Kominers’ Conundrums: Poker with zero privacy

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By Scott Duke Kominers, Bloomberg Opinion

LAST week’s puzzle was completely hidden, so this week I’m putting everything on the table — the poker table, that is:

Daffy and Donald decide to play a game of five-card draw poker. They hate randomness, so they play with all 52 cards faceup. Daffy goes first, and gets to pick whichever five cards he wants; Donald chooses five cards from those that remain. Then Daffy can discard up to five of his cards and pick replacements from the cards left in the deck; after that, Donald does the same. (Both see which cards the other chooses and discards, and discarded cards are removed from the game.)

The goal is to have the best poker hand at the end. Since Daffy goes first, Donald wins if the hands tie.

Who wins, and what’s their winning strategy? And what happens if Daffy and Donald play the same game but add in two “wild” cards, which can represent any card of any suit?

The poker hands are ranked as follows:

And for the purposes of this puzzle, the scoring just uses hand-quality ranks, rather than hand-and-suit ranks. That means if Daffy and Donald both get royal flushes, it’s a tie — resulting in a win for Donald. (Otherwise, the game would be boring because Daffy could just grab the royal flush of spades and guarantee his victory every time.) Similarly, once the wild cards are added to the mix, there’s no special bonus for “five of a kind.”

When you’ve got a role to fill, NICOLAS CAGE is always the answer. The puzzle came with essentially no instructions, but astute readers spotted a number of hyperlinks on individual letters throughout the column. (“Notice anything”; “Work your way”; “solve the mystery”…) Each link pointed to a video clip from an iconic Cage film, queued to one of Cage’s sublime lines. Meanwhile, if you kept track of which letters were linked and wrote them out in sequence, they spelled “NAME OF ACTOR,” indicating that the answer to the puzzle was indeed the star’s name.

Most solvers would probably declare victory there — myself included, if I were figuring out the puzzle instead of writing it. But one of the fun things about these sorts of mysterious brainteasers is that they often have many layers. Especially clued-in readers might have noticed a few other hints pointing to Cage, such as my apology for being “cagey” about the puzzle format, plus the fact that the part of the column with the single-letter links was bracketed on both sides by Cage-related links that didn’t quite fit the format, such as a trailer for the movie National Treasure.

And there was a deeper layer still: If you look again at the words with links, you’ll notice that the linked letter isn’t always in the same place — it’s the first letter in “Notice,” the second letter in “way,” and so forth. If you write out the names of characters Cage was playing in the linked scenes (using last names when possible for consistency) and look at the same letter positions as in the clue words, you’ll see NICOLAS CAGE spelled out.*

That next-level clue uses a puzzle feature called “indexing,” whereby the puzzle gives numbers that point to specific letters in clues. The trick with indexing is to figure out which numbers are the indexes (in this case, letter positions in the linked words), and what’s being indexed (in this case, character names).

Marc Del Mar and Tan Yi Jun — literally within seconds of each other — were the first to figure out this Exotic puzzle; there were 80 other solvers — including Derek Byrne, Jean Cunningham, Rauan Khassan, Stephanie Lo, Stirling Newberry, Jonathan Schachter, and Iolanthe Stronger — plus over 700 who solved a much simpler variant posted to Instagram. Special shout-out to Andre De Janon, whose solution e-mail was written using the same encoding format as the puzzle itself.

Try to solve the Mission’s mysterious boarded-up window puzzle (; or Smithsonian Magazine’s new crosswords ( Last week we transformed the game Magic: The Gathering into Uno (; this week, why not make it into an all-purpose computer ( Read up on Frank Ramsey, “The Man Who Thought Too Fast” (; take virtual tours of seven spectacular libraries (; or explore the World’s most Bohemian Geography ( Play hide-and-seek with a virtual cat(; ogle Animal Crossing’s best virtual hats( And inquiring minds want to know: If black holes trap light, then why are they bright (

In addition to solutions, please send paradoxes, paraphernalia and/or your favorite puzzles to

*Did you know that “NICOLAS CAGE” and “NAME OF ACTOR” have the same number of letters? More fun facts courtesy of Conundrums!