games

Shooting the Moon

·5 min read
This one is playable.

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“Each player must accept the cards life deals him or her. But once they are in hand, he or she alone must decide how to play the cards in order to win the game.”

— Voltaire

Voltaire had it half right. You do have to accept the cards you’re dealt, and how you play them is on you. But at a card table — and in life — you are never only playing your own hand. What you can win depends just as much on the cards sitting around you: in your partner’s hand, in your opponents’, face down in the middle. The opportunity is the whole table, not your twelve cards.

And so collaboration turns out to be the real game. Almost nothing worth winning is won from your hand alone — it’s won by making big bets together, with partners and friends, at a table that is actively competitive. Pinochle is the cleanest lesson in that I know: a small, honest model of information theory in a market — what to share, when to share it, and how to get the value to the person who can use it before the cards are locked in. Learn to play it well and you have practiced the same skill that sits under every negotiation and every deal.

Here is the whole problem in a single hand.

I pick up my twelve cards and there it is, almost — the ten, king, queen, jack and nine of spades. One card short of a run. The ace of spades would finish it. As dealt, this hand is worth 90 points before a single card is played. With the ace of spades it is worth 200. One card, 110 points.

The ace is sitting in someone else’s hand right now, and to them it is nearly worthless — in the play it wins one trick and scores one point. To me it is 110. My partner might be holding it. And I am not allowed to say a word about what I need.

Everything that happens before the cards hit the table is an attempt to move information across that silence. You get a bid, which is one number. Then your partner slides you four cards face down. That is the entire conversation. That is the market: an asymmetric channel, a counterparty who doesn’t yet know what you’re worth to each other, and a narrow window to make the trade before the cards — the prices — are locked in.

And the biggest prize that channel can buy you is the one this essay is named for: shooting the moon — winning all twelve tricks in a single hand.

Two decisions, six endings

The round comes down to two choices. First, what your bid tells your partner — do you promise meld and ask for aces, name your long suit and ask for trump, or bid a minimum that means nothing in particular? Second, what you send back — keep everything useful, or empty out a whole suit so you can trump it later.

Two decisions, six possible endings. Here is where each one lands, over 12,000 simulated deals apiece:

What the bid means What you send back Avg. score Shoots the moon
“I have meld — send aces” Keep everything useful 179 7.2%
“I have a long suit — send trump” Keep everything useful 174 7.1%
“I have a long suit — send trump” Empty a whole suit 153 9.4%
“I have meld — send aces” Empty a whole suit 145 8.9%
“Nothing in particular” Keep everything useful 131 0.6%
“Nothing in particular” Empty a whole suit 121 1.5%

The agreement is worth more than the cleverness

Look at the spread. The best ending scores 179, the worst scores 121, and the gap between them has nothing to do with card skill. The bottom two endings are the ones where partner had no idea what the bid meant, so they sent their four worst cards and hoped. That one difference — having agreed ahead of time what a bid stands for — is worth about 48 points. Every clever decision after that moves the number by roughly half as much.

This is the part that transfers straight to business and negotiation. Your bid is not really a description of your hand. It is an instruction telling your partner which set of rules to follow. The value isn’t in the message; it’s in the shared code that makes the message mean something. Two people who have agreed what a signal means will beat two smarter people who haven’t, every time. The rules do the talking.

When shooting the moon is actually on

Going for all twelve tricks is a gamble, and the numbers show its shape. Emptying a suit to set it up costs you meld and costs you average score, and what it buys is moon shots. It only starts paying once you are already holding a pile of trump.

Spades in hand Keep all Empty a suit
5 spades 0.2% 0.3%
6 spades 1.1% 1.7%
7 spades 4.0% 6.0%
8 spades 9.8% 15.5%
9 or more 23.4% 29.8%

Below six spades it does nothing at all. At eight it adds more than five points of moon probability. This is why the move feels obviously right to players who go for it and obviously wrong to players who don’t — they are describing different hands. Knowing when the swing is worth it is the same judgment that separates a reckless bet from a well-timed one anywhere else.

What you are waiting for

Exact odds on the twelve cards you are dealt:

The hand Odds
A pinochle (queen of spades and jack of diamonds) about 1 hand in 5
A run — ace through jack of one suit 1 hand in 26
An ace of every suit 1 hand in 36
Double pinochle 1 hand in 393
Two aces of every suit 1 hand in 762,000
A double run 1 hand in 24.8 million

Single-deck partnership pinochle. Aces, tens and kings count one point each in the play, plus one for the last trick. Branch figures come from 12,000 simulated deals apiece, dealt to hands worth opening the bidding on. The odds in the final table are exact, not simulated.