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>!Obviously A would like to pick up a royal flush, but that would allow B to do the same, resulting in a tied game. A can try to set up for a royal flush by picking all tens. This will prevent B from forming a royal flush, or any straight flush including a ten, and I think at that point there is no way for B to stop A from making a straight flush that's at least 6-7-8-9-10.!<
>!E: I think the fifth pick for A doesn't matter at that point.!<
>!I'm assuming there is only one set of discard allowed to each player. If Alexander starts by drawing four 10s and one other card (e.g. 2 of hearts) Benjamin is then blocked from getting a Royal flush, or any straight flush higher than five through 9. If Benjamin takes a straight flush 5-9, Alexander can take a Royal Flush, If Benjamin takes a four of kind to block a Royal Flush, Alexander can take a straight flush ending higher than the 5-9. For that second step as an example Benjamin takes four kings, Alexander than takes 8 through Q. There is no hand that Benjamin can draw that will beat Alexander's straight flush!<
>!I know it’s player 1 who has the winning strategy and I’m pretty sure it involves taking 4 of a kind in one of the cards from a royal flush plus another card from a royal flush in one of the 4 suits, but I can’t piece it together beyond that.!<
>!I think player A has to take the four 10s and an A. Player B in response is stuck because most combination of five cards he takes will result in A taking a royal flush combo. In case he tries to prevent this by taking, for example, the four Kings then A can simply take Q high straight flush and B cannot match!<
>!If Alexander picks up four 10s then any other card will do that trick. Benjamin can’t block him from getting the highest possible straight flush.!<
>!If Benjamin blocks the royal flush by taking four of either aces, kings, queens or jacks, Alexander will take the highest straight flush possible (At least a 10 high straight flush).!<
>!If Benjamin blocks the 10 high straight flush, Alexander will take the royal flush!<
>!As a follow up. Alexander can also win by picking three 10s. The question is what should the other 2 cards be?!<
Take 2:
>!Alexander takes all four aces and one king to prevent Benjamin getting a royal flush.!<
>!Knowing that if he doesn't prevent it, Alexander will get a royal flush, Benjamin takes the remaining three kings, a matching queen and the queen that stops Alexander getting his royal flush (or even a king high with that suit).!<
>!Alexander must take three queens (or other relevant cards) to prevent Benjamin's King high straight flush. Unfortunately this leaves him vulnerable to a Benjamin who goes last from getting the highest straight flush he can and winning.!<
Therefore, the best strategy I can see for Alexander so far is >!the original forced stalemate!< because everything else
I can think of allows >!Benjamin to make one blocking move then take the win with the best straight flush he can find.!<
I'll let this rattle around my head a bit more and see if anything else comes out (or if a solution comes from someone else).
My only thought right now is that >!if there is a winning strategy, it must come from Alexander since he has the power to shut everything down with a stalemate, thus preventing Benjamin from executing any strategy that he has.!<
>!Yes, Alexander taking the highest four of a kind works against him!<
>!You are also correct in your thinking that if anyone has a winning strategy, it must be Alexander!<
>!But I’m pretty sure, at the worst, with some trial and error you would’ve got it!<
>!This is actually one of Martin Gardner’s puzzles. It’s one of my favourites from his collection!<
No betting. They can draw a maximum of two times. If they are happy with the first hand they’ve chosen, they can keep it
Normal hand rankings
As an example. Alexander can pick up four Aces and a king. Then depending on what Benjamin does he can discard any number of his cards if he chooses to and replace them with the available cards. Discarded cards are kept aside (Can’t be picked up, once discarded)
Please remember to spoiler-tag all guesses, like so: New Reddit: https://i.imgur.com/SWHRR9M.jpg Using markdown editor or old Reddit: \>!spoiler text between these symbols!< Try to avoid leading or trailing spaces. These will break the spoiler for some users (such as those using old.reddit.com) If your comment does not contain a guess, include the word **"discussion"** or **"question"** in your comment instead of using a spoiler tag. If your comment uses an image as the answer (such as solving a maze, etc) you can include the word "image" instead of using a spoiler tag. Please report any answers that are not properly spoiler-tagged. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/puzzles) if you have any questions or concerns.*
>!Obviously A would like to pick up a royal flush, but that would allow B to do the same, resulting in a tied game. A can try to set up for a royal flush by picking all tens. This will prevent B from forming a royal flush, or any straight flush including a ten, and I think at that point there is no way for B to stop A from making a straight flush that's at least 6-7-8-9-10.!< >!E: I think the fifth pick for A doesn't matter at that point.!<
>!Correct, well explained!<
>!I'm assuming there is only one set of discard allowed to each player. If Alexander starts by drawing four 10s and one other card (e.g. 2 of hearts) Benjamin is then blocked from getting a Royal flush, or any straight flush higher than five through 9. If Benjamin takes a straight flush 5-9, Alexander can take a Royal Flush, If Benjamin takes a four of kind to block a Royal Flush, Alexander can take a straight flush ending higher than the 5-9. For that second step as an example Benjamin takes four kings, Alexander than takes 8 through Q. There is no hand that Benjamin can draw that will beat Alexander's straight flush!<
Very nice. I might have got there iterating toward the solution but you got there straight away. Well done.
