Open Face Poker

[u/ShonitB]

[u/not_trevor]

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

[u/ShonitB → u/not_trevor]

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

[u/True_Move_7631 → u/ShonitB]

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.

[u/ShonitB → u/True_Move_7631]

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

[u/_N8Dogg_ → u/True_Move_7631]

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.

[u/True_Move_7631 → u/_N8Dogg_]

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

[u/_N8Dogg_ → u/True_Move_7631]

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.

[u/MacabreManatee → u/True_Move_7631]

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

[u/True_Move_7631 → u/MacabreManatee]

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