeks ago a reader asked whether the odds of hitting the progressive were the same on Wheel of Fortune machines with different max bets. 0032% Edit: Obviously I have to clarify. Suppose that an avid poker player sees 100 hands a week, 52 weeks a year, for 20 years. 1. 000032: Straight flush: K-9: 4,140: 0. If you find the right answer and can somehow confirm it, it'd be nice if you edited the post to show it. There are 624 possible hands that can make a four-of-a-kind, and the probability of getting this hand is 0. Assuming you are the first Player being dealt out, the odds are 0. The royal flush is the strongest hand you can get in poker. 04 =0. As the 2s significantly increase your chances of getting a winning hand, the game is also designed to have lower odds than other video poker types. Hole x flop odd = 0. Question: Find the probability of getting a royal flush poker hand when 5 cards are dealt from an ordinary deck. Mississippi Stud is a popular poker-based table game by Scientific Games. 6 So the event that you will have pocket aces that will turn to quads and lose will happen 1 in (221 122. Royal Flush 500 to 1 Straight Flush 50 to 1 Four of a Kind 10 to 1 Full House 3 to 1 Flush 3 to 2 Straight 1 to 1 All other Push are the typical payouts on the blind that being said its supposed to be like 2. Case 1: 9 is on the board. for $27,101 on a $1. So the final probability is 21620/936491920, or 1 in 43316. 31,600 posts. However, due to its specific card requirements and the limited number of possible combinations, the odds of obtaining a royal flush are incredibly slim. 33% chance of completing the flush on the turn and seeing another flush card on the river. You have a double gut-shot draw with two cards valued at two points. Player hands are 5 cards total. It is followed by Straight Flush, which is formed by 5 consecutive cards of the same suit. The cards dealt are not wild and the player keeps all the cards. 00168067, the probability of a straight flush is 0. The top prize is a royal flush, which pays out 250x. Here is a runthrough of the probabilities and house edge in Video poker and tips and strategy that you should bear in mind when playing. 00002476) 3200 = 0. To put that in perspective, using an example of playing 2,000 hands of video poker every day (four hours at medium speed), it would take an average of 325 days to get a dealt royal (with a lot of variance in the actual time it takes). 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. Incidentally, the chances of getting a royal flush in 7-Card Stud are the same as in Hold ‘Em. = 40 / 2,598,960 = 0. (b) straight flush (five in a sequence in a single suit, but not a royal flush). Statistics and Probability questions and answers. Yes. 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. Poker Hand Nbr. A royal flush is the highest-ranked hand in poker. The probability of no royal flush in one hand is: 1 − 1 649740 = 649739 649740 1 − 1 649740 = 649739 649740. 0000) 3 of a kind (4. This includes the four royal flushes (Diamonds, Spades, Clubs and Hearts). We need only seek the probability for obtaining 2 of 13 cards in 1 from 4 suits, when selecting 2 from 52 cards. Then, against all odds, he hit another royal flush 20 minutes later in another tournament! 2 Royal Flushes Hit In 20 Minutes. However, because of variation you could easily hit a royal flush. So, the odds of one specific player flopping a royal flush would be 4-in-2598960, or 1-in-649740. Royal Flush. The thrill of hitting a royal flush in poker is undeniable. com The royal flush is a case of the straight flush. A very good approximate formula for the probability of not getting a royal in a particular number of cycles, N, is: P = e -N. If anyone is interested in how to calculate the odds of completing a royal flush with one card saved, here is how it works. 