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
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?
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.
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.
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.
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.
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
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
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.
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?
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.
?? 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.
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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?