What to Lead in Hearts: Lead Rules Tested Over 100,000 Deals

After the 2 of clubs, lead low, and let your spades pick the suit. With none of the queen, king and ace of spades (or with the ace or king and three or more lower spades), lead spades below the queen to flush the queen out. Holding the queen (or the ace or king of spades), lead low from your shortest suit so you can throw it away later. Once hearts are broken and you don't hold the queen, lead your lowest heart.

In our computer tests, those leads cut a player's points by 0.44 per hand compared with the standard computer's leads, and lifted their share of games won from 25.8% to 31.2%. Below is how we tested more than 20 lead rules, what each one costs or saves, and a real deal where one lead decided who took the queen. For the rules themselves, see how to play Hearts.

How we tested

Everything here comes from the computer players in Poozee's Hearts, with the game's own rules engine. We dealt 100,000 hands, made everyone's pass the way the game's Medium computer passes, and played each hand once with every lead rule. Passing rotated left, right, across and hold, as in a real game.

South changed only its leads, from the second trick on (the holder of the 2 of clubs always leads it to the first trick). West, North and East played like Medium, and South played every card it didn't lead like Medium too. Medium leads like this:

• If it holds none of the queen, king and ace of spades and the queen hasn't been played, it fishes: it leads its highest spade below the queen.
• Otherwise it leads its lowest safe card: not a heart, not the queen of spades, and not the ace or king of spades while someone else may hold the queen. On a tie it picks the shorter suit.

Every rule plays the same deals as Medium's leads, so the luck of the cards cancels out. With Medium's leads, South took 6.93 points per hand. In the tables, a negative number means fewer points than Medium's leads, which is better, and each rule's difference from Medium's leads over all 100,000 deals has a 95% margin of error under 0.05 points.

The rules are the standard ones the game plays. You can't lead a heart until hearts are broken, which happens the first time a heart is played, unless you hold nothing but hearts. The queen of spades doesn't break hearts.

Low or high, suit by suit

Each rule below leads from one suit whenever it can do so safely, its lowest or its highest card, and otherwise leads like Medium. Fishing still comes first in every rule, so only the other leads change. "Shortest suit" means your shortest suit other than hearts. The change in South's points per hand:

The lowest safe card from any suit is Medium's own lead, so its row starts at 0.00. Low beat high in every row. A high lead wins tricks, and whoever wins a trick is who the other players throw hearts and the queen onto. Leading low from your longest suit cost 0.11.

The popular idea of cashing high cards early, while nobody is out of a suit yet, didn't hold up either: leading your highest safe card on tricks 2 to 4 and then leading like Medium cost 0.29 points per hand.

The two leads that saved points, the shortest suit and hearts, both depend on which spades you hold.

Your spades decide the lead

Here are the same kinds of leads, split by the high spades South held after the pass: the queen, the ace or king without the queen, or none of the three.

Every number in this table has a 95% margin of error under 0.1 points.

Holding the queen: empty a suit

With the queen in your hand, you want to run out of a suit, so that you can throw the queen away when that suit is led. Leading your short suit gets you there faster. Holding the queen, you took it in 29% of hands with Medium's leads and 26% leading low from your shortest suit. With the queen, even leading your highest safe card helped a little, probably because high leads use up a suit too, but low leads from the short suit did best.

Here's how it plays out in deal 115 of our test set, a hold hand with no passing: 3♣ 10♣ 2♦ 3♦ 4♦ 10♦ 4♠ Q♠ 3♥ 4♥ 6♥ 7♥ 10♥. Your queen has only one lower spade with it, and you can't pass it. West leads the 2♣ and you win the trick with the 10♣, so you lead the second trick.

• Medium leads the 2♦, its lowest card. On trick 5, West leads the 9♠, the queen is your only spade left, and it wins the trick.
• The checklist leads the 3♣, your last club. On trick 3, East leads the 6♣, you're out of clubs, and you throw the queen onto West's J♣.

Medium's leads cost you 13 points on this deal and the checklist's 0. Single deals swing a lot, so trust the averages, not any one hand.

Not holding the queen: lead hearts once they're broken

Medium leads a heart only when it has no other safe card, so only 14% of Medium's leads after the first trick were hearts. Leading your lowest heart whenever hearts were broken saved 0.34 points per hand when you held none of the queen, king and ace of spades, and 0.26 with the ace or king. With the queen still in your hand it cost 0.19: your leads are better spent emptying a side suit.

You don't need the heart to be a sure loser: leading a heart only when it was lower than every heart still out saved only 0.07 points per hand, against 0.18 for leading your lowest heart whenever hearts were broken. It saved more on each hand where it changed a lead, but it changed a lead in 16% of hands, against 63%.

