The Pocker Game's UNRESOLVED answer

[Vinny]

In the puzzle archive there is a puzzle named "The Poker Game" in which the answer introduced another problem (since Minotaur claimed that the first answer was flawed). Has any of you figured out the 2nd part of the puzzle yet? I pulled out my deck of cards last night and had a heck of a time trying to crack it. Is there an answer?

Here's a quik refreshener:

Standard 5 card draw pocker, winner takes the pot. Exception to the rule is that all cards are facing up and players get to choose the cards they want, both for initial dealing and drawing. Cards discarded are returned to the drawing deck.

You, the sucker, have to go first. The first answer that was posted is the hand "Ace(H), Ace(S), Ace(D), Ace(C), 10(H)". This is the "almost" absolute wining hand, but there is a way to beat it or tie it. That's simple enough, i think. (Opponent choose a straight flush, you drop four cards and pick a heart royal flush, opponent picks another royal flush and ties your hand, is that it?)

The 2nd part of the puzzle is to pick a combination that can't be beat. Is there one out there? or is this just a bad puzzle to begin with?


[This message has been edited by vinny (edited 06-13-2000).]

[Ghost Post]

Vinny,
I haven't spent much time on this one yet, I'll let you know if I come up with something. I just wanted to say that as I interpret the puzzle, discards are not returned to the drawing deck during the hand. Cards are only returned when a hand ends in a draw at which time all cards are returned and there's a re-deal.

[Vinny]

Hi Helmet,
You are right, I goofed. The discarded cards are NOT returned to the decks. I assumed they were because of how I play poker (with the cards face down of course), where discarded cards are returned to the bottom of the deck. Those cards wouldn't be redrawn unless there are 6 or more players in the game and almost everybody draw 4 cards.

I should have read the puzzle more closely.
So how does the "nigh-unbeatable" hand of 4 Aces and a 10(S) get beaten? What was the "what if..." that Minotaur was talking about? The only hand that will beat 4 of a kind with Aces is a straight flush, which give me the option on the draw to obtain a royal flush. Hm...I don't know. Guess I should break out my deck and start dealing...

[Ghost Post]

Four J/Q/K and a suitable fifth card (that allows a straight flush) works against the four aces.

[Ewan]

well if the cards arent returned untill the end of the game pick 4 kings and an ace, your opponent draws a straight flush, you exchange your hand for a royal flush useing one of your kings you opponent can't draw this hand since all the kings are now out of play his striaght flush will allways be of lower value than yours?

[Vinny]

Ewan, I am not sure your 4 kings and an Ace is a sure win...

This is your solution (please double check) -

Me : K(H), K(S), K(D), K(C), A(H)

The highest straight flush he can get then is with Queen high.

Him : (straight flush) Q(H), J(H), 10(H), 9(H), 8(H)
(H)
Then I discard 3 kings and get a royal flush with spades.

But what if instead of the straight flush he chooses Q(h), Q(s), Q(d), Q(c) and J(h)?

When its my turn, I could keep the 4 of a kind Kings which will beat his 4 of a kind Queens, but then he has the option of selecting a straight flush on his draw with Queen(h) high, which will then beat the 4 kings....and I can't draw a straight flush with Jack high to beat his 4 Queens because then he would still have that option to draw that Q(h) straight flush.


[This message has been edited by vinny (edited 06-13-2000).]

[IrishJoe]

Silly thought, but why not pick a royal flush in the high suit to start with, since your going first?

Then don't draw.

It can't be beaten, and if suit rank is used it can't be tied.

[Ghost Post]

In poker all suits are equal (the is no suit rank.) So two royal flushes is a draw.

[Ewan]

Vinny, hmm. no I think im still right, say he draws 4 queens and a jack, you can still discard 3 kings and the ace and draw a king high straight flush. He cant beat or draw this becuase (at least from my reading of the puzzle) the discarded kings(and other discards) are now out of play ie. not reshuffled into the deck, hence the highest hand he can draw is a queen high straight flush.

Ahh no wait DOH! of course you cant! hmm yes. OK carrying this logic on how about drawing 4 nines and an ace? he takes 4 kings, you exchange for a 9 high straight flush which is unbeatable? If he trys to stop this by drawing 4 eights you can exchange for a king high straight flush (using one of your nines as the lowest card!)

[Ghost Post]

If you draw 4 nines and an ace, then he can draw a royal flush.

[Ewan]

yes? but only an 8 high one, in which case you draw a king high royal flush and he cant beat it becuase all the nines are gone

(unless you are allowing A K Q J 10 9 straight flushes in which case draw 4 10s)

[Ewan]

oops i mean a k q j 10 straight flushes

[mithrandir]

A,10,10,10,10 looks good to me... 2nd player must draw to defend against all royal flushes (he can't draw a royal flush himself since you have all the 10s), for example he could draw all the Js. But, then you are guaranteed a 10high straight flush, and the best that 2nd player can get is 9high.

