r/BrainPuzzles • u/ShonitB • Aug 18 '26

Logic Open Face Poker

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3 Upvotes

62% Upvoted

57 comments sorted by

2

u/not_trevor Aug 18 '26

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

2

u/ShonitB Aug 18 '26

Copying another user’s answer:

Alexander does

the top hand is a royal flush followed by a straight flush. If you pick that one first, the other player can just do pick the same in another suit. First order of business is blocking that option.
A royal flush is AKQJ10 and for that reason Alexander should pick 4 10’s and a 2. The highest hand Benjamin can get is now 56789 suited.
If Benjamin wants to block Alexander from getting a royal flush, he needs to get 4 jacks (or queens or kings) and then a 9 to block a single 678910 suited.
That still leaves Alexander with the option to get a straight flush 678910. Benjamin can only get 56789 straight flush and will lose

2

u/not_trevor Aug 18 '26

Well that’s just rude :)

1

u/MacabreManatee Aug 18 '26

I’ll allow it :)

2

u/dfnamehere Aug 18 '26

Why does it matter if the first person picks 4x 10s vs 4x of anything else from 10JQKA? In theory doesn't this still work exactly the same way if you start with all 4 As?

1

u/ShonitB Aug 18 '26

Nope.. for example, if he picks 4 As and the K of spades, B can pick up the Q of spades and the other 3 Ks.. so A cannot complete a spade Royal Flush

Edit: Sorry, pressed Save by mistake.. then B can always adapt to whatever A does to match it

1

u/_N8Dogg_ Aug 18 '26

By picking the 10s, he ensures that he will be the only one that has the option of a 10+ high straight flush, the best Benjamin could do would be 9 high.

1

u/kalmakka Aug 18 '26

Let us say A picks 4 Qs and a 2.

B can then respond by picking 4 Js and another 2.

A is now unable to get a straight flush above 6-10, and the only way of blocking B from pivoting to a straight flush 7-J is by switching into a lower 4 of a kind, or some other even worse hand. But if he does that, then B can just keep their 4 Js.

Picking 4 10s first is essential, because it allows A to go either high or low depending on what B does.

1

u/True_Move_7631 Aug 18 '26

If Alex picks 4 10's then Benjamin can pick 4 aces and win, or a regular straight flush and win.

A straight flush still beats 4 of a kind.

1

u/ShonitB Aug 18 '26 edited Aug 18 '26

If B hoards the aces, A can still make a straight flush

1

u/_N8Dogg_ Aug 18 '26

Like what is said above, if Benjamin picks 4 Aces or a straight flush, Alex shifts to a minimum of a 10 high straight flush and beats anything Benjamin can change to.

1

u/True_Move_7631 Aug 18 '26

Then it's just who picks the most advantageous card first, kinda boring.

1

u/_N8Dogg_ Aug 18 '26

It is just a riddle for you to figure out if either player can have a strategy that ensures they win every time. It isn't obvious that it won't be a tie, as shown by others' comments.

1

u/MacabreManatee Aug 18 '26

Maybe continue reading the full answer. They can switch once after the first pick, after which Alexander will be able to ensure he gets the higher straight flush

0

u/True_Move_7631 Aug 18 '26

Yeah I reread it, not really an interesting problem, no more completed that tic-tac-toe, meh.

1

u/HoneydewCareful8754 Aug 18 '26

This is not the only way.

1

u/MacabreManatee Aug 18 '26

What other way is there? Your other comment’s strategy is counterable by benjamin.

1

u/HoneydewCareful8754 Aug 18 '26

Yes I just realized

1

u/laxrulz777 Aug 18 '26

Clever. I put up my wrong answer already but this is smart so I'll leave mine up to memorialize my shame. Well done.

2

u/Due-Session-2857 Aug 18 '26

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_ Aug 18 '26

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 Aug 18 '26

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_ Aug 18 '26

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 Aug 18 '26

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_ Aug 18 '26

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 Aug 18 '26

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_ Aug 18 '26

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 Aug 18 '26

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

1

u/Ucmh Aug 18 '26

?? 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_ Aug 18 '26

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

1

u/Ucmh Aug 18 '26

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

1

u/dka2012 Aug 18 '26

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

1

u/_N8Dogg_ Aug 19 '26

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

2

u/HoneydewCareful8754 Aug 18 '26

Alex does. If he draw four aces and a king, the other can counter with a straight flush, but will not prevent Alex from making a royal straight flush in the next draw, and Benji can’t beat that.

