Euchre

You sit opposite your partner, North, with the two opponents either side. The dealer gives everyone five cards in packets of two and three, puts the last four face down as the kitty and turns the top one up. That card is an offer. Starting on the dealer's left, each player can order it up — its suit becomes trump and the dealer takes it into hand, throwing out one card — or pass. If all four pass, the card is turned face down and there is a second round, in which each player may name any other suit as trump, or pass again.

The side that chose trump are the makers, and they have to take at least three of the five tricks. The player to the dealer's left leads, everybody follows suit if they can, and the highest trump — or the highest card of the suit led, if nobody trumped — wins the trick. The deal moves one seat to the left after every hand, and the first side to 10 points wins. If you have played spades or hearts, the trick-taking is the same; the bidding, the short hands and the two jacks are what make euchre its own game.

They are the two jacks of trump's colour, and they outrank everything. The right bower is the jack of the trump suit itself. The left bower is the other jack of the same colour — the jack of diamonds when hearts are trump, the jack of clubs when spades are. The left bower stops belonging to the suit printed on it: it is a trump for every purpose, including following suit. Lead the jack of diamonds with hearts trump and you have led a heart.

So the trump suit always has seven cards and its colour-mate only five. The chance that your five cards include at least one of the two bowers of a named suit is exactly 38% — 16,170 of the 42,504 possible hands — and the chance of holding no card at all of that suit, bowers included, is 14.6%. Three or more of them, the hand that usually wants to make it trump, turns up 12.6% of the time.

Only one side scores in a hand, so the game cannot finish in a tie. Being euchred is the risk that keeps the bidding honest: calling trump on a weak hand does not merely fail to score, it hands the other side two points. At this table the makers are euchred on 16% of hands and march on 17%, and a game to 10 takes 11.6 hands on average.

Look at where the turned card will end up before you look at how good it is. If you or your partner dealt, ordering it up puts that card in your side's hands; if an opponent dealt, it puts it in theirs, and a turned jack in an opponent's hand is a trick you will not get. So the same cards are worth ordering up from the seat opposite the dealer and not worth it from the dealer's left. The computer seats count exactly that way, and the turned card is taken in round one on 81% of deals here — mostly by the dealer's own side, which makes trump on 78% of hands.

Going alone doubles a march from 2 points to 4 and changes nothing else: a lone hand that takes three or four tricks still scores 1, and one that is euchred still gives away 2. So it is right when your own five cards can take all five tricks — the right bower, two more trumps and aces or trumps beside them — and wrong on a hand of loose aces, however many there are. The computer players go alone on about one hand in nine, and 42% of those lone hands march.

A popular house rule for the moment everybody has passed twice. Played straight, the cards are thrown in and the next player deals. With stick the dealer, the dealer is not allowed to pass in round two and must name a suit — any suit but the one turned down — whatever their hand looks like. It speeds the game up and punishes a dealer's side that passed too often in round one.

It is an option in the menu above the board, and your choice is remembered. It matters less than it sounds: with it switched off, 18% of deals here are decided in round two and only 7 deals in 1,000 are thrown in at all.

They play the way a careful club player does, and they never look at a card they could not see at a real table: their own hand, the cards already played, the turned card and who has shown out of which suit. With that they draw trumps when their side made it, cash off-suit aces before they can be trumped, win each trick as cheaply as it can be won, never trump a partner's winning card, and throw away their least useful card when they cannot win.

Their bidding was tuned against itself in duplicate — the same deals played twice with the two partnerships' settings swapped, so the luck of the cards cancels out — until moving any threshold either way cost points. A partnership of them beats a partnership playing random legal cards in 97 games out of 100, which is the floor, not the boast: it is what shows the card play is doing real work.