The Poker Game
We goofed. When this puzzle was originally posted, we had a particular solution in mind. However, after studying the problem carefully, we discovered that our flawless strategy has a minor flaw. Which sort of ruins a very nice puzzle. Fortunately, in the Grey Labyrinth we have learned humility and wisdom. The wisdom we have learned is this: Blame Harry Anderson.
No, wait, the real wisdom we have learned is that everything is a puzzle. So we'll transform our goof into a new puzzle. (At least we didn't discover the goof by posting the solution and having some else find it.)
The solution we had in mind was the nigh-invulnerable hand of four aces and the ten of spades (or hearts, whatever). For months this was considered unbeatable. Then, today as I was writing the solution, I thought, "Hey! What if..." And so it goes.
Obviously, a tie may be assured by the first player by selecting a royal-straight flush. But for a while we thought a guaranteed victory could be obtained with the four-aces-ten combo. So as an exercise for the reader, see if you can figure out the counter-attack. This may not be an entirely fruitless effort, since the hustle described here is a REAL hustle described in at least two books (and now apparently wrong).
Finally, if anyone thinks they have come up with a bullet-proof opener (no, not a royal straight flush) which is guarenteed a win rather than a tie, please let us know. And, if anyone ever offers you this bet, play the sucker*.
Note: It has been pointed out that the hustle as described in Harry Anderson's book did not use the rule prohibiting discarding four cards unless the card being kept is an ace (standard though it may be). Without this rule, there is a winning hand for the first player, that being a hand containing four tens (this hand can be extended into a straight flush in whatever direction is left open by the second player, guaranteeing at least a ten-high straight flush, while the second player can only get a nine-high straight flush).