# Poker hand puzzle you might enjoy **URL:** \ **Category:** In My Humble Opinion\ **Created:** [April 7, 2005, 4:23am UTC](https://boards.straightdope.com/t/poker-hand-puzzle-you-might-enjoy/298169 "2005-04-07T04:23:17Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![Otto](https://avatars.discourse-cdn.com/v4/letter/o/bbe5ce/32.png) [@Otto](https://boards.straightdope.com/u/Otto)\ **Post date:** [April 7, 2005, 4:23am UTC](https://boards.straightdope.com/t/poker-hand-puzzle-you-might-enjoy/298169/1 "2005-04-07T04:23:17Z")
This was posted on another site and I think I have the answer. Take a bite out of it and see what you come up with. I’ll post it exactly as it was posted on the other site. > [@](#): > > you’re playing heads up 5-card draw poker with no rankings of suits (so that, for example, 2 royal flushes split the pot). the only difference is, instead of being dealt cards, you can see them all and pick any card you want (that isn’t already mucked or in the other person’s hand). the first person picks all his cards, then the second picks his, then the first mucks up to 5 cards and replaces them, then second does the same. the question is: > > if you’re the first to choose, what 5 card hand should you pick first to guarantee a win (not a tie)? ---
**Author:** ![Eonwe](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eonwe/32/240_2.png) [@Eonwe](https://boards.straightdope.com/u/Eonwe)\ **Post date:** [April 7, 2005, 6:02am UTC](https://boards.straightdope.com/t/poker-hand-puzzle-you-might-enjoy/298169/2 "2005-04-07T06:02:55Z")
So, after each person picks a hand, you go around the circle again and each person can trade in any number of cards? ---
**Author:** ![Eonwe](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eonwe/32/240_2.png) [@Eonwe](https://boards.straightdope.com/u/Eonwe)\ **Post date:** [April 7, 2005, 6:08am UTC](https://boards.straightdope.com/t/poker-hand-puzzle-you-might-enjoy/298169/3 "2005-04-07T06:08:32Z")
And, if I am understanding correctly, I’m not sure you can. Picking four aces prevents anyone else from getting a royal flush, but there’s still a straight flush that’ll beat four aces. I don’t think there’s a way to prevent someone else from getting a straight flush. Er, wait, that’s it. Four aces. Then you chuck all but one and go for the straight flush, ace high. Yay, what do I win? 🙂 ---
**Author:** ![hightechburrito](https://avatars.discourse-cdn.com/v4/letter/h/f6c823/32.png) [@hightechburrito](https://boards.straightdope.com/u/hightechburrito)\ **Post date:** [April 7, 2005, 6:23am UTC](https://boards.straightdope.com/t/poker-hand-puzzle-you-might-enjoy/298169/4 "2005-04-07T06:23:24Z")
Take four tens. If your opponent takes four higher cards, you much three of the tens and make a ten-high straight flush. The other three tens being in the discard pile, the best hand possible is a nine-high straight flush. If you opponent makes a straight flush (which must be nine-high at best, as you have all the tens), you can make a royal flush. ---
**Author:** ![DKW](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dkw/32/3118_2.png) [@DKW](https://boards.straightdope.com/u/DKW)\ **Post date:** [April 7, 2005, 6:30am UTC](https://boards.straightdope.com/t/poker-hand-puzzle-you-might-enjoy/298169/5 "2005-04-07T06:30:51Z")
I’ve seen this before (two places, in fact; an old book about gambling scams and the Grey Labyrinth website). I’m going to do everyone a favor and nail this one shut right here: Pick four tens and any other card, then on the draw (regardless of what your opponent does), discard three tens and the odd card and build to a straight flush of at least ten-high. Since without any tens, the best your opponent can do is a nine-high straight flush, you win. Caveat: This only works if you’re not using the rule prohibiting 4-card discards unless the remaining card is an ace (which I’ve _never_ seen anywhere other than Grey Labyrinth, BTW). With the rule in effect…as far as I can tell, there’s no solution. ---
**Author:** ![DKW](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dkw/32/3118_2.png) [@DKW](https://boards.straightdope.com/u/DKW)\ **Post date:** [April 7, 2005, 6:32am UTC](https://boards.straightdope.com/t/poker-hand-puzzle-you-might-enjoy/298169/6 "2005-04-07T06:32:34Z")
Man, that was fast… Well, now that that’s settled, anyone want to tackle it with the variation? (Last I’ve heard, there’s still no definitive answer from GL.) ---
**Author:** ![Dead\_Cat](https://avatars.discourse-cdn.com/v4/letter/d/9fc29f/32.png) [@Dead\_Cat](https://boards.straightdope.com/u/Dead_Cat)\ **Post date:** [April 7, 2005, 9:58am UTC](https://boards.straightdope.com/t/poker-hand-puzzle-you-might-enjoy/298169/7 "2005-04-07T09:58:24Z")
> [@Eonwe](#): > > And, if I am understanding correctly, I’m not sure you can. Picking four aces prevents anyone else from getting a royal flush, but there’s still a straight flush that’ll beat four aces. I don’t think there’s a way to prevent someone else from getting a straight flush. > > Er, wait, that’s it. Four aces. Then you chuck all but one and go for the straight flush, ace high. > Yay, what do I win? 🙂 This is wrong because if you take four aces and, say, one king, your opponent takes four queens and a king. Then the best hand you can make is a jack-high straight flush, and you won’t be able to prevent his queen-high straight flush. Took me a while to work this out, though! ---
