Gin Rummy

Ten cards each from one shuffled deck. One more card is turned face up to start the discard pile, and the 31 cards left over become the stock. On your turn you take exactly one card — the top of the stock, which nobody has seen, or the top of the discard pile, which everybody has — and then you throw one card away. That is the whole turn, and it repeats until somebody ends the hand.

You are trying to arrange your ten cards into melds: three or four of the same rank, or three or more in sequence in one suit. Whatever will not fit into a meld is your deadwood, and it is counted against you. The moment your deadwood is down to ten points or less you may knock — lay your hand out, announce the count, and have the hand scored on the spot.

An average hand of ten cards is dealt holding 65 points of cards and 57 points of deadwood, so there is a long way to travel — the deck holds 340 points in all, 120 of them in the twelve court cards. About two hands in five arrive with a meld already in them, and roughly one hand in fourteen hundred is dealt light enough to knock before a single card has been drawn. Being dealt gin has not happened once in sixty thousand hands measured on this shuffler.

• A set is three or four cards of the same rank — three sevens, or all four of them.
• A run is three or more cards in sequence in a single suit: four, five and six of hearts. Longer runs are better, not two separate melds.
• The ace is low only. Ace-two-three is a run; queen-king-ace is not a run at all — it is a queen, a king and an ace sitting in your hand for 21 points of deadwood, which is the single most expensive shape a beginner keeps hold of.

That puts 340 points in the deck, 120 of them in the twelve court cards alone. It is why an unattached king is the first card most players throw and an unattached ace is the last: the king costs ten times as much to be caught with, and the ace can sit in the hand almost for free while you wait to see whether it finds a partner.

Because a card is one card. Hold the five, six and seven of hearts together with the seven of spades and the seven of diamonds and you are looking at two melds that both want the same card, and you may only have one of them. That single restriction is what makes counting your own hand harder than it looks, and it is where hand-rolled implementations quietly go wrong.

The set wins that one. Move the identical shape down to the two, three and four of hearts with the two of spades and the two of diamonds and the answer flips: melding the deuces leaves a three and a four behind for seventeen, while running the hearts leaves two deuces for fourteen. No rule of thumb about sets before runs gets both cases right, so this board does not use one — it searches every legal arrangement of your ten cards and shows you the cheapest, every time your hand changes.

Knocking is not free. The moment you lay your melds down, your opponent gets to lay off their own loose cards onto them — the fourth seven onto your three sevens, the eight of hearts onto your five-six-seven — and if what they have left is equal to or less than your count, they take the hand off you and collect a 25-point bonus on top. That is an undercut, and it is the single most expensive thing that can happen to a careless knock.

So the size of the knock matters enormously. Knocking on two or three points is nearly safe, because the defender needs a hand of two or three to catch you. Knocking on the full ten is an invitation. In self-play on this board, about one hand in ten ends in an undercut and about one in ten ends in gin; the remaining four-fifths are ordinary knocks, and they are usually worth far less than the 25 a single undercut swings.

The computer plays that trade explicitly. It takes gin whenever gin is available, because gin cannot be undercut and carries its own 25-point bonus. It knocks at once on four points or less. Above that it keeps drawing while there is stock left to improve the hand, and stops waiting once the stock is down to twelve cards, because a hand that runs out of stock scores nobody anything at all.

Hands are played until one player is past 100 points. That player then adds a 100-point game bonus, and both players add 20 points for every hand they won — the box, or line, bonus. A match on this board runs about ten hands, so roughly 200 points of boxes are handed out between the two players — twice the game bonus itself, which is why winning several small hands is worth far more than it looks during play.

Worked through: you knock with 10 and your opponent, having laid one card off, is left with 30. You take the difference, 20. Now suppose they had been left with 11 — you would take 1. Left with 10 instead, one point lower, they undercut you and take 25. That single point is worth 26 points, and it is the whole argument against knocking on a full ten.

This is the rule most implementations skip, and skipping it quietly changes who is on lead. The card turned up after the deal is offered first to the non-dealer. If they want it, they take it and discard, and the hand begins with them a card ahead. If they pass, the dealer gets the same choice. Only when both have refused it does the non-dealer draw — and it must be from the stock, because the upcard has now been turned down twice and is closed to them.

It is a real decision, and it is public. Taking that first card tells your opponent a rank and a suit you are working on before a single other card has moved, which is exactly the information a good player uses against you for the rest of the hand. The computer here refuses the upcard unless it measurably improves the hand, for that reason and no other.

One more rule follows from the same principle: you may never discard the card you have just taken from the pile. Picking a card up and putting it straight back down would be a free look at the pile at no cost, and the board will not let you do it — that card is dimmed and disabled until your next turn.

It does not quite run out. Once a discard leaves only two cards in the stock and nobody has knocked, the hand is dead: it is thrown in, nobody scores, nobody takes a box, and the same dealer deals again. Some households play on to the last card instead; the two-card floor is the standard rule and it is what this board enforces.

In practice it almost never happens — fewer than one hand in a hundred ends this way in self-play, because a player sitting on a knockable hand with the stock running down will knock rather than let the hand die. That is the practical lesson: a knock worth five points beats a dead hand worth nothing, and once the stock is short the cost of waiting for a better hand is the whole hand.