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 odds of the board being a set vs top pair, jajo, 9. Dec 2003 16:41 | ||
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| I am trying to calculate who is the favorite among the following two hands Ac,Kd vs Qh,Qs. In doing part of the calculation, I need to find out how many boards will contain at least one "ace or king" AND atleast one queen. I am having a hard time coming up with the right formula. I appreciate any help. BTW, there are 48 C 5 = 1,712,304 possible boards and 861,636 of them will contain atleast one ace or king. | ||
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| Re: odds of the board being a set vs top pair, rambler, 9. Dec 2003 17:19 | ||
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| the Q,Q would have the edge winning 53 percent of the time to the A,K assuming everyone else folded out. | ||
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| Re: odds of the board being a set vs top pair, mkpoker, 9. Dec 2003 17:40 | ||
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| on 9. Dec 2003 16:41 jajo wrote: > I am trying to calculate who is the favorite among the following two hands Ac,Kd > vs Qh,Qs. > > In doing part of the calculation, I need to find out how many boards will > contain at least one "ace or king" AND atleast one queen. I am having a hard > time coming up with the right formula. I appreciate any help. > > BTW, there are 48 C 5 = 1,712,304 possible boards and 861,636 of them will > contain atleast one ace or king. I'm rounding off a bit in answering your question...I'm sure others will correct me! Assuming you stay until the end (which is a big if), there is a 19 percent chance that least one more Q will come up by the river. That leaves 4 other cards, in which you might hit an A or K. There are 6 other A or K in the deck.. Hence, the formula you seek (I think) is (6/50 + 6/49 + 6/48 + 6/47) * .19 = x Rounded off to: .48 * .19 = x OR .09 = x. Hence, there is a 9 percent chance (or 10:1 odds AGAINST) a Q AND and an A or K hitting the board. | ||
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| Re: odds of the board being a set vs top pair, jajo, 11. Dec 2003 15:13 | ||
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| on 9. Dec 2003 17:40 mkpoker wrote: > on 9. Dec 2003 16:41 jajo wrote: > > I am trying to calculate who is the favorite among the following two hands Ac,Kd > > > vs Qh,Qs. > > > > In doing part of the calculation, I need to find out how many boards will > > contain at least one "ace or king" AND atleast one queen. I am having a hard > > time coming up with the right formula. I appreciate any help. > > > > BTW, there are 48 C 5 = 1,712,304 possible boards and 861,636 of them will > > contain atleast one ace or king. > > I'm rounding off a bit in answering your question...I'm sure others will correct me! > > > Assuming you stay until the end (which is a big if), there is a 19 percent chance > that least one more Q will come up by the river. That leaves 4 other cards, in which > you might hit an A or K. There are 6 other A or K in the deck.. Hence, the formula > you seek (I think) is > > (6/50 + 6/49 + 6/48 + 6/47) * .19 = x > > Rounded off to: > > .48 * .19 = x OR > > .09 = x. Hence, there is a 9 percent chance (or 10:1 odds AGAINST) a Q AND and an A > or K hitting the board. > How did you get 6/50 when there are only 48 cards in the deck. Remember, I'm holding AK and my opponent is holding QQ. So you probably mean 6/48 + 6/47 + 6/46 + 6/45. But I don't understand why you are using these numbers. Could you explain this? | ||
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| Re: odds of the board being a set vs top pair, Aisthesis, 11. Dec 2003 19:23 | ||
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| Honestly, I'd just run the hands through pokerstove because it's a pretty complicated calculation. It's also not clear to me whether you're only wanting cases of EXACTLY one A or K and EXACTLY one Q or what. As to the winning/losing question, even one A AND one K against the one Q will lose (except with straight or flush situations), but two aces or two kings will still win against the Q with no improvement. To really do an accurate win-lose assessment of these things, you have to consider quite a few exceptional cases, and pokerstove will give you the same result in just a few seconds. It wouldn't be inordinately hard to calculate how many flops have exactly one A or K and exactly one Q, but due to straights and flushes, not all of those are going to be wins for QQ. | ||
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| Re: odds of the board being a set vs top pair, Chris W, 12. Dec 2003 12:49 | ||
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| There are six remaining A's and K's and there are two remaining queens. Given that we need at least one of each there are 12 combinations where two of the cards contain one ace or king and one queen. There are C(46,3) ways to choose the remaining cards. So there are a total of 12 x C(46,3) = 182160 boards containing at least one ace Or king and 1 Queen. good luck. | ||
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| Re: odds of the board being a set vs top pair, jajo, 16. Dec 2003 14:06 | ||
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| on 12. Dec 2003 12:49 Chris W wrote: > There are six remaining A's and K's and there are two remaining queens. Given that > we need at least one of each there are 12 combinations where two of the cards contain > one ace or king and one queen. There are C(46,3) ways to choose the remaining cards. > So there are a total of 12 x C(46,3) = 182160 boards containing at least one ace Or > king and 1 Queen. > > good luck. This calculation is wrong. The number is too big. You are counting many combinations twice. That's because you are only considering the possibility that the FIRST two cards contain the a/k and the queen. What if we choose the 3 cards out of 46 first? Now we can't do 2x6 because those very cards may have alreayd been selected since we chose three from 46. This is a complicated question and I think that permutations must be used and then we must eliminate some of them. None of the previous answers are satisfactory. Any help is appreciated. | ||
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| Re: odds of the board being a set vs top pair, FlopDaNutz, 16. Dec 2003 14:28 | ||
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| I'm not going to attemp the statistics you are looking for. But I would like to add my opinion on something. You said you are trying to figure out who is the favorite between AK and QQ? I really started cracking up when I read this. I don't think this is even questionable? Who in their right mind would take AK over QQ??? I am not trying to criticize you but isnt it obvious that QQ is a better hand? With AK, you have 6 outs to pair. With QQ, you have a made pair. Ruling out a straight possibility with AK...since TJQ is a long shot. Also taking into consideration that if a Q hits the board to make s traight with AK, there is a possible boat out there with QQ. Point being, QQ is a made pair, against drawing out with AK looking to hit one of 6 outs out of 48 cards? That is not even comparable and I would take QQ 100 out of 100 times. Heck, I would prob take 99 or 88 over AK if we were heads up and all-in preflop. | ||
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| Re: odds of the board being a set vs top pair, Jeremiah, 16. Dec 2003 14:59 | ||
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| I would take 22 over AK all day. You have to draw out one of 6 outs that you have with only 1 possible way to make a straight. I have a gaurenteed pair with 2 outs for a set, and multiple ways to make a straight. So, to answer your question, not only is QQ a better hand than AK, but I would say 22 is as well. This is all in a heads up situation of course | ||
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| Re: odds of the board being a set vs top pair, GenHawk, 17. Dec 2003 06:42 | ||
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| According to the calculator at cardplayer.com the Queens are the favorite 57.2%. No clue how to calculate that though. =) | ||
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| Re: odds of the board being a set vs top pair, jajo, 18. Dec 2003 17:12 | ||
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| As you can see it's a very close call. And you're right it doesn't matter much if the pair is QQ or 88 since we're talking about an opponent who is holding two overcards. However, a 22 has the disadavantage of losing to the AK whenever two pair comes up on board. So theoretically the higher the pair the better. But I'm interested in seeing the math behind this. I know that a QQ is slightly better, but I want to calculate all the possible boards and see how many of them will go to the AK and how many to the QQ. We are assuming that the four cards are all of a different suit, so that there is no flush advatage in either hand | ||
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