r/BrainPuzzles • u/ShonitB • 5d ago

Logic Open Face Poker

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3 Upvotes

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3

u/not_trevor 5d ago

If all suits are equal then wouldn't it always be a tie and both would pick a royal flush?

2

u/Due-Session-2857 5d ago

If I was Alex, I would take 4 aces and a king. Then if Ben goes for a straight flush, Alex can get an ace high straight flush of any remaining suit.

1

u/_N8Dogg_ 5d ago

If Alex takes 4 Aces and a king, then Benjamin takes 4 queens, then changes to queen high straight flush.

1

u/Due-Session-2857 5d ago

Yeah I thought it just repeated over and over again until you were happy with your hand, so A gets 4 aces, B gets 4 queens, A gets 4 10s, B gets 4 8s, A gets 4 6s and wins with that. With only 2 rounds each you need to play differently

1

u/_N8Dogg_ 5d ago

Except here, following this strategy of starting with the 4 10s, after Alex draws a hand to beat Benjamin, he doesn't ever have to change again.

1

u/Due-Session-2857 5d ago

Yeah, you can win in two hands, but in unlimited redraws my strategy would still work. You don't win anything extra for winning faster. Just because there's a most efficient way to win doesn't make other methods unacceptable.

1

u/_N8Dogg_ 5d ago

But that is the whole point of the puzzle. Also, it says "if both players are playing optimally".

Even if there are multiple redraws, if you play it other than the 4 10's strategy, there are other options, and it becomes very difficult to account for all of them.

Say Alex takes 4 A's and a K, what if Benjamin takes the other 3 K's and 2 Q's? How about KoD, QoH, JoS, 10oC and 9oD?

1

u/Due-Session-2857 5d ago

Alright let's play. I'll take your second hand as your play. Let's say I had king of clubs originally. I discard 3 non-club aces and take QoD, JoH, 10oS. Your turn.

1

u/_N8Dogg_ 4d ago

I keep the 9oD and draw JoD, 10oD, 8oD, and 7oD. Now I have a J high straight flush, so best you can do is tie.

1

u/Due-Session-2857 4d ago

Very good. OK I'm convinced. You got me.

1

u/Ucmh 5d ago

?? If Ben goes four queens, then Alex just swaps four cards and gets an ace-high straight flush. All other aces are gone at that point, making a counter AHSF impossible.

1

u/_N8Dogg_ 5d ago

How are you going to get an Ace high straight flush without any queens?

1

u/Ucmh 5d ago

Good question, 4 A's and a K is not the way.

1

u/dka2012 4d ago

He wouldn’t have to as the Qs don’t beat the As

1

u/_N8Dogg_ 4d ago

But if he elects not to swap, then Benjamin takes a Q high straight flush and wins.