0000154%. Except the sub is named for a quote from a movie in which "Never tell me the odds" is said after having been told the odds. So, the probability of a four aces losing to a royal flush is 8,448/2,781,381,002,400 = 0. This will enable you get a Royal. In summary, the conversation discusses the statistical chances. A quick recap. I guess I won't celebrate my royal flush : ( ( /j. And, from Problem 1, we know that there are 2,598,960 distinct poker hands. There are ${52 \choose 5} = 2,598,960$ different equiprobable hands you can be dealt when you are dealt five cards from a standard deck of fifty-two. 60% of the time you get a royal flush every time. The expected value will be calculated of each, and the player is given the best one as his hand on the deal. Considering the low odds of making a royal flush or straight flush, those hands are often included in a bad-beat jackpot. But the other player must have the two specific cards to complete the royal flush and the probability of that happening is 1/45 * 1/44 = 1/1980. 000001539. For each poker holding be- low, (1) find the number of five-card poker hands with that holding; (2) find the probability that a randomly chosen set of five cards has that holding. Getting your royal flush cards at the very beginning can give you incentive to go all-in or to double down on your bets. There are just four ways to make a royal flush (one in each suit). e. Royal flush: The strongest five cards in sequential order and of the same suit. Dividing by the number of possible hands gives the probability: or 1 in 649,740. The program is about 600 lines of code and takes about six hours to run. A royal flush usually appears about once in every 40,000 hands when a player uses optimal strategy. What happens in a game of poker? What is a flush and what happens if two players have a. For hands that have four ways to flop a straight flush (suited connectors 54 through JT), you have an 0. A royal only comprises about 2% of a video poker game’s overall payout percentage. A royal flush is a rare, but not impossible, occurrence in poker. They are ranked by high card, from Ace-High (AKQJT) down to five-high (5432A). $4^5 imes 9/inom{52}{13}$. For example, an ace, king, queen, jack and 10 of hearts. However, those three top hands all pay the same as a 5-card royal flush at 1000. Essentially, a royal flush is a synonym for an ace-high straight flush such as A ♥ K ♥ Q ♥ J ♥ 10 ♥. Royal flush: 6,000-1: 0. Royal flushes are unbeatable and extremely rare. That's less than a 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). • 4 days ago. But what are the actual odds of getting a royal flush? And how can you increase your chances of hitting this elusive hand? Skip to content. The odds are so tough to beat that buying. The Royal Flush is the rarest hand in Texas Hold’em Poker. 000154%, a straight 0. 00119909. ) The bottom line is as long as the pay schedule is the same for a particular video poker. The odds of hitting a royal flush are 649,739-1, while the next best hand, a straight flush, has odds of 72,192-1. The odds for a royal flush are 0. Therefore, the probability of being dealt a straight flush (P. Joined Jul 10, 2017 If you draw five cards randomly from a 52-card deck, the probability of making a royal flush is 0. 0032%, with the odds against making a royal flush at 30,939-to-1. After your first, though, the royal after that has the same 1-in-48,048. I've had two royal flushes in live play. This means that villain will get 2 royal flushes in one game every 194,000 stretches of a hundred hands. With all poker hands, we use the highest-ranking card to determine which wins. 96 is 2. So for a given pocket pair 10 or above, the combined probability is 1/221 * 1120/1712304 * 1/1980 = 7/4,682,937,402. The chances of picking up a royal flush are 1 in 30,940 hands or 0. 44% and then you double the flop odds for a total of 1 / 1,951,025. Your odds of getting a royal flush are around 40,000:1. 24M hands What are the odds of a Royal Flush? 0. An Ace high Straight Flush is a Royal Flush. Here's a tricky one: You should hold the three-card royal; drop the king and 4. 00000732 Royal straight flush 26,132 0. 8% house edge with basic strategy. It represents the pinnacle of hand rankings, standing above all other combinations. For a traditional video poker game (9-6 Jacks or Better), you’ve got a 1 in 40,391 chance of hitting a royal. If you’re holding a suited connector like J ♠ T ♠ there are exactly 4 flops which will give you a straight flush: A ♠ K ♠ Q ♠ (for a royal flush), K ♠ Q ♠ 9 ♠, Q ♠ 9 ♠ 8 ♠, and 9 ♠ 8 ♠ 7 ♠. 