Pro tip: Leading high hearts was one of the worst habits we tested (+1.13 points per hand). If you lead a heart, lead your lowest.

Fishing for the queen with low spades

Fishing means leading spades below the queen so that whoever holds it has to play it, sooner or later, onto a higher spade. Our Hearts strategy guide showed that fishing pays on average. Whether it pays for you depends on the spades in your own hand.

The change in your points per hand from fishing (leading your highest spade below the queen while the queen is out) instead of not fishing, by your high spades and how many spades below the queen you held after the pass. Negative means fishing was better:

Each cell has a 95% margin of error of 0.16 points or less. Three findings:

• With none of the three high spades, always fish. It paid at every length, most with three lower spades.
• With the ace or king, fish only with three or more lower spades. With one or two, a couple of spade leads can leave your ace or king with nothing below it, ready to catch the queen. With three or more, you still have low spades to play while the queen comes out.
• With the queen, don't fish. It never helped, and with two or more lower spades it cost about 0.3 points per hand.

Which low spade matters less: fishing with your lowest spade instead of your highest one below the queen cost 0.04 points per hand. What matters a lot is never leading the ace or king of spades while the queen is out. Leading them to get rid of them cost 4.02 points per hand on the 32,181 deals where you held one. You took the queen in 62% of those hands, against 29% with Medium's leads.

Exit cards: keep one, or lead low now?

An exit card is a low card you hold on to so that you can lose the lead late in the hand. It sounds wise, but it didn't pay. Keeping your lowest card back while you had four or more cards cost 0.12 points per hand, compared with leading it as Medium does. One likely reason is the way Medium follows suit: it plays the highest card that still loses the trick, which keeps its low cards for later anyway.

Leading a card lower than every card of its suit still out, a lead that can't win the trick, saved 0.04 points per hand. It changed a lead in only 7% of hands, so it's a small edge, not a rule to build your play around.

What the Hard computer leads

The game's Hard player looks ahead: it plays each legal card out over many guesses of the hidden cards and picks the best on average. To check our rules against it, we let Hard choose South's leads, with everything else as before. On 2,000 deals, Hard's leads saved 1.03 points per hand compared with Medium's, and the checklist 0.35 on the same deals. So simple rules get you part of the way, and reading the hand gets you more.

Hard's choices point the same way as the checklist, without following it every time:

• Hard fished in 64% of the spots where Medium fishes.
• With hearts broken, a heart and another safe card to lead, no queen and no fishing lead, it led a heart 38% of the time. Medium never does.
• Holding the queen with safe cards in two or more other suits, it led from the shortest one 49% of the time, against 32% for Medium.
• Holding the ace or king of spades while the queen was out, it led the ace or king in 12 of 533 chances.

The lead checklist

Put together, here's what to lead on each trick:

1. First trick: the 2 of clubs, if you have it. You have no choice.
2. The queen is still out and you don't hold it: with none of the king and ace of spades, or with three or more spades below the queen, lead your highest spade below the queen.
3. Holding the queen, or the ace or king of spades while the queen is out: lead the lowest card of your shortest suit other than hearts. Never lead the queen, and never the ace or king while someone else may hold the queen.
4. Hearts broken and no queen in your hand: lead your lowest heart.
5. Otherwise: lead your lowest safe card.

The checklist changed at least one lead in 68% of hands, and it saved 0.44 points per hand on the deals above. On another 100,000 deals that we didn't use to build it, it saved 0.43.

Step 3 comes before step 4 even though, in the table of leads by your spades, the lowest heart beat the short suit for a player holding the ace or king. The two work best together, short suit first. On hands with the ace or king, the checklist saved 0.38 points per hand, more than the lowest heart (0.26) or the short suit (0.13) on its own. We also tried the checklist with the heart ahead of the short suit for those hands: it cost 0.03 points per hand more than the checklist on the first 100,000 deals and 0.03 on the other 100,000.

Finally, we played 10,000 whole games to 100 for each of these ways to lead, against three Medium players. A tie for the lowest score counts as a win for everyone tied, so four equal players each win a little over 25%:

Each win rate has a 95% margin of error under 1 percentage point. Leads are only part of the game: the cards you pass matter too, and our guide to what cards to pass in Hearts measures them the same way.

Keep playing

• Play Hearts and try the checklist against Medium and Hard. The Hint button shows the card Hard would play.
• Hearts strategy: how to follow suit, pass and throw away cards, tested the same way
• What cards to pass in Hearts, 13 passing rules tested in every direction
• How to shoot the moon in Hearts, the one time you want to win tricks