[Ghost Post]

Ewan - A royal flush IS an A, K, Q, J, 10 straight flush. It is the highest possible poker hand and is most definitely allowed.

Mith - If you draw A, 10, 10, 10, 10 I only have to stop you from a striaght flush using your ace because you can only draw 4 if the card you keep is an ace. So, if I draw the jack in the same suit as your ace then you CAN'T draw a straight flush at all!

[Murray]

Alright, let's have it out: Somebody play me in an experimental game. I'll draw the "unbeatable" hand first.

I choose:

As Ah Ad Ac 10s

[ewan]

OK, I choose K K K K 2
this stops you drawing a royal flush but leaves me the option of using my final change to get a king high straight flush.

Drew, I dont know what you mean when you say you can only draw 4 to an ace, usualy you can draw any number of cards (up to five) its just that 3 is the optimal amount.

I thought that A high striahg flushes were allowed becuase it seems to imply it in the question (by saying that your royal flush can be drawn, but KKKK allows you to win against AAAA so *shrug*

[Ghost Post]

Ewan, everyone I have ever played poker with has agreed that you can draw 1, 2 or 3 cards unless you hold an ace. If you have an ace then you can draw up to four cards if the card you keep is the ace. I have never seen anyone allow you to draw five cards.

I guess these are the sort of rules that just vary depending on where you play. They do change the puzzle though.

Actually, with your rules drawing four 10's on the first move is a winning hand. The second player has to stop you from getting a royal flush, so he takes he takes one of A,K,Q,J in each suit plus some fifth card. Now you can take a 10 high straight flush and the best he can do is a 9 high so you win!

[This message has been edited by Drew (edited 06-23-2000).]

[Quailman]

That's how I play with real cards and real opponents. With video poker you can draw up to and including five cards, but it's much more difficult to peek and choose your cards.

[Murray]

OK, Ewan. Seeing as you can only draw three cards, I'm gonna hold my four Aces and the ten. Best you can do is hold the cards you have. I win.

Next competitor...step right up:

I'll start again

As Ah Ad Ac 10s

[Ghost Post]

Js Jh Jd Jc 10c

[ZenBeam]

I'll give it a shot:

Js, 10h,10d,10c,9d

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It is so clear, and so it is hard to see.

[ZenBeam]

Drew, if Murray discards the 10s, and selects 9c, what will you do?

Oh, and isn't it about time someone posted a link to the original puzzle?

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It is so clear, and so it is hard to see.


[This message has been edited by ZenBeam (edited 06-23-2000).]

[Ghost Post]

Oh yeah, good point.

Yours works better.

[ZenBeam]

If you set your preferences to go back a year, instead of 30 days, Murray already posted a soluion here.

Apparently, the forums don't go back far enough to where the puzzle was new.

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It is so clear, and so it is hard to see.

[ZenBeam]

And finally, how come the minotaur never posted a solution for this?

[Ghost Post]

Murray shows why A A A A 10 isn't a winner, but that still leaves the question of if a winning hand exists at all. I suspect that it doesn't, but haven't been able to come up with a convincing proof.

[ewan]

well in offical poker you can discard as many card as you like. HOWEVER the reason why many versions only allow you to discard 3 cards is becuase discarding more than 3 is not a very good idea as it dosnt imporve your chances of winning, it is allways better to lkeep the two best cards and discard three rather than discard 4 or 5.

In the puzzle though it implies that you can discard your entire hand and I dont think it works unless you can.

ie. if you can discard you entire hand the answer is 4 tens, which is quirky becuase it dosnt seem to be a very exceptional hand at first glance.

[ewan]

if you can only discard 3 card (4 to an ace, (hang on this would reveal that you had an ace? do you have to show your hand?) then surly AAAA wins every time? your oponent can either draw a king high straight flush, in which case you draw a royal flush which he cant beat since all the aces are out of play. or your opponent draws a card in each suit to stop your royal flushes and another card adjacent in number to one of those four to enable a striaght flush with 3 discards. in which case you can chance your 5th card to stop him drawing a straight flush in that suit and stick with the four aces?

if AAAA is the winning hand this is too obvious so the puzzle must allow 5 discards (as in REAL poker!! not the namby pamby kind you guys obviously play!! usualy I play texas holdem though)

[ZenBeam]

The standard rules of poker allow discarding up to three cards, up to four if the kept card is an ace. I can find the site I read this on later, if someone wants. Regardless, the problem clearly states The first player may then discard up to three cards, or four if the last card they are holding is an ace [...] The second player then does the same, so stop arguing about how many cards may be discarded.

Ewan, four aces and, say, 10s, loses to Js, 10h,10d,10c,9d. See Murray's description at the lnk from my post on Friday at 4:39 pm.