9/6 Double Double Bonus. Calculate Total 5 Card hands Choose 5 cards from 52 cards. the Wizard of Odds, whose book Gambling 102 is coming out in a new edition very soon. This is not to be confused with a Sequential Royal, which pays in the 10-J-Q-K-A direction only. Same with a Royal, or if the board is quads with an ace. This hand is simply a straight flush kind of thing. After the player makes a bet, the dealer will deal the player and himself seven cards each. But, since you’re only starting. 00000153907 which is computed as 4 possible royal flush hands divided by 52C5 total cases as you pointed out. We just discussed how players can receive certain parts of a royal flush and improve their opportunities of getting video poker's best hand. b) A straight-flush (excluding royal flush) is all cards the same suit and showing consecutive numbers (but not the highest 5 consecutive numbers). This indicates that you have a 0. Texas Holdem uses 7 cards to make the best five card hand. The probability of getting a Royal Flush is 0. 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. What are the odds of a royal flush in Texas Hold em? 1 in 30,940. combin (48,3) = 17,296. All the comments so far are wrong. In a standard 52-card deck there are: 4 suits (spades, hearts, diamonds,. 00197 Straight 10,200 0. It is important to understand that these odds represent an overall probability and not an individual event, as poker is a game of chance and each hand is distinct. Your chances of a royal flush on the deal are 1 in 649,740. All that is left to do is to carry out easy division. The probability of a royal match is 4×n 2 /combin(52×n,2). First, choose the suit. In fact, every pot odds article you've ever read uses either a flush or a straight draw (or both if you're lucky) as their main example to help explain how it all works. 00002476. (36 straight . 00016927: 150 to 1: Straight flush: 750-1: 0. 005% or 1 in 19,600. We can now calculate the probability of a flush as 5108/2,598,960 = 0. Of those, 40 are straight flushes. Many gaming experts say the odds of these. 00015 percent (or 1 chance in 649,740). For example, Th-Jh-Qh-Kh-Ah would be a sequential royal flush, but Jh-Th-Qh-Kh-Ah would be a normal royal. 000154% of the time, or once every 650,000 hands (odds against of 649,740:1 to be precise). In a standard 5-card poker hand for 1 deck: Calculate P(Royal Flush) Royal Flush Hands. 00196 To find the probability, we need to find the fraction where the numerator is the number of ways to have a flush and. There are 19,600 possible flops in total. Sorted by: 1. The probability of just a case 1 bad beat is 1 in 439 million. Because there are 7 cards, the odds go way down:royal flush if it were the card above the king. You might think that with those long odds, you’ll never be lucky enough to be dealt a. The odds against getting a royal flush in poker on first five cards dealt is 649740 to 1 Find the probability of this event? I will assume you numbers are correct, and the odds of NOT getting a royal flush is 649740 to 1, then the odd of a royal flush is the reciprocal of that. If you drew five random cards from a 52-card deck, you’d have an 0. The odds for getting a specific royal flush in 5-card poker would be 1 in. The probability of being dealt a royal flush is 0. 01%), and one-way straight flush hands (0. So, even with the extra pair of cards in an Omaha hand, the odds of one player getting two such rare hands in so short an order. So, ÷1081 for each of the two hands, = 1 in 3,594,493,636. This rarity is further emphasized by the fact that the least likely situation of being dealt a Royal Flush in Texas Hold’em is flopping a Royal Flush. In other words, with a five-card poker hand, there is a 0. An example of the diamond flush poker hand combination is Rank 10 (10), Jack (J), Queen (Q), King (K) and Ace (A) (10 J Q K A), all. That means your chances of. The royal flush is the best hand available in poker. Full expected value table. The probability of being dealt a royal flush can be calculated based on the number of royal flushes divided by the total number of poker hands. The odds of royal flush in Texas hold’em are 30,939:1. Congratulations! You experienced a very rare event. According to Upswing Poker, the odds of a royal flush in Texas Hold'em are 0. as a royal flush. Except the sub is called "Never tell me the odds. 000154%. dystopianview • 5 yr. Find the probability that the hand is a Flush (5 nonconsecutive cards each of the same suit). But it’s still a massive 30,940 to 1 one against. You should never play video poker with the idea that you are going to hit a royal flush. A royal flush consists of the Ace, King, Queen, Jack, and Ten, all of the same suit. Your chance of getting a pocket pair is 1 out of 221 while the likely hood for the dealer to also have the same card is less than 0. Level Contributor . For a broader explanation, each card has a corresponding probability of being drawn. Different post-flop methods yield probabilities of around 2. 