5
$\begingroup$

During a round of a card game big two, two players decide to show off their hands.

The 1st player has ♥3 ♥4 ♥4 ♥6 ♥6 ♥8 ♥8 ♥K, and

the 2nd player has ♠7 ♠9 ♠9.

It's the 1st player's turn, and he can start with any single card or valid pairs. Now they've seen each other's hands, who will win?

$\endgroup$
  • $\begingroup$ Welcome to Puzzling SE! Take the tour to earn a badge! $\endgroup$ – NL628 Apr 19 '18 at 1:55
  • $\begingroup$ Here's the tour @North mentioned! $\endgroup$ – puzzledPig Apr 19 '18 at 3:17
  • $\begingroup$ It seems that there are duplicate cards in here - four of hearts, six of hearts, eight of hearts and nine of spades are all duplicated... Is there a mistake or is this game being played with multiple decks? $\endgroup$ – Chris Apr 19 '18 at 12:30
4
$\begingroup$

Answer

2 will win.

Observations:

Player 1 cannot put out any pairs first, as then Player 2 will win by beating it with 9 pair, and then using their final card in the next turn.

As such, P1's goal would be to bait out one of P2's 9s. Beat it with King, and remove the remainder of their hand in pairs. Their pairs will always win now, so after that they will have a chance to put out one last card. As such, If P1 only has at most one non-pair card at this moment, P1 wins.

Conversely, P2's goal would be to make sure that after countering one of your 9s with K, P1 has more than one non-pair cards in their hand.

As such

P2 would win, because there is no possible way for P1 to remove the cards in their hand one-by-one without giving an opportunity for P2 to achieve their win condition. P2 is always able to use both their 7 and 9 to force P1 to lose their winning hand.

P2 should wait until P1 uses their first 4 or 6.

At this moment, if P1 still has an even amount of 8, P2 should use 7.
- If P1 doesn't do anything, you use your 9s as a pair next turn and win.
- If P1 counters with 8, their hand will become suboptimal [e.g. 4, 6, 6, 8, K]. You will win.
- If P1 counters with K, your two 9s will become the highest cards in the table and you will win.

On the other hand, if P1 only has one 8 remaining, P2 should use 9.
- If P1 doesn't do anything, you use your 7 next turn.
Now no matter what P1 does, their hand [e.g. 4, 6, 6, 8, K] cannot win against your 9.
- If P1 counters with K, your remaining 9 will become the highest card in the table.
Since P1 has two individual cards remaining (4 and 8), they cannot win before you.

TL;DR: As long as P2 is patient and plays their card correctly, they will win. P1 has no way of using up all their cards without P2 intercepting and creating their own victory condition.

$\endgroup$
  • $\begingroup$ Wow nice one @votbear $\endgroup$ – NL628 Apr 19 '18 at 2:52
  • $\begingroup$ I did not have an answer, but you convinced me that yours is correct. $\endgroup$ – user1032613 Apr 19 '18 at 4:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.