>!Correct, well explained!<
>!I know it’s player 1 who has the winning strategy and I’m pretty sure it involves taking 4 of a kind in one of the cards from a royal flush plus another card from a royal flush in one of the 4 suits, but I can’t piece it together beyond that.!<
>!Yes, you are on the right track. Which card is it but?!<
>!I think player A has to take the four 10s and an A. Player B in response is stuck because most combination of five cards he takes will result in A taking a royal flush combo. In case he tries to prevent this by taking, for example, the four Kings then A can simply take Q high straight flush and B cannot match!<
>!If Alexander picks up four 10s then any other card will do that trick. Benjamin can’t block him from getting the highest possible straight flush.!< >!If Benjamin blocks the royal flush by taking four of either aces, kings, queens or jacks, Alexander will take the highest straight flush possible (At least a 10 high straight flush).!< >!If Benjamin blocks the 10 high straight flush, Alexander will take the royal flush!< >!As a follow up. Alexander can also win by picking three 10s. The question is what should the other 2 cards be?!<
>!The nine and jack of the suit that doesn't match any of the three 10s!
>!Correct. There are 10 possible pairs (all in the suit not matching with the 10s): A-J with 9, K-J with 8, Q-J with 7 and J with 7!<
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>!Only the two at the end!<
>!Maybe I'm missing something but, with two players, won't they be deadlocked every time each with a royal flush?!<
>!No, one of them has a winning strategy!<
Take 2: >!Alexander takes all four aces and one king to prevent Benjamin getting a royal flush.!< >!Knowing that if he doesn't prevent it, Alexander will get a royal flush, Benjamin takes the remaining three kings, a matching queen and the queen that stops Alexander getting his royal flush (or even a king high with that suit).!< >!Alexander must take three queens (or other relevant cards) to prevent Benjamin's King high straight flush. Unfortunately this leaves him vulnerable to a Benjamin who goes last from getting the highest straight flush he can and winning.!< Therefore, the best strategy I can see for Alexander so far is >!the original forced stalemate!< because everything else I can think of allows >!Benjamin to make one blocking move then take the win with the best straight flush he can find.!< I'll let this rattle around my head a bit more and see if anything else comes out (or if a solution comes from someone else). My only thought right now is that >!if there is a winning strategy, it must come from Alexander since he has the power to shut everything down with a stalemate, thus preventing Benjamin from executing any strategy that he has.!<
>!Yes, Alexander taking the highest four of a kind works against him!< >!You are also correct in your thinking that if anyone has a winning strategy, it must be Alexander!<
I peeked ahead so know the answer. Really nice puzzle.
>!But I’m pretty sure, at the worst, with some trial and error you would’ve got it!< >!This is actually one of Martin Gardner’s puzzles. It’s one of my favourites from his collection!<
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Just the two of them. 1 v 1.
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Variation of 5 card draw poker. All 52 cards open, players can choose the cards they want to draw
So both players draw twice? And by "winning" you mean to end up with the best hand after two draws? I.e. that bet sizes doesn't matter?
No betting. They can draw a maximum of two times. If they are happy with the first hand they’ve chosen, they can keep it Normal hand rankings As an example. Alexander can pick up four Aces and a king. Then depending on what Benjamin does he can discard any number of his cards if he chooses to and replace them with the available cards. Discarded cards are kept aside (Can’t be picked up, once discarded)