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Server Time: 8/20/2008 3:44:29 AM PACIFIC |
 Royal flush odds, magicman99, 10. Apr 2003 02:24 | ||
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| I was just playing at truepoker.com and had k's full get beat by a Royal Flush, about an hour later my aaa got beat by another royal flush what are the odds of 2 royal flushes in an hour??? and has anybody had any suspect tables at truepoker?? thanks for any input Tom | ||
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| Re: Royal flush odds, Schuster, 10. Apr 2003 04:09 | ||
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| This is a tricky question. It's very similar to the old one, "what are the odds of pocket aces back to back hands?" Once there has been 1 royal flush, the odds of another coming up are the same as the odds of one coming up if the first had never hit. The two events are completely independent. I don't know what the odds of a royal in 7 cards are off the top of my head, but obviously, they're pretty small. That said, if you were to ask, "what are the odds that I see two royal flushes in the next hour I play?" Well... they're astronomically bad. However, this doesn't mean that you're being scammed by any means! If you instead reworded your question to, "What are the odds that sometime in my life, I will see two royal flushes in one hour?" the odds improve significantly. The chances of it happening in any specific hour are horribly bad, but over a long period of time, it is statistically likely for statistically unlikely things to happen. I think I saw quads 3 or 4 times in one 3 hour session not too long ago. Weird stuff happens. I was just happy that I didn't get beat by them! Lee | ||
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| Re: Royal flush odds, JunglingS, 10. Apr 2003 09:37 | ||
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| As far as statistically unlikely events go, over a long enough period of time, the occurrance of a statistically unlikely event occurring is a certainty. I know a lot of you will say that I shouldn't use absolutes, but think about it - Over a long enough period of time, the probability of no statistically unlikely events occurring is itself statistically unlikely. So, if you see no statistically unlikely events in your entire life, that, in and of itself, is statistically unlikely, and you have therefore witnessed a statistically unlikely event. Don't discount anything. I've seen a lot of strange stuff happen online, but when I compare it to the strange stuff I've seen in person, it seems more inevitable than strange. | ||
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| Re: Royal flush odds, stdioh, 10. Apr 2003 09:57 | ||
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| heheh...in response to this, I offer the proof that all integers are interesting: We shall proceed by induction. Base case: 0 is interesting, 1 is interesting, -1 is interesting. By inspection, if X is an interesting number then -X is an interesting number. Assume that the first k integers are interesting. Show that k+1 is interesting. Now we proceed in proof by contradiction. If k+1 is uninteresting then it is the smallest uninteresting integer. Hmmm...interesting. Contradiction. Thus all positive integers are interesting. Therefore all negative integers are interesting. Thus all integers are interesting. | ||
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| Re: Royal flush odds, timmer, 10. Apr 2003 21:28 | ||
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| Hey Ive read that before.... on 10. Apr 2003 09:37 JunglingS wrote: > As far as statistically unlikely events go, over a long enough period of time, the > occurrance of a statistically unlikely event occurring is a certainty. > | ||
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| Re: Royal flush odds, stdioh, 10. Apr 2003 07:53 | ||
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| It really depends on the board. If you have 2 royal cards in your hand, then your odds of getting a royal flush are about 1/2000. If you count royals that are made with only one card from the hand then they happen a lot more. Pretty much any board with 4 royal cards has a good chance of giving somebody a royal. For this discussion, let us limit it to players with 2 cards of the royal in the hole. Your chance of starting with 2 royal cards is 20/52*4/51= ~ 1/33. Given that you have it, the chance of hitting the royal is roughly 1/2000, so they should come up for a given player about once every 66,000 hands. And most players who have two cards of a royal will not fold them before the flop or have a flop that doesn't look good but backdoor the royal anyway, so let's assume, for the sake of argument that we always get a royal when we have the cards in the right order for one. So there's a table getting dealt 35 hands an hour (double this if on the internet) with 10 players. That is 350 hands. The chance that given that particular hour two royal flushes come in the above manner, is 1 : 35,559 against...so it is pretty slim, but not out of the realm of possibility. Now if you allow for royals with one card, then there is a (20/52)*(47/51) chance that you have one royal card ~ 1/3 chance. Given that you have one royal card, your odds of making the royal are about 1 : 1,105,440 - looking grim, but it can happen. Thus you have a 1/55,974 chance of getting either a 1 or 2 card royal on a given hand. Thus there is a 1: 25,576 chance that two royals will come in a given hour at a table if they are made with at least one hole card. Now there's also the chance of a royal hitting the board (if you want to count this). The chance of that is easy to work out. Now there are two ways to figure this - we could figure that we know your two cards and thus you could be blocking one royal, blocking two royals, or blocking no royals, and each will yield a different result, but that is too much work for me to bother with (so I will leave it as an excersice to the reader GRIN) We will just assume that you are playing your hand blind. Then there is a 1/77,968,800 chance of the royal hitting the board. Thus there is a 1/55,934 chance that some given player makes some kind of royal on a given hand, but in the last case, the chances of it happen counterfeit eachother, since either all players get a royal on board or no players get a royal on board and the numbers must be adjusted accordingly. Thus there is a 1 : 25576-((25576-25540)/10) chance or 1 : 25,572 chance that in any given hour there will be 2 royal flushes at the table. Now these numbers might be off very slightly due to rounding and we have made some assumptions about the hands dealt. For instance, if you are holding pocket aces and get beat by a royal flush, it is only half as likely to have happened, since by holding 2 aces you have made 2 royal flushes of the 4 impossible. That said, you can more than divide these numbers by 2 when you are dealing twice as many hands per hours since there is a square involved. If there are 70 hands per hour being dealt then I'd guestimate the odds of 2 royal flushes in a given hour would drop to somewhere in the neighbourhood of 1 : 11,000 (but again I am too lazy to do the math). So to make the long story short, it sucks, but I don't think it is evidence of any kind of cheating. Things like that happen all the time. It would be odd if they never did. This time, you were in the path of the tornado. | ||
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| Re: Royal flush odds, Risky Business, 10. Apr 2003 11:42 | ||
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| While you're at it.................I've beaten a straight flush with a straight flush. Talk about odds.............have we worked up the possibility of 7 consecutive suited cards being held through the river? Of course not, that's absurd!! | ||
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| Re: Royal flush odds, stdioh, 10. Apr 2003 15:29 | ||
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| Actually, straight flush over straight flush isn't too crazy...if you have 4 straight flush cards on the board, then there are only two cards you need, one per player. Now when there are 3 straight flush cards on board and 2 players still have straight flushes, that is much more rare. | ||
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| Re: Royal flush odds, 4 POKER, 10. Apr 2003 14:56 | ||
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| Man O' Man, You really know your stuff! Very impressive. 4 POKER | ||
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| Re: Royal flush odds, stdioh, 10. Apr 2003 15:29 | ||
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| Thanks. I try to keep up to date with obscure trivia :) | ||
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| Re: Royal flush odds, 4 POKER, 10. Apr 2003 15:34 | ||
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| Hey, If THAT IS trivia, remind me to never play trivial pursuit with you! | ||
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| Re: Royal flush odds, stdioh, 11. Apr 2003 09:51 | ||
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| Hey, I did represent my province at the national level in trivia twice back in my highschool days. I think a game of trivial pursuit against me would be a -EV play for most players...unless we were playing the sports edition in which case I would be creamed by most special olympics participants. | ||
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