Trick-Taking Card Games: Hearts, Spades and Euchre

Taking tricks is simple; not seeing is not

The mechanic fits in a sentence: everyone plays one card, the highest takes them, repeat. A child can learn it, and it has carried some of the deepest card games of the last several centuries — not because of the rule, but because of the information.

A board position is fully public; both players look at the same truth. Cards are not. You see your thirteen and must infer the other thirty-nine. What the game hands you is one exceptionally reliable clue: **who failed to follow which suit**. Following is compulsory when you can, so a player who fails to follow has demonstrably run out of that suit — a conclusion that holds for the rest of the hand and cannot be faked. That table is what a strong player is running mentally.

Three different objectives

Hearts turns trick-taking into a penalty: each heart costs 1 and the Queen of Spades 13, and the lowest score wins. You are not competing for the lead but looking for ways to push the scoring cards onto somebody else. It belongs to the avoidance branch descended from Reversis, recorded in sixteenth-century Spain — inverting the winning condition forces every technique to be rewritten.

Spades runs the other way: name how many tricks your partnership will take, then make the number exactly. It only appeared in the 1930s, built to strip out Bridge's memorised bidding conventions and leave a single number. But it adds a rule found almost nowhere else — overtricks accumulate as bags, and the tenth bag costs 100 points. Bidding accurately therefore beats bidding safely, and even winning too much has a price.

Euchre goes further still: trump is bid each hand, and **naming it changes what the cards are**. With hearts as trump the jack of diamonds joins the hearts and stops being a diamond at all — so trump holds seven cards this hand, its colour partner holds five, and even the arithmetic of void inference shifts. In nearly every other card game a suit is an intrinsic property of a card; Euchre makes it something decided afresh each hand. Twenty-four cards and five tricks make it fast enough to feel like a warm-up, with all the depth loaded onto a few seconds of bidding.

Why the AI here is unusually hard

An engine for a perfect-information board game can simply search: the position is known, so look ahead. Cards do not permit that — without knowing the other hands there is no single position to look ahead from.

The standard answer is **determinization**: guess a complete deal consistent with everything known (each hand the right size, played cards gone, no inferred void violated), search that guessed deal, then guess again. The hard part is the guessing, not the searching. Late in a hand the void constraints grow dense enough that random guessing finds a legal deal well under one time in a thousand, so the AI burns its budget sampling and reads as weakest exactly when the hand matters most. We solve it as a bipartite matching problem instead, which finds a deal whenever one exists.