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Server Time: 2/13/2012 6:54:21 PM PACIFIC |
 situational trivia #7, Aisthesis, 29. Nov 2003 18:37 | ||
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| Here's one to which I don't know the answer, so anything goes... :) Here goes: The question regards simply holdings heads-up pre-flop and their relative values. There are some obvious cases where hand A completely dominates hand B, but hand C, which is a slight underdog to hand B, is also just a slight underdog to hand A. Example: hand A: 99, hand B: 22, hand C: AKs. 99 will completely dominate 22 but is only a slight favorite over AKs, which 22 will generally also beat. So, the question is: Are there any 3 poker hands A, B, and C such that heads-up, A is a favorite over B, B is a favorite over C, and C is a favorite over A? I'm kind of doubting their existence, but it just might be possible... any ideas? | ||
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| Re: situational trivia #7, Angel, 29. Nov 2003 19:10 | ||
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| Yes there is - but two of three have already been mentioned in your series... I'll give someone time to find it - but that''s a hint. :) | ||
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| Re: situational trivia #7, maniacmath13, 29. Nov 2003 19:34 | ||
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| well one way i can think of would be 6 7 suited pocket 2's and 6 jack offsuit. the 6/7 suited would be ahead of the 2's, but the 2's would be ahead of the 6/J and the 6/J would be ahead of the 6/7 | ||
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| Re: situational trivia #7, Flakes, 29. Nov 2003 19:38 | ||
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| Tell me, how is 6-7 suited a favorite over 2-2 preflop? If 2-2 is a slight favorite over A-Ks, then 2-2 is a favorite over 6-7s, no? | ||
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| Re: situational trivia #7, Schuster, 29. Nov 2003 20:42 | ||
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| No. The extra straight potential gives medium suited connectors a small edge over the pocket pair. There's tons of possible combinations... Any two overcards, a small pair, and some medium suited connectors will qualify. Lee | ||
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| Re: situational trivia #7, Angel, 29. Nov 2003 21:22 | ||
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| Ok, you want the tough question that Lee implied? *eg* How many ABC's are there in a 52 card deck such that the original conditions in this post are met ? | ||
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| Re: situational trivia #7, Schuster, 29. Nov 2003 21:48 | ||
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| Heh... does an ABC such as AKo, JTs, 33 count as one combo or however many different combos there are of making those 3 hands? Actually, I think either way, I'm way too tired to figure it out. =P Lee | ||
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| Re: situational trivia #7, Angel, 29. Nov 2003 21:56 | ||
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| Oh no - that would be one combo. lol No need worrying about AK suited in spades, then hearts, the diam... | ||
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| Re: situational trivia #7, Angel, 29. Nov 2003 20:40 | ||
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| Well there ya go - and you thought you didn't know any. The one in particular that I was thinking of was AKs, JTs, 22. BTW, I like your series - it gets the brain going and it's nice to see the interest they generate. | ||
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| Re: situational trivia #7, Aisthesis, 29. Nov 2003 22:15 | ||
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| Wow! that's a good one! So, there really are cases where transitivity doesn't apply to poker hands!! (I hadn't been able to find any myself and was beginning to think of how one might go about showing they don't exist) | ||
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| Re: situational trivia #7, Aisthesis, 29. Nov 2003 22:17 | ||
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| just also checked AKs, 76s and 22, same thing--whether or not the AKs is in the same suit as the 76s. | ||
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| Re: situational trivia #7, Aisthesis, 29. Nov 2003 22:41 | ||
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| I just checked (moving toward an answer to Angel's question) on 33, 44 and 55 vs. 76s. 33 and 44 still lose, but 55 wins (taking away too many straight chances). Also, 65s still qualifies as a winner against 22 and 33, and 54s beats 22 AND (barely) 33. And 22, 33 and 44 (but not 55 and above) all lose to KQs according to pokerstove, although I would have figured the lack of full extension on the KQ straight would make it a loser even to the low ones. JTs still beats 77 but loses to 88. So, without giving an exact number, we can say that any hands of the following sort will qualify: Hand A is a pair no greater than 77 and lower than the lowest card of hand B (the required gap for some reason gets bigger the higher you go) Hand B is a suited connector from 54s to KQs. Hand C is a non-pair hand with at least one big card and significantly reduced straighting chances (sorry about the vague description of hand C, but there are a lot of different ways to construct it. K2o beats 76s but loses to 22, just as another example). I'm pretty sure these are going to be the only hands that qualify (nope, correction, T8s also beats 22, so some suited one-gappers are going to work as well for hand B). | ||
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| Re: situational trivia #7, Robert M, 2. Dec 2003 12:17 | ||
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| Can I link this? Lesson # 4 http://www.cardplayer.com/?sec=caro Talks about 22 beats AKo AKo beats J10s J10s beats 22 ---------------------------------R | ||
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