# Higher or Lower: counting what is left in the deck

A 5 is showing and the other 51 cards of the deck are still unseen. How many of them are higher, how many are lower, and how many are equal? Once you can answer that quickly, every guess in Higher or Lower becomes a small, honest calculation instead of a hunch.

## The rules in brief

[Higher or Lower](../play/higher-or-lower.html) uses one shuffled deck. One card is face up, and you guess whether the next card will be higher or lower. Only rank counts, never suit, and Aces are low, counted as 1.

- A correct guess adds one to your streak.
- An equal rank is a tie: it neither adds to the streak nor ends it.
- A wrong guess ends the round, and the round counts as lost.
- A streak of 10 correct guesses wins the round.

The game also shows how many of the remaining unseen cards are higher, lower and equal, so you never have to keep the count in your head.

## Counting from a 5

Each rank appears four times in a deck, once in each suit. With a 5 showing and nothing else seen:

- **Lower:** A, 2, 3 and 4. That is 4 ranks × 4 cards = 16 cards.
- **Equal:** the other three 5s, so 3 cards.
- **Higher:** 6, 7, 8, 9, 10, J, Q and K. That is 8 ranks × 4 cards = 32 cards.

Check: 16 + 3 + 32 = 51, the whole of the unseen deck.

If you guess Higher, 32 of the 51 cards make you right, 3 give a tie and 16 end the round:

- right: 32 ÷ 51 ≈ 62.7%
- tie: 3 ÷ 51 ≈ 5.9%
- wrong: 16 ÷ 51 ≈ 31.4%

So Higher is clearly the better guess, but it still fails almost one time in three. No guess is safe unless one of the counts is zero.

## When a count is zero

Because Aces are low, nothing can be lower than an Ace. With an Ace showing, Higher can only be right or a tie. In the same way, nothing is higher than a King, so with a King showing, Lower cannot lose. These are the only free guesses at the start of a round; later on, a count can also reach zero because all the cards on one side have already appeared.

## How the on-screen counts help

The counts include every card you have already seen, so you do not need to remember the history of the round. The simple rule is to guess the side with the bigger number.

Rank alone is a rough guide at the start. A 7 is the middle card: with a 7 showing and 51 cards unseen, 24 are lower (A to 6), 24 are higher (8 to K) and 3 are equal, so it is an even call either way. A 6 leans Higher (20 lower, 28 higher) and an 8 leans Lower (28 lower, 20 higher). As the round goes on, the cards already seen shift those balances, and that is exactly what the counts show you.

## Worked example: three guesses

The round starts with 5♣ showing. The counts are 16 lower, 3 equal, 32 higher. You guess Higher, and the next card is J♦. Streak: 1.

Now J♦ is showing and 50 cards are unseen:

- Lower: A to 10 is 10 ranks × 4 = 40 cards, minus the 5♣ already seen, so 39.
- Equal: 3 Jacks.
- Higher: Q and K, 8 cards.

Check: 39 + 3 + 8 = 50. You guess Lower, right 39 ÷ 50 = 78% of the time. The next card is 9♠. Streak: 2.

Now 9♠ is showing and 49 cards are unseen:

- Lower: A to 8 is 32 cards, minus 5♣, so 31.
- Equal: 3 nines.
- Higher: 10, J, Q and K is 16 cards, minus J♦, so 15.

Check: 31 + 3 + 15 = 49. You guess Lower again, right 31 ÷ 49 ≈ 63.3% of the time. The next card is 9♥: a tie, so the streak stays at 2.

With 9♥ showing, 48 cards are unseen: 31 lower, 2 equal, 15 higher. The tie changed only the equal count, from 3 to 2. Lower is now right 31 ÷ 48 ≈ 64.6% of the time.

## Why ten in a row takes care

Every guess is a fresh risk, and a single wrong guess ends the round, while a tie only pauses it. The middle ranks, 6, 7 and 8, give the closest calls; cards near either end give the clearest ones. Reading the counts every time, rather than guessing from habit, is the one thing fully under your control.

## Try it

A round so far: 3♠ was showing, you guessed Higher and Q♣ came; you guessed Lower and 10♥ came. Your streak is 2, and 10♥ is showing. Work out the higher, lower and equal counts, and decide what to guess.

Answer: 49 cards are unseen. Lower: A to 9 is 36 cards, minus 3♠, so 35. Equal: 3 tens. Higher: J, Q and K is 12 cards, minus Q♣, so 11. Check: 35 + 3 + 11 = 49. Guess Lower, which is right 35 ÷ 49 = 5 ÷ 7 ≈ 71.4% of the time.

Then compare your own counting with the on-screen numbers on [Higher or Lower](../play/higher-or-lower.html). For more card arithmetic, read [Soft 17 explained](blackjack-soft-seventeen.html), and for a game of pure memory, try the [Memory Pairs method](memory-pairs-method.html). The full rules of every game are on [how to play](../how-to-play.html).