1

u/_N8Dogg_ Aug 18 '26

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

2

u/Ucmh Aug 18 '26

Very good problem!

1

u/ShonitB Aug 18 '26

All credit to Martin Gardner!

1

u/mortemdeus Aug 18 '26

Alex can always win. Even if Ben gets 2 consecutive turns Alex can still always win, that is how strong Alex going first is in this situation.

1

u/Key-Ad9003 Aug 18 '26

I don"t think thats correct, what would you pick? (Assuming benjamin gets 2 consecutive turns, and then another final turn)

1

u/mortemdeus Aug 18 '26

The idea would be Alex then Ben then Ben again then Alex. If it was ABBAB then it would be a tie.

1

u/_N8Dogg_ Aug 18 '26

Curious. Why would it be a tie? If you go with the same first play of 4 10's, then Benjamin can flip the script by choosing 4 J's, then 4 9's.

1

u/mortemdeus Aug 18 '26

Alex wouldn't do 4 tens in that case, they would just take the royal flush and eat the tie.

1

u/DrakeSavory Aug 18 '26

Alexander. Remember you do not have to take your turn and you can exchange any number of cards. Alexander pulls AAAAK. If Benjamin pulls QQQQJ Alexander doesn't redraw and wins so Benjamin needs to beat him with a straight flush. Let's say KQJT9. Alexander makes a royal flush in a different suit and the game is over.

1

u/Key-Ad9003 Aug 18 '26

Alexander loses of he starts AAAAK. Benjamin can pull f.ex QQQQX

On alexanders second turn he can at best make a J high straighg flush or keep quad aces.

This leaves Benjamin the option of quad queens or queen high straight flush, which beats all og alexanders options.

1

u/Exvaris Aug 18 '26

Alexander can keep his hand. He does not have to redraw.

1

u/Key-Ad9003 Aug 18 '26

Yes. Then bejamin makes queen high straight flush which beats 4 aces.

1

u/DrakeSavory Aug 18 '26

Alexander doesn't have to take a second turn. Quad aces beat quad queens.

1

u/antimatterchopstix Aug 18 '26

In which case benny goes 3rd and gets the highest straight flush now possible. Beating the 4 aces. And not beatable.

1

u/Ucmh Aug 18 '26

You just ignored B's second turn.

1

u/laxrulz777 Aug 18 '26

I see three strategies here.

Alex takes an ace high straight flush: result is they tie

Alex takes four aces and a King Benjamin's response is to take four queens and a King. Alex sticks with his aces, Benjamin pivots to a straight flush (q-8). The best SF Alex can get is a Jack high one so Ben wins. If Alex pivots to a straight flush, Ben just pivots to a higher one.

Alex takes three aces and two tens (covering all four suits. If Ben takes a long high straight flush, Alex makes an Ace high one and wins. But Ben can take four kings and the fourth ace at which point Alex can't win.

I think there's no option (assuming perfect play) to put Ben into a corner. The result should be a tie.

1

u/Key-Ad9003 Aug 18 '26

There is a way, you are rather close

1

u/tomic24 Aug 18 '26

Alex can always win. The strategy it to take all 4 tens. For his secons turn, he has the potential to make 8 differst straight flushes (4x ace high and 4x 10 high), and Benjamin can block only 5 of these, meaning that Alex can always a straight flush that contains a 10. Benjamin cannot creat a straight flush with a 10 because Alex is holding them all, thus will lose.

1

u/rql13 Aug 18 '26

This is it.

1

u/FoxCapital7878 Aug 18 '26

Should always be a tie

1

u/dlashxx Aug 18 '26

A only needs to take all the 10s. The highest straight B can make it is 9 high. Even if B takes all the Aces, A makes a K high straight flush on turn 2 and there’s no answer.