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Trivia Question

Discussion in 'Poker Strategy General' started by fish72, Dec 14, 2014.

  1. fish72

    fish72 Well-Known Member
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    Hopefully a few people got a kick out of the trivia/puzzle questions that I posted a while back. Here's one more.

    Which of the following hands is more likely to make quads?
    A) pocket 3's
    B) AK
    C) pocket Aces
     
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  2. TenPercenter

    TenPercenter Administrator
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    AK just based on a certain logic I won't explain to let others think about it.
     
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    Last edited: Dec 14, 2014
  3. Gear-X

    Gear-X Well-Known Member
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    Pocket 3s. Fewer players are likely to be holding the other two 3s when you see a flop.
     
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  4. DrStrange

    DrStrange Creativity Alliance
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    Pocket threes have the edge in a contested pot. The cards held by players voluntarily in the pot are biased towards aces and against threes.

    DrStrange
     
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  5. posnera

    posnera Well-Known Member

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    Any pocket pair is as likely as any other to make quads, answer must be AK.
     
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  6. TenPercenter

    TenPercenter Administrator
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    That's why I answered AK. I wasn't taking into account likelihood of certain cards remaining in opponent's hands post flop.
     
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  7. JeromyinWV

    JeromyinWV ChipTalk.net Supporter
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    Probability is the same for both pocket pairs but probability does not equal likelihood. It's much easier to get 2 cards than 3 cards so I vote 33. I would like to see the maff on this one. Would you be able to do math on this. Thanks to my maffmatical skills (and Google) the probability of any pocket pair making quads is about 0.82% compared to about 0.10% for non paired so that would knock out the AK. Assuming that a contested pot would have people playing bigger cards lowers the AA. Gimme 33 for the win.
     
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  8. stocky

    stocky Well-Known Member
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    I see a lot of people mentioning players will more likely hold a A or K. This doesn't change the cards dealt. Because other players will likely be folding a 3.

    So I pick AK
     
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  9. MrWitti

    MrWitti Lifetime Supporter
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    I go for AA.
    33 will fold more often than Aces.
    Therefore My argument is that AA sees more community cards...
     
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  10. atomiktoaster

    atomiktoaster Well-Known Member

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    Yeah, I did the same math. 8x more likely to get quads from the pocket pair, so AK is knocked out of contention. Same thoughts on 3s vs aces.
     
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  11. catalyzeme

    catalyzeme Well-Known Member

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    I'm with you on this one. If you are looking at actual hand results and calculating the % of the time AA, 33, and AK actually turn into quads, I think AA wins because 33 is folding too often.

    If it's just the absolute number of quads that result from AK, AA, or 33, then we would think that AK is dealt about 2.5 times as often as AA but if other people's math in this thread is correct, AA is 8 times more likely to make quads and AK is still going to be folded more often preflop, so still AA.

    I go with AA.
     
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  12. TenPercenter

    TenPercenter Administrator
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    Good trivia question!
     
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  13. fish72

    fish72 Well-Known Member
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    Well, I'm not sure now:)
    I don't think my original answer is right.
    I think most people picked up on the way the question was worded. We aren't assuming that 33 and AA get to see all 5 streets. If so then obviously the odds would be the same. I'm ruling out AK since it is so much less likely to make quads with one card.
    Originally I was thinking the answer would be AA since 33 will sometimes be forced to fold preflop. And 33 will also have to fold on almost all flops that don't hit a set which removes the chances of runner-runner quads (10% of quads will come from runner-runner). AA is going to see more flops and more rivers. But...
    I wasn't considering all the times that AA folds out other hands preflop and therefore doesn't get to see a flop at all. (Remember we aren't talking about 33 and AA in the same hand.) I suspect that these odds are going the overcome the odds of 33 being folded preflop and on 'missed' flops.