**Author:** ![Eonwe](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eonwe/32/240_2.png) [@Eonwe](https://boards.straightdope.com/u/Eonwe)\ **Post date:** [April 7, 2005, 3:27pm UTC](https://boards.straightdope.com/t/poker-hand-puzzle-you-might-enjoy/298169/8 "2005-04-07T15:27:20Z")
> [@Dead Cat](#): > > This is wrong because if you take four aces and, say, one king, your opponent takes four queens and a king. Then the best hand you can make is a jack-high straight flush, and you won’t be able to prevent his queen-high straight flush. Took me a while to work this out, though! Thanks! I was looking at this after other folks seemed to have the right answer and couldn’t quite get how aces wouldn’t also work. ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [April 7, 2005, 4:34pm UTC](https://boards.straightdope.com/t/poker-hand-puzzle-you-might-enjoy/298169/9 "2005-04-07T16:34:36Z")
> [@DKW](#): > > Man, that was fast… > > Well, now that that’s settled, anyone want to tackle it with the variation? (Last I’ve heard, there’s still no definitive answer from GL.) The variation is going to be quite tough to analyze I think, my gut feeling is that it’ll end up with either player able to force a draw (or better, if the other player plays sub-optimally.) Here’s where I’ve gotten so far. Without the ‘draw four to the ace’ exception, I’m pretty sure B can win unless A leaves him an opening to get a royal flush (and then gets one himself.) if A plays to prevent B from getting a royal flush, then he can have only two cards that are in sequence for a straight flush of his own. B can block that straight flush, and set up two potential straight flushes… one below A’s, and one in another suit. If A plays defensively on his second round to keep B from making a straight flush, then B should be able to annhililate him with a combination (four of a kind or a full house.) Drawing four to the aces is the complication that I haven’t quite sorted out yet. My first thought was that A might be able to win through by starting with four aces and a king, thus giving him the potential to draw down to a royal flush in all four suits or stick with the best non-straight-flush hand possible. B would not be able to defend against this successfully with four queens and a king, or four queens and a jack, because A could move his king to block off B’s only straight flush possible. However, the counter-play would be: A: Four aces and the king of hearts B: Four tens and the nine of spades. B is now threatening to build 9-T of spades into a straight flush either up (K-Q-J-T-9) or down (T-9-8-7-6) or some combination of both. for A to defend against all possible straight flushes in spades, he would need to break up his four aces. But if he does, B can stand pat with his four tens. Am I missing some other opening move of A’s that he might have better luck with? 😉 ---
**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\ **Post date:** [April 11, 2005, 2:42am UTC](https://boards.straightdope.com/t/poker-hand-puzzle-you-might-enjoy/298169/10 "2005-04-11T02:42:32Z")
Hope nobody minds if I bring this thread back based on an interesting development. I actually was fooling around with a deck of cards and played both sides of the following ‘game’, which seems to indicate a first-person win in the variant unless there’s a counter-play that I’m not seeing. A draws Ace H, Ace S, Ace C, Jack D, Ten D _(This is quite a good opening… he is threatening four royal flushes and a straight flush jack-high in diamonds, as well as two other straight flushes in diamonds that depend on building J-T both up and down.)_ B considers, draws King H, King S, King C, Queen D… and then Queen S _(This is the only countermove I can see that even hopes to give B a leg up in straight flushes. It blocks off all of B’s royals and everything above the jack-high in diamonds, and it threatens a king-high straight flush for B in spades.)_ However, after a big of thought, A discards his diamonds, draws the Ace D and the Jack S. _(He now has the highest possible non-straight-flush hand (excepting four aces with a higher court card) and has blocked off B’s only possible SF. )_ B: “Darn it!!” Reluctantly throws away his Queen D for a King D, just about the only improvement he can make, and it isn’t enough. So, is there a counter for this?? It would presumably involve B taking the Ace D in his turn, but is there a way to do that and keep A from walking away with a winning SF??