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Server Time: 12/2/2008 9:19:51 AM PACIFIC |
 Royal Flush odds, Boftx, 18. Sep 2003 09:50 | ||
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| Just what are the odds of any one player in a 10-player HE game getting a royal flush at any point in a hand, excluding a royal on the board? To put this another way, if I were to make a side bet that at a given table a player, any player, would make a royal, what odds would I need to get? I assume the odds are higher against it happening at a 6-player table. . | ||
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| Re: Royal Flush odds, stdioh, 18. Sep 2003 13:55 | ||
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| Well, if you are holding 2 Royal cards in your hand then you have a 1/2000 chance of making a royal flush. If you are holding 1 royal card your chances are a lot smaller. Sheesh ... I don't remember the odds of that offhand and I don't have time right now to do the math. Basically look at it this way: If you hold 2 royal cards then you need to figure out the chance of the exact 3 cards you need coming out of the 5 that come to the board. If you hold one royal cad then you need to look at the chances of the exact 4 cards you need coming out of the 5 board cards. Once you've got those down then you just need to find out your chances of starting with 2 royal cards and your chances of starting with exactly 1 royal card. Multiply each by the chance of a good board, add the two together and you'll have your answer. | ||
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| Re: Royal Flush odds, Bungus, 18. Sep 2003 19:52 | ||
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| Who plays a ten person table anyway? is this at a casino, or just online? | ||
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| Re: Royal Flush odds, Boftx, 18. Sep 2003 22:40 | ||
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| Online for this question. Once I see the real math I can work it out for anything else. Just can't come up with a good model for doin the math. | ||
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| Re: Royal Flush odds, GeneM, 19. Sep 2003 10:46 | ||
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| I'll try to take a stab at this... Okay, if you have 2 qualifying cards in your hand, the chances of getting the other three cards on the board are: (3/50) * (2/49) * (1/48) = 1/19600 To get 2 qualifying cards, you first must be dealt any A through 10. There are 20 in the deck, so it's 20/52. Then you must get one of the 4 cards that goes with it, so that's: (20/52) * (4/51) = 1/33.15 Multiply them together: (1/19600) * (1/33.15) = 1/649740 With 1 qualifying card, your chances are: (4/50) * (3/49) * (2/48) * (1/47) = 1/230300 The odds of getting 1 card are (this part could be wrong): (20/52) + (20/51) = 1/1.287 (approx.) Multiply them together: (1/230300) * (1/1.287) = 1/296483 Now add the two (and multiply by 10 for the 10 people at the table): ((1/649740) + (1/296483)) * 10 = 1/20358 (approx.) All-in-all, it looks like you could give 20,000-to-1 odds and still be comfortable. Unless my math is horribly wrong. | ||
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| Re: Royal Flush odds, GeneM, 19. Sep 2003 11:36 | ||
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| I could've been completely wrong with my last post. If you look at it strictly from a combinations perspective... There are 133,784,560 different combinations of 7 cards. 4,324 of them include a royal flush. Therefore, the odds are: 133,784,560 / 4,324 = 30,940-to-1. That includes getting it on the board, however. Oops, don't forget to multiply by the 10 people at the table... so we'll call it 3,094-to-1. | ||
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| Re: Royal Flush odds, Andrew Wells, 20. Sep 2003 20:36 | ||
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| Once you figure out a sure way to collect (on line) such side bets, you've done 99% of the work. | ||
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| Re: Royal Flush odds, stdioh, 19. Sep 2003 09:40 | ||
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| I play at 10 handed games at my home casino. | ||
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| Re: Royal Flush odds, TrippH, 19. Sep 2003 12:27 | ||
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| I started to do this by calculating odds for any specific player to have 2 RF cards, 1 RF card, etc., but it seems easier to think of it in terms of the whole table (there could very easily be some mistakes here - some of it got a little tricky considering I haven't done much of this kind of thing since my high school math contest days) odds that exactly 4 RF cards (same suit) will hit the board: ((20/52)(4/51)(3/50)(2/49)(47/48))(5!/4!1!) = 47/129948 = .0003616831 = roughly 1/2765 odds that exactly 3 RF (same suit) cards will hit the board: ((20/52)(4/51)(3/50)(47/49)(46/48))(5!/3!2!) = 1081/64974 = .0166374242 = roughly 1/60 odds that exactly 4 RF cards hit the board and someone at a 10-handed table holds the other: (47/129948)(20/47) = 20/129948 = .0001539077 = roughly 1/6497 odds that 4 RF cards hit the board and someone at a 6-handed table holds the other: (47/129948)(12/47) = 12/129948 = .0000923446 = roughly 1/10829 odds that exactly 3 RF cards hit the board and someone at a 10-handed table holds the other two: (1081/64974)((20/47)(1/46)) = 21620/140473788 = .0001539077 = roughly 1/6497 odds that exactly 3 RF cards hit the board and someone at a 6-handed table holds the other two: (1081/64974)((12/47)(1/46)) = 12972/140473788 = .0000923446 = roughly 1/10829 odds that in any one hand, someone at a 10-handed table will make a royal flush (excluding RF on the board and assuming no one folds): 2(.0001539077) = .0003078154 = roughly 1/3249 odds that in any one hand, someone at a 6-handed table will makea royal flush (excluding RF on the board and assuming no one folds): 2(.0000923446) = .0001846892 = roughly 1/5415 then of course the odds of whether anyone will make a royal flush (excluding RF on the board and assuming no one folds) over the course of an entire session (x) depends on the number of hands played (n) where at a 10-handed table x = 1 - (3248/3249)^n and at a 6-handed table x = 1- (5414/5415)^n | ||
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| Re: Royal Flush odds, ADAM THE EXPERT, 20. Sep 2003 23:53 | ||
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| to get the exact odds, would require more of adam the experts brain power, than i am willing to give for free. The WORKABLE odds, for ten players, are approximately 2500 to one, based on ten players. However, this assumes that all of the players, will call with any hand, that could POSSIBLY produce a royal, including things like jack deuce suited. So, the PRACTICAL Odds, would be much higher. So, just for fun, as long as you're getting around 3000 to one, and can trust the person to pay off, go ahead and bet a buck here and there, just for kicks. Adam the expert, does NOT approve of taking advantage of people by LAYING these proposition bets, so I won't tell you what odds to LAY, to make a long term profit. | ||
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