# Aces and Kings in Higher or Lower: the guesses you cannot lose

In Higher or Lower almost every guess carries some risk: even a good call can be beaten by the next card. Two ranks are different. With an Ace or a King showing, one of the two guesses cannot end your round. Here is why, with the exact counts, and how the same idea comes back later in a round.

## Why the ends of the deck are safe

On [Higher or Lower](../play/higher-or-lower.html), only rank counts and Aces are low, counted as 1. The order runs from Ace up to King, so the Ace is the lowest card and the King the highest.

At the start of a round one card is showing and 51 are unseen. With an Ace showing:

- **Higher:** 48 cards, every 2 through King.
- **Lower:** 0 cards.
- **Equal:** the other 3 Aces.

Guess Higher, and you are right with 48 of the 51 cards, about 94.1%, and tie with the other 3, about 5.9%. No card makes you wrong. A King is the mirror image: 48 lower, 0 higher and 3 equal, so Lower is either right or a tie. The only way to lose on these cards is to guess the other way: Higher on a King is wrong with 48 cards and at best a tie.

Eight of the 52 cards are Aces or Kings, so a round starts on one of them with chance 8 ÷ 52 ≈ 15.4%.

## Ties: the only other outcome

An equal rank is a tie. It neither adds to your streak nor ends it, and the new card becomes the one showing. After a tie on an Ace, another Ace is showing, so the next guess is just as safe.

Say the round starts with A♣ and you guess Higher. The next card is A♥: a tie, and your streak stays at 0. Now 50 cards are unseen: 48 higher, 0 lower, 2 equal. You guess Higher again, 9♦ comes, and your streak is 1. Because each rank has only four cards, no more than three ties can follow one another on the same rank.

## The near ends: 2s and Queens

One step in from either end, the guess is nearly as safe:

- **2 showing:** 4 lower (the Aces), 3 equal, 44 higher. Higher is wrong with 4 of 51 cards, about 7.8%.
- **Queen showing:** 44 lower, 3 equal, 4 higher (the Kings). Lower is wrong with the same 4 of 51.
- **3 or Jack showing:** the losing side grows to 8 cards, about 15.7%.

Each step towards the middle adds four cards to the side that can beat you.

## When a count reaches zero later

The counter on screen shows how many unseen cards are higher, lower and equal. Whenever one of those numbers is 0, the opposite guess cannot lose, whatever rank is showing. That can happen in the middle of a round too: a 2 becomes a free Higher once all four Aces have appeared, and a Queen becomes a free Lower once all four Kings are gone.

## Worked example: a round near the ends

Here is a real sequence of seven guesses, with the counts the game shows before each one.

1. K♥ is showing: 0 higher, 48 lower, 3 equal. Lower; A♠ comes. Streak 1.
2. A♠, 50 unseen: 47 higher, 0 lower, 3 equal. Higher; A♦ comes. A tie, so the streak is still 1.
3. A♦, 49 unseen: 47 higher, 0 lower, 2 equal. Higher; K♣ comes. Streak 2.
4. K♣, 48 unseen: 0 higher, 46 lower, 2 equal. Lower; Q♦ comes. Streak 3.
5. Q♦, 47 unseen: 2 higher (K♦ and K♠), 42 lower, 3 equal. Lower is wrong with only 2 of 47 cards, about 4.3%. Lower; 3♣ comes. Streak 4.
6. 3♣, 46 unseen: 37 higher, 6 lower (two Aces and four 2s), 3 equal. Higher is wrong with 6 of 46, about 13.0%, the riskiest call of the round. Higher; K♠ comes. Streak 5.
7. K♠, 45 unseen: 0 higher, 44 lower, 1 equal. Lower; Q♠ comes. Streak 6.

Now Q♠ is showing with 44 unseen: 1 higher (K♦), 41 lower, 2 equal. Lower is wrong with a single card, about 2.3%. If K♦ turns up later, every Queen for the rest of the round is a free Lower.

Five of those seven guesses could not lose at all, and the other two were wrong with at most 6 of 46 cards.

## Reading the counter, not just the rank

You need not keep any of this in your head: the counts already include every card seen so far. Check for a zero first; if there is one, guess the other way. If there is none, the larger number is the side that leaves the fewest cards able to beat you, and Hint lights up that side for you.

## Try it

1. A round starts with K♦. How many unseen cards are lower?
2. 2♥ is showing, and all four Aces have appeared earlier in the round. What is the lower count, and what should you guess?
3. An Ace is showing and you guess Lower. What can happen?

Answers: 1) 48, with 0 higher and 3 equal. 2) 0, so Higher cannot lose. 3) Only a loss or a tie: any higher card ends the round, and another Ace is a tie.

To count a whole round from a mid-ranking card, read [Higher or Lower: counting what is left](higher-or-lower-odds.html), and the [glossary](../glossary.html) explains how a streak works.