    So I think the answer is 33. (I'm glad I didn't include JJ)

    I also wasn't thinking that other player's cards would come into play but I think I was wrong there too. Of the hands that AA doesn't fold out preflop, there is a greater chance that those hands will contain another Ace which makes quads very unlikely.

     
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    Last edited: Dec 16, 2014
  14. JeromyinWV

    JeromyinWV ChipTalk.net Supporter
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    There are a lot of variables that the question does not address. I assumed the same thing that fish72 did. You would have to assume all play to showdown and would help to know how many were in the hand. You can't hit quads if you fold pre-flop. Think of all of the quad hands you have seen and how many were aces? I don't know if I've ever seen quad aces (unless you count online but we all know online poker is rigged). It is usually smaller cards and people set mining and get lucky.
     
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  15. Mojo1312

    Mojo1312 Well-Known Member

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    I have made quads four times, three with pocket pairs, and once with K,J. I have seen quads a number of other times, and the overwhelming majority of them involved pocket pairs.

    I saw a player flop a set fives and quad up against a flopped set of Queens at $2/$5, and another who flopped quad fives against a player who made a set of Kings on the turn at $1/$2. I stubbornly stayed in a hand with pocket sixes after a hefty pre-flop re-raise in a .50/$1 home game. The other player had pocket Jacks, and we both flopped a set. All of the money went in, and I hit the case six on the river.

    Mathematically, this proves nothing, but it is interesting to see how often the player with the worst set ends up winning.
     
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  16. abby99

    abby99 Admin / Chip Magpie
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    I suggest that both AA and 33 are equally likely to make quads. The question doesn't mention any conditions such a requirement that a hand not be folded or the likelihood of another player being dealt an Ace or a 3 (assuming a randomized deck). Obviously a hand that is folded preflop is never going to make quads, but I don't see that as being part of the question.

    A similar question would be "Which of the following hands is more likely to flop quads?" I suggest that the math is not only similar but also easier to understand. Introducing another variable, such as whether one would fold pocket 3s OOP to a raise, is a legitimate strategy issue but it doesn't change the math. This is where pot odds, implied odds, and RIO would come into play.

    The math for both of these questions ignores the likelihood of somebody else being dealt an Ace or a 3. Assuming a random shuffle, the other Aces and threes have equal chances of being dealt to another player or appearing on the board.

    I do agree that if the problem were "If quads are shown down after the river, which hand is more likely to show down the quads?", the correct answer would be AA because pocket 3's are more likely than AA to be folded preflop. To support this, think about how many times you've heard "Oh, crap, I would have made quads" come from someone who folded pocket threes versus someone who folded AA.
     
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  17. lnlver

    lnlver Well-Known Member

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    I ran a simulation for Hold'em using two hands, 3-3 versus A-K. That left 48 cards in the deck, and dealing out a board of 5 cards makes 1,712,304 different combinations.

    Here are the results:

    [[​IMG]
     
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  18. atomiktoaster

    atomiktoaster Well-Known Member

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    Wow! How did you get the time machine to run that under DOS 3.0 in 1992? Is that a CRT monitor?
     
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  19. CaptLego

    CaptLego Super Moderator
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    I'll take this at face value. So the odds of making quads depends not only on the random dealings of cards, but also the likely way they'd be played and how opponents are likely to play.
    Taking pairs as favored over AK for the moment, that leaves pocket aces and 3's.
    While pocket threes might be folded more often pre-flop, I think there's a bit better chance that the 3's will see the turn and river on their way to quads. I haven't worked out all the probability chains, but consider this:

    Suppose the flop makes a set. The odds of a set are the same for aces and 3's. Now an ace on the flop will be much more scary than a 3. If you're holding pocket aces, there's only a small chance that anybody else is holding the case ace, but they surely have overcards to the 3. I suppose you could slow play the aces to try to see the turn and river... But you'll surely get more action on the 3's. I'm betting that the Aces will see fewer turns/rivers and consequently fewer quads.
     
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