cute Gardner problem involving pseudo-poker

gumpzilla · #1 10-11-2007, 02:09 AM

I saw this problem last night flipping through an old Martin Gardner book. I don't think it's very hard, but it's kinda fun, and I'll present a slightly more open-ended version of the question.

Two players A and B agree to play a game. They spread a normal 52 card deck face up. Player A first draws five cards, and then player B draws five cards. Following the initial draws, player A may discard any number of his cards that he chooses and draw from the remaining unchosen cards; his discards are out of play. Player B does likewise.

Does either player have a winning strategy? If so, what is it?

Nielsio · #2 10-11-2007, 02:27 AM

I think the first player has to take all the tens and force the opponent to lose because A can now make the highest straight flush no matter what.

tshort · #3 10-11-2007, 02:47 AM

Nielso: Maybe change to white?

Nice ... looks right.

<font color="white">
Player B would have to pick up say the jacks and other card won't matter. Player A will end up with a T high straight flush and Player B can only have 9 high. </font>

onesandzeros · #4 10-11-2007, 03:33 AM

Player A. He gets to go first and since the deck is spread face up he draws akqjt of spades for the nut royal flush.

TomTom · #5 10-11-2007, 07:27 AM

[ QUOTE ]
Player A. He gets to go first and since the deck is spread face up he draws akqjt of spades for the nut royal flush.

[/ QUOTE ]

And then player B draws AKQJT of one of the three remaining suits and they chop.

OP asks for a winning strat, not break-even.

Nielso seems to have nailed it.

onesandzeros · #6 10-11-2007, 08:06 AM

ya I think he got it. I was thinking the spades would out rank since this is not a typical poker game.

NNNNOOOOONAN · #7 10-11-2007, 08:13 AM

i believe that's only in the deal for the button phase of poker.

playing 7 stud two royal flushes chop the pot.

vhawk01 · #8 10-11-2007, 08:44 AM

Wait are there multiple draws? Reading the problem it seems like single draw. If player A draws all the tens, he is going to have 4 tens. And lose.

Nielsio · #9 10-11-2007, 08:51 AM

[ QUOTE ]
Wait are there multiple draws? Reading the problem it seems like single draw. If player A draws all the tens, he is going to have 4 tens. And lose.

[/ QUOTE ]

Reading comprehension?

"Following the initial draws..."

gumpzilla · #10 10-11-2007, 11:07 AM

The 4 tens is right.

It turns out 3 tens, and then the A and 9 in the suit in which you don't have a T also works, I believe.