5%. SUBSCRIBE MENU. Probability of Royal Flush. 5d6d7d8d9d. The best hand in the game, a royal flush, has the biggest odds of the game, while the lowest ranked hand, a high card, has the shortest odds of happening. " Taking this to be your intention, i. e. There are about 327 million people in America, so it's almost like randomly. However, if you use a perfect strategy, you improve your chances of hitting the hand. This sub is called r/nevertellmetheodds. It can. The diamond flush poker hand combination consists of the royal flush but with all diamonds. The chances are much lower that more that one person gets a royal flush, though. The diamond flush poker hand combination is one of the best hand combinations for a player to have. In poker, players form sets of five playing cards, called hands, according to the rules of the game. The four possible combinations of Royal Flush in poker: A ♠ K ♠ Q ♠ J ♠ 10 ♠ – Royal Flush of spades; A ♥ K ♥ Q ♥ J ♥ 10 ♥ – Royal Flush of hearts; A ♦ K ♦ Q ♦ J ♦ 10 ♦ – Royal. A ♦ K ♦ Q ♦ J ♦ 10 ♦. The odds of being dealt a Royal Flush on the flop in a random 5-card hand are 1 in 649,740. The board shows a royal flush: 0. 000031: Straight flush: J-7: 4,140: 0. Here are a few more fun poker probabilities: Chances of getting four Aces in 5-Card Draw: 1 in. 1 / 72,192. There are 2,598,960 unique poker hands. Your odds are best after getting two suited pocket cards usable in the Royal flush. In one of those tourneys, he flopped a royal flush. The odds of getting the highest possible payout here are nearly as slim as getting a royal flush since it requires pocket aces from both you and the dealers. The payout rates and the true odds are two completely different beasts. The probability of being dealt a straight flush is 0. combin (48,3) = 17,296. In one suit, there are 8 different 7-card straights possible. Jersey. Odds of a Royal Flush. Probability; 1) If you were playing with a single deck of cards, What is the probability of drawing a Royal Flush in SPADES? How does the probability change if the question asked the probability of drawing a Royal Flush of ANY suit? 2) If you were to flip a coin 3 times; a. 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. Regarding the lottery example, a one in 29,000,000 chance of winning is really quite high. 38815913) 3 to a straight flush, spread 5 and suited 346,356 2,3,4 (0. Below is a table that explains the odds of getting a specific hand when holding four, three, two. Question: 4. Paul Phua says that to start with, you will have to play 30,940 poker hands before you get dealt a Royal Flush. 199910% chance to get a royal flush Option 2 : i know the chance of a flush and a straight, and multiply them to come up with the chance for bother events to occure. Dividing the total possible hands by four – a dealt royal flush is one out of 649,740 possible hands. If you draw five cards randomly from a 52-card deck, the probability of making a royal flush is 0. The discarded suited card would be called a flush penalty card because it could have been used to complete a flush. Odds of Making a Royal Flush on the FlopThe chances of hitting a Royal Flush after the flop in community card games of Poker significantly rise, providing a more realistic chance to get this hand. The latest puzzle is: NYT 11/20/23. 00119788: 50 to 1: Four of a kind: 500-1: 0. How large must n be to render the probability of having no royal flush in n hands smaller than 1/e? My answer is: since this is for one success, use a geometric distribution instead of a negative binomial. A "bug" is a card (typically a Joker) that can be used to fill a straight or flush, but is otherwise just an Ace.