Recent discoveries near the Tiber River cast a new light on the life of Saint Valentine.
On the banks of the Tiber near Ponte Milvio, archaeologists discovered artifacts relating to the lifestyle of Valentinus, patron saint of Rome. While generally considered a devout Christian, new evidence shows that Valentinus was hardly a saint but a gambling addict at poker and bridge, as well as an alcoholic. On the Ides of December, a marble slab was unearthed with the following inscription:
Victor triplici→ Cum regia ruborem, cor quattuor, et in celia. -Valentinus CCLVII
A few familiar words from high-school Latin, but I needed Google Translate to obtain:
Triple winner→ Royal flush, four hearts, and a brew. -Saint Valentine A.D. 257
Etched on the reverse side of the slab was a curious diagram:
Saint Valentine evidently was South with a royal flush versus everyone else’s king-high straight flush, which would win a huge pot at poker (imagine all the raising). Further, at bridge he was cold for 4 , while East-West could make at most 3 . But what about the brew? Aha! South can win a beer by discarding a diamond from dummy as trumps are drawn, then the last trick could be won with the 7.
For those who think bridge did not exist in ancient Rome, you are wrong — and I offer proof!
Alas, third-century gaming is ancient history. Poker these days has hit a roadblock, with many casinos forced to close their doors because of the pandemic, so forget about winning. Now is the time to think losing at poker, which brings me to the puzzle:
Construct a deal with bad poker hands where South can make 4 and win a beer against any defense.
Gazillions of such deals exist. Ties will by broken by worst poker hands, in the priority: North, South, West, East. Poker hands are determined by choosing whichever five cards (out of 13) produce the best hand. Challenge yourself — or be lazy and try this poser:
1. Which “two pair” is the worst poker hand in a bridge hand?
Quit
Congratulations to Tim Broeken, not only for this Valentine’s Day victory, but as the winningest participant of this web site. I believe this is his twelfth outright win — four hat tricks? — but I may have lost count, as it feels like a ‘broeken’ record. Tim was the first of six to submit optimal solutions, ranked below by date-time of entry.
Over the years I’ve run a number of puzzles involving poker hands within a bridge hand. Most notable was World Series of Bridge, the only puzzle which eluded an optimal solution — hey, I won! Others were The Seven Percent Solution, Victory Celebration, Just Another Zero, Reese’s Pieces and Toughest Beer in Bridge. The last also involved the beer card, and I can assure you from my Army days that poker and beer come together often.
There are 7462 distinct poker hands. The following table shows the breakdown by generic type, the number of distinct hands, and how many of each can be best in a bridge hand (13 cards).
The worst possible poker hand in a bridge hand is two pair, specifically threes and twos with an ace kicker, which the top eight solvers managed to give both North and South. One pair is obviously impossible because the remaining 11 cards would have to form a straight, another pair or three-of-a-kind.
The best poker hand that cannot be best in a bridge hand is four aces with a three kicker, because one of the remaining cards must be higher than a three. If you ignore kickers, the answer is three tens, because the remaining cards are forced to form a straight or full house. Likewise for three fives; in fact all three-of-a-kind bridge hands must contain every card rank but a five and ten, with one of them tripled.
The rarest best poker hand in a bridge hand is four deuces with a five kicker, because the 13 cards are forced to be 2222333444555.
Congratulations! You now know everything you will never need to know.
Now let’s look at some constructions. The first is by Foster Tom, who notes that 4 is easily made, and declarer can maneuver to win a beer by losing a club and two spades early.
Foster Tom: The worst possible poker hand is 3322A, and giving that to North and South leaves 11 card ranks for West. Two must be removed to eliminate straights, [which necessitates] four repeated card ranks, so 7766A is the worst poker hand for West. East must then have three tens and two of whichever high card rank is absent from West, [optimally TTTJJ].
The next solution relies on singletons instead of finesses, but 10 tricks roll home with a brew.
Tom Slater: Black-suit leads seem to be poor choices, as they tend to aid declarer’s timing. Win a red-suit lead expensively in North to lead a club, and subsequent red-suit leads in South (unblocking diamonds as required) and there are enough entries to ruff two clubs and draw trumps while retaining one trump for control to safely exit.
And based on a similar deal:
Samuel Pahk: Declarer can score six trumps and four diamonds.
David Brooks: This satisfies the conditions: 4 by South with the 7 winning the last trick, and 3 by East or West.
Puzzle conditions did not require East-West to make 3 , so all it earns is style points. But they’re valuable! In my Frequent Solver Program, all you need is three style points (plus $3.00) for a cup of coffee.
This last entry didn’t fare as well in the poker department, but I enjoyed the novel approach of a Moysian fit and topless diamonds, yet still bringing home the bacon, er beer.
Nicholas Greer: The defense cannot touch the late entry in clubs to cash the beer card, nor set up a tap by playing spades, in time to prevent declarer establishing diamonds. If the defense plays a forcing game, spades can be ruffed high in dummy (note the 10 onside) to avoid any blockage issue.
Another curiosity of Nicholas’s deal is that East-West make nothing; even one spade is routinely defeated. I think I see the picture: ‘Saint’ Nicholas went out of his way to please Saint Valentine.
Foster Tom: Careful play wins a beer…
David Brooks: …on a really boring hand!
Inquiring minds need to know: Are these two guys a reincarnation of Foster Brooks?That would explain the beer, but then they’d be too drunk to solve the puzzle.
Tom Slater: Hard to double-dummy solve for the beer.
Nicholas Greer: Manipulating bridge hands for poker fries my brain.
Of course! Last month in I Have a Dream… he cites “French influence,” and now he has fries.
© 2021 Richard Pavlicek
by Richard Pavlicek by Richard Pavlicek