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It is so clear, and so it is hard to see.

[Murray]

Good job, ZenBeam. I didn't think anyone would remember my old solution. I figured I could win several hands before someone found the counter.

[ewan]

hmm why dose Js 10d 10h 10c 9d win?

I cant frind murrays solution please post link.

presumably this hand gives you the option of changing 3 cards for a straight flush with the 10d and 9d and blocking thge first player from selecting higher striaght flush with your other cards.

Ahh i see you can have either the king high or 10 high striaght flush so he cant stop you by discarding only one card.

clever

[ewan]

so what happens if you draw this hand first?

player #2 cant draw a royal flush, he cant stop you getting a royal flush and also draw 4 of a kind but he can draw a queen high straight or a diamond flush to prevent you getting a straight flush by using the Qd and 8d

in which case you can exchange for a diamond flush a full house or four of a kind (if he uses a dimaond flush)

ahh but if he used an ace high diamond flush he could exchance for 4 aces, hmm unless you changed to a fullhouse 10s over aces in which case he would have changed for 4 kings.. you lose

In fact why am I bothering, player #2 can just draw 4 kings and the 8d to win


(hang on can't player one beat this hand with a diamond flush? using the Ad and drawing Qd Jd 8d

it prevents you drawing the striahgt flush both ways, a flush beats any normal straight you draw to the 10d 9d. ahh wait you can exchange for a full house.)

[Murray]

Phew! You are thoroughly confusing.

If you start with

Js 10d 10h 10c 9d

The best hand you can get on the redraw is a straight-flush in hearts.

Your opponent can stop this by drawing

Kd 8d x x x

The next best hand you can draw is a 4-of-a-kind (J, 10, or 9).

Your opponent doesn't care if you get a piddly 4-of-a-kind because he'll get a better one by drawing

Kd 8d Ad x x

If you go for the 4-of-a-kind in either J or 9, you use all three of your discards to draw the three cards you need. If you go for the 4-of-a-kind with 10, you need to discard three, draw the 10 you don's have (10s) and then you have two cards left with which you can block him. Not enough. If you draw an A and a K, he can draw all four Q to win.
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I'm almost completely convinced that there is no hand player one can guarantee a win with. I've tried many, many different things. Nothing works.

If I was ever forced to play this game and felt that my opponent knew the winning defense against the A,A,A,A,10, I would try this hand:

As Kh Qd Jc 10s

There's a real simple hand that beats it, but I would hope it would throw my opponent for a loop.

[ewan]

King high striaght flush in diamonds? (or whatever you had the ace in) yeah you could try and put your opponent off while he was working through the answer. I think you are problably right pabout there being no wining hand, since this would seem to be the scam that the sharp in the puzzle is trying to pull. After all he lets you go first, it wouldnt be a scam unless there was no way you could win. it would be interesting (but difficult) to prove that it was imppossible to win, maybey somone with a supercomputer could work through all the possiblities.

Hmm that gives me an idea, somone could wright a screen saver program like the seti project witch would work trying to solve these sort of puzzles by brute force, people could log onto GL and download the latest version to work on unsoloved riddles

[ZenBeam]

[Murray]

That's it. Like I said, it's easy to beat. But if I had to try something...

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They say it's the thought that counts, but, in your case, I think you'd be better off using your fingers.

[kdawg]

won't Ks Qs Js 10s 9s win?

[Wonko the Sane]

I haven't read all the posts so I don't know if someone said this. But there is an infallable way to beat the hustler.

If you draw
A(s) A(h) K(s) K(h) K(c)

Then the hustler can't draw a royal flush anymore because you're covering all suits with the aces and kings. He also can't block you from drawing your own royal flush unless he draws out 4 of a kind queens. However, if he does that, you can draw the remaining two aces, or the remaining king (depending on which he takes at the fouth card).
Now, someone out there is going to say that he can screw you over by drawing Q(h) Q(c) J(h) 10(h) 9(h), which is one card away from a straight flush, and prevents you from drawing a royal flush. If they do that, you respond by dropping both kings and picking up the 8(h) and the remaining ace.
If he tries to draw any straight flush at all, then you can draw out the royal flush.

Anyone have a way to beat it? I'm sure it's probably beatable or someone would have thought of it already.

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It's not the size of the spork, it's whether or not it's made of #7 recyclable plastic.

[Wonko the Sane]

Nevermind, I think I beat it.

I can't find a way for the first player to win if the hustler responds with
A(c) K(d) Q(h) Q(s) J(h)

Anyone else have a way to beat that response?

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It's not the size of the spork, it's whether or not it's made of #7 recyclable plastic.

[CzarJ]

*pops head in*

Or the hustler could just draw a royal flush of diamonds...

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But when we wake,
It's all been erased...