Puzzle 8S77   Main

# Valentine’s Hat Trick

by Richard Pavlicek

Recent archaeological discoveries along the banks of the Tiber near Ponte Milvio cast new light on the lifestyle of Valentinus, the patron saint of Rome. While generally considered a righteous, devout Christian, evidence now reveals Saint Valentine was hardly a saint but had a gambling addiction at poker and bridge, as well as a lust for alcoholic beverages. 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

Some words rang a bell 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:

 Cor quattuor 4 3 2 9 8 K Q J 10 9 4 3 2 K Q J 10 9 4 3 2 8 A 8 7 5 A 8 6 7 6 5 6 5 K Q J 10 9 Cum regiaruborem 7 5 A K Q J 10 A 7 4 3 2 6

Saint Valentine apparently was South, with a royal flush versus everyone else’s king-high straight flush, which would win a huge pot at poker (imagine the raising). Further, at bridge he was cold for 4 , while the most East-West could make was 3 . But what about the brew? Aha! South can win a beer by pitching a diamond from dummy as trumps are drawn, then winning the last trick with the 7.

For those who think bridge did not exist back then, you are wrong — and I have 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 where South can make 4 and win a beer against any defense, but with bad poker hands.

Of course gazillions of such deals exist, especially with “How bad is bad?” undefined. Ties will by broken by worst poker hands, in the order of priority: North, South, West, East. Poker hands are determined by choosing whichever five cards (out of 13) produce the best poker hand.

 Puzzle 8S77   Main Top   Valentine’s Hat Trick

## Tim Broeken Wins

This contest ran from December 17 (2020) to February 14, 2021. There were 19 entries from 14 persons (multiple entries were allowed but only the latest one counted) of which 10 were successful. Cool! Publishing a Top Ten List could be the break I need to get into show business. Hey, it worked for David Letterman.

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.

Winner List
RankNameLocationPoker Hands: N S W E
1Tim BroekenNetherlands3322A 3322A 7766A TTTJJ
2Duncan BellEngland3322A 3322A 7766A TTTJJ
3Foster TomCalifornia3322A 3322A 7766A TTTJJ
4Tom SlaterEngland3322A 3322A 7766A TTTJJ
5Jurijs BalasovsLatvia3322A 3322A 7766A TTTJJ
6David BrooksAustralia3322A 3322A 7766A TTTJJ
7Samuel PahkMassachusetts3322A 3322A JJTTA QQTTA
8Jean-Christophe ClementFrance3322A 3322A JJTTA QQTTA
9Nicholas GreerEngland3322A QQ22A TT88A AQ965
10Stephen MerrimanNew Zealand3322A KK22A 6655A TTTJJ

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## Solution

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.

### Bridge Poker 101

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).

Generic TypeHandsBridge
Straight flush1010
Four-of-a-kind156130
Full house156156
Flush12771277
Straight1010
Three-of-a-kind85811
Two pair858309
One pair28600
High card12770
Totals76421903

The worst possible poker hand (in 13 cards) 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.

What is the best poker hand that cannot be best in a bridge hand? Answer: 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.

What is the rarest best poker hand in a bridge hand? Answer: Four deuces with a five kicker, because the 13 cards are forced to be 2222333444555.

Congratulations! You now know everything you’ll 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.

 4 South 7 6 4 J 9 8 2 A Q 3 2 K 3 K Q 10 9 7 6 5 6 4 A 7 5 4 A J 8 5 K 10 10 9 5 Q J 10 8 3 2 A Q 4 3 K J 8 7 9 6 2

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].

Foster neatly explains the logical path to obtain worst poker hands in the priority order: North, South, West, East. Six of the 10 solvers accomplished this feat.

The next solution relies on singletons instead of finesses, but 10 tricks roll home with a brew.

 4 South 8 6 4 2 A Q 3 2 K J 9 7 3 A Q 7 5 10 6 4 6 5 4 K 9 7 K J 10 9 8 5 10 8 A Q J 10 5 3 K J 9 7 A Q 3 2 8 6 4 2

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.

Samuel Pahk [for a similar deal]: Declarer can score six trumps and four diamonds.

David Brooks [for a similar deal]: 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 with a Moysian fit and topless diamonds, yet still bringing home the bacon, er beer.

 4 South 3 2 A K 3 2 Q 8 6 J 9 7 4 J 10 7 4 8 5 4 A K 10 8 5 3 A Q 9 6 5 10 7 6 J 9 5 K 10 K 8 Q J 9 7 4 3 2 A Q 6 2

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.

I also liked this deal because East-West cannot make anything; even one spade is routinely defeated. I think I see the picture: ‘Saint’ Nicholas went out of his way to please Saint Valentine.

## Final Notes

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 any puzzles.

Tom Slater: Hard to double-dummy solve for the beer.

Jurijs Balasovs: Good there are only four suits!

Nicholas Greer: Manipulating hands for this poker criterion fries my brain.

Of course! In last month’s I Have a Dream.. he cites French influence in the deep South.
Now he has French fries.

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