If you take 4xJ and they take 4x10 you cannot discard and make a royal flush. If you discard the highest hand you could make would be a 9 high straight flush, which they could beat with a 10 high straight flush.
I think if your 5th card in any of your scenarios is a 10 then you still win?
Discourse has revealed that this is quite the old puzzle.
Yeah, if you listen to the broadcast, they spell everything out. If you just read the transcript in the OP, relevant stuff gets left out (or, if you’re feeling charitable, glossed over, for folks who they’re maybe guessing already heard it).
For whatever it’s worth, I read somewhere that the suits themselves are ranked. Hearts represent the clergy, the highest social class; spades the knights, the second-highest social class; diamonds the merchants, the third-highest social class; and clubs the peasants, the lowest class.
HOWEVER, I don’t think modern poker recognizes these distinctions. If Player A has a Royal Flush in Hearts, and Player B a Royal Flush in Clubs,* I think it’s still a split pot. But I could be wrong.
*Obviously this isn’t possible in the most popular poker variant - Texas Hold 'Em - but my point still stands.
No takers for taking a Joker to make five 10s? 
There is no rank of suits in poker.
I believe you, and the source whence I read that may have been one of those “Startling Facts You Didn’t Know!” lists whose factuality is … questionable.
The only way that can happen is if you are playing poker with, say, the joker cards being wild cards. If you got 4 of a kind and a joker card, that would qualify as 5 of a kind, and 5 of a kind beats a straight flush.
I assume you mean the 10 of diamonds, since you don’t have the ace.
He drew 5 cards, all the 10s and an ace
But the person picking second has 4 aces, so the ace isn’t player 1’s fifth card.
If player 1 picks 4 10s and the ace of diamonds, player 2 would have to pick 4 kings (and another ace just for kicks). You’d end up in the same endgame, with P1 having a queen high straight flush (instead of a king high straight flush) and the best P2 could get would be the same 9 high straight flush. The only difference would be whether the winning hand starts with a queen or a king.
Hmmm. In Bridge, the suit ranking is Spades - Hearts - Diamonds - Clubs, so that would be knights over clergy over merchants over peasants.
Now, in Sheepshead, it’s Clubs - Spades - Hearts - Diamonds (although diamonds are always trump), so that would be peasants over knights over clergy over merchants, but money trumps anything else.
Here’s the full breakdown.
You have a standard fifty-two card deck. No jokers. No wild cards. You’re following standard poker hand rankings. The top three hands in order are royal flush>straight flush>four of a kind. In case of a tie, high card wins.
Player #1 has access to the full deck. They can take any five cards they wish into their hand. Then Player #2 is handed the deck and they can take any five of the remaining forty-seven cards into their hand. This is all down openly with both players being able to see what cards are taken. (Even if they can’t see the cards that are taken, each player would know by seeing what cards remain in the deck.)
Player #1 now has the opportunity to discard any cards in their hand and choose replacement cards out of the forty-two card deck. Player #2 can then discard any cards in their hand and choose replacement cards out of the deck. Player #2 cannot take any of the cards Player #1 discarded.
Scenario 1:
Player #1 chooses all four tens and a random card. Call it 10-10-10-10-x.
Player #2 cannot choose the cards to form a royal flush because a royal flush is A-K-Q-J-10 (in one suit) and there are no tens left in the deck.
Player #2 can draw a straight flush by choosing cards to form a 9-8-7-6-5 (in one suit). If they do, Player #1 can draw A-K-Q-J in a different suit and match it to the 10 they already have in that suit. Player #1 now has a royal flush.
Player #2, as noted above, cannot create a royal flush.
Player #1 beats Player #2.
Scenario 2:
Player #1 chooses all four tens and a random card. Call it 10-10-10-10-x.
Player #2 chooses all four aces and a random card. Call it A-A-A-A-x.
Player #2’s four of a kind outranks Player #1’s four of a kind.
Player #1 draws a K-Q-J-9 in any suit and matches it to the 10 they already have. Player #1 has a king-high straight flush.
Player #2 cannot form a royal flush because they cannot get a 10. They cannot form a king-high straight flush because they do not have a 10. The best hand they can form is to choose 9-8-7-6-5 in any suit that isn’t the one Player #1 chose.
Player #1’s king-high straight flush beats Player #2’s nine-high straight flush.
Scenario 3:
Player #1 draws four aces and a random card. Call it A-A-A-A-x.
Player #2 draws four kings and a random card. Call it K-K-K-K-x.
Player #1’s ace-high four of a kind beats Player #2’s king-high four or a kind. But a royal flush or a straight flush will beat a four of a kind.
Player #1 cannot form a royal flush because Player #2 took all the kings. But they can choose a Q-J-!0-9-8 of any suit and form a queen-high straight flush.
Player #2 cannot form a royal flush because Player #1 took all the aces. But they can choose a Q-J-10-9 in any suit other than the one Player #1 chose and form a king-high straight flush.
Player #2’s king-high straight flush will beat Player #1’s queen-high straight flush.
Scenario 4:
Player #1 draws four jacks and a random card. Call it J-J-J-J-x.
Player #2 draws four tens and a random card. Call it 10-10-10-10-x.
Player #1’s jack-high four of a kind beats Player #2’s ten-high four or a kind. But a royal flush or a straight flush will beat a four of a kind.
Player #1 cannot form a royal flush because Player #2 took all the tens. But they can choose a 9-8-7-6-5 of any suit and form a nine-high straight flush.
Player #2 cannot form a royal flush because Player #1 took all the jacks. But they can choose a 9-8-7-6 in any suit other than the one Player #1 chose and form a ten-high straight flush.
Player #2’s ten-high straight flush will beat Player #1’s nine-high straight flush.
Hopefully all of this tedious detail will illustrate all of the possible plans and demonstrate why drawing four tens first will beat any other move.
I think most of the confusion comes from the scenario as originally presented did not indicate:
1 - There were two goes.
2 - The players could discard and draw.
The few times suit ranks have come up at local informal games have used reverse alphabetical as described but I never considered the tools and occupations behind the icons.
I’ve never understood the need to single out a royal flush as a distinct ranking. An ace-high straight flush beats a king-high straight flush; no special name or ranking is necessary.
I think the idea is that a straight flush can be beaten but a royal flush is unbeatable. So they came up with a special name for the unbeatable hand.
A big fad these days is “AI note-taking”. It’s even a feature in Microsoft Teams at work. It will listen to a chat (for example, a meeting) and try to take notes like a human admin assistant.
Except that AI is more like a digital parrot and doesn’t really understand anything, so it will often miss the point and omit important details that help everything make sense.
I’m almost positive that’s what Cartalk did here.
This puzzler was indeed recycled from September 2000. The correct transcript is found here: