Middle cards in Higher or Lower: how to call a 6, 7 or 8

A 7 is showing, the round has barely started, and you have to choose. The middle cards, 6, 7 and 8, give the closest calls in Higher or Lower, and they are where a little counting pays off most. Here are the exact numbers, and how the cards you have already seen change them.

The starting counts

On Higher or Lower, only rank counts and suits are ignored, so 7♦ after 7♣ is simply a tie. Aces are low. At the start of a round, 51 cards are unseen:

• 6 showing: 20 lower (A to 5), 28 higher (7 to K), 3 equal.
• 7 showing: 24 lower (A to 6), 24 higher (8 to K), 3 equal.
• 8 showing: 28 lower (A to 7), 20 higher (9 to K), 3 equal.

Each count is just ranks times four: the five ranks below a 6 make 20 cards, and the seven ranks above it make 28.

With a 6 showing, Higher is right with 28 of 51 cards (about 54.9%), wrong with 20 (about 39.2%) and a tie with 3 (about 5.9%). An 8 is the mirror: Lower has the same numbers. A fresh 7 is a dead heat: right with 24 of 51 (about 47.1%) whichever way you guess, and wrong with the same 24.

Leaving the ties out

A tie neither adds to your streak nor ends it, so it only postpones the decision. The cards that settle a guess are the 48 that are not equal. Among those, Higher on a 6 wins 28 of 48, which is 7 in 12, about 58.3%. A 7 wins exactly half. For comparison, a 2 wins 44 of its 48 decisive cards. That is why a middle card deserves a look at the counter every time.

How seen cards tip a 7

For a 7, the lower count is 24 minus the Aces to 6s already seen, and the higher count is 24 minus the 8s to Kings already seen. Sevens that have appeared change only the equal count. So the rule is simple: the side that has shown up more often is now the thinner side.

Here is the start of a real round, with the counts before each guess:

1. 9♠ is showing: 32 lower, 16 higher, 3 equal. Lower; 3♦ comes. Streak 1.
2. 3♦, 50 unseen: 8 lower, 39 higher, 3 equal. Higher; K♣ comes. Streak 2.
3. K♣, 49 unseen: 46 lower, 0 higher, 3 equal. Lower; 10♥ comes. Streak 3.
4. 10♥, 48 unseen: 34 lower, 11 higher, 3 equal. Lower; 7♦ comes. Streak 4.

Now 7♦ is showing with 47 cards unseen. One low card has gone (3♦) and three high ones (9♠, K♣ and 10♥). The counts are 23 lower, 21 higher and 3 equal. Lower is right with 23 of 47 (about 48.9%) and wrong with 21 (about 44.7%); among the 44 decisive cards it wins 23, about 52.3%. A small lean, but a real one.

Suppose you guess Lower and the next card is 7♠, a tie. Your streak stays at 4, and the counts become 23 lower, 21 higher and 2 equal, out of 46. A tie never moves the higher or lower count, so the same guess is still the better one.

The lean can go the other way just as easily. In another round, Q♥ was followed by A♠, 3♥ and 5♣, and then 7♣ appeared. Three low cards and one high card had gone, so the 7♣ showed 21 lower, 23 higher and 3 equal, and Higher became the better side.

When does a 6 or an 8 flip?

A 6 starts with 8 more cards above it than below it. It only becomes a Lower card once you have seen at least nine more cards from 7 to K than cards from A to 5. With exactly eight more, the counts are level: after 7♦ 8♦ 9♦ 10♦ J♦ Q♦ K♦ and 9♠, with no low cards, a 6 shows 20 higher and 20 lower. One more high card, such as 10♠, makes it 19 higher against 20 lower.

An 8 is the mirror: it only becomes a Higher card once at least nine more cards from A to 7 than from 9 to K have gone, and eight more makes it level. It takes a very lopsided run to flip a 6 or an 8, while a 7 can tip on a single card.

The Hint on a level count

Hint lights up the side with the larger unseen count. When the two counts are level, as on a fresh 7, it lights up Higher. Treat that as a tie-break rather than a lean: on a level count the two sides really are equal.

Try it

1. A round starts with 8♣. What are the counts?
2. A 7 is showing, and 2♠, 4♦, 5♥ and J♣ have appeared earlier. What are the counts, and which side is better?
3. A 6 is showing after eight cards from 7 to K and no cards from A to 5. Which side is better?

Answers: 1) 28 lower, 20 higher, 3 equal. 2) With 47 unseen: 21 lower, 23 higher, 3 equal, so Higher. 3) Neither: 20 higher and 20 lower.

For the full method of counting a round, read Higher or Lower: counting what is left, and the rules of every game are on how to play.