A card game against the house

The HiLo game: probability and multiplier for every card

One card lies face up, and you guess whether the next one will be higher or lower. Here is the chance for each card worked out, how the multipliers are multiplied together, and why the house edge grows with every step.

HiLo is a house game where you guess whether the next card will be higher or lower than the card lying face up. Guess right and the multiplier rises, and you can either cash out or carry on with the next card. Guess wrong and the stake for the round is lost. The whole thing is one card at a time, and you make a new decision at every step.

The game looks like an ordinary card game, but the mathematics is simpler than it appears. Once you know the chance for each card, you can work out the multiplier yourself and check the figures the game shows. That is what we do below, with examples you can follow with a calculator. If you want to see how HiLo stands in relation to other house games and operators, the whole overview is at the Kryptospill comparison.

HiLo: four cards in a row

Each card turned moves the multiplier one step, either up or down according to the probability of the next card. The numbers in the figure are examples.

How a round of HiLo works

A round follows the same pattern from start to finish:

The stake. You choose an amount in the coin your balance is held in.
The first card. The game shows a card, from ace to king.
The guess. You choose «higher or equal» or «lower or equal». The buttons show both the chance and the multiplier.
The next card. If the guess is right, your multiplier is multiplied by the multiplier for the step.
Cash out or carry on. At any time you can take out the stake multiplied by the combined multiplier, or guess on a new card.

In many versions the ace is lowest and the king highest, and the suit of the card plays no part. The versions still differ in the details: some use a deck where each draw is independent, others draw from a deck that empties, and the buttons may be «higher» and «lower» without «equal». The information window in the game tells you which variant you have in front of you.

The probability for each card

The calculations below use the most common model in house games: each draw is independent, and each of the 13 values has the same chance, 1 in 13. The ace counts as 1 and the king as 13.

If a card of value r is showing, the chance of «higher or equal» is (14 − r) / 13, and the chance of «lower or equal» is r / 13. The multiplier for the step is (1 − the house edge) divided by the chance.

A worked example with a 1% house edge. The percentage is an example figure; the actual house edge at your operator may be a different one:

Ace (1): higher or equal is certain, 100%, and gives only 0.99×. Lower or equal means another ace: 7.69% and 12.87×.
Three (3): higher or equal 84.62% and 1.17×. Lower or equal 23.08% and 4.29×.
Seven (7): both choices give 53.85% and 1.84×. The middle of the deck is the most balanced card.
Ten (10): higher or equal 30.77% and 3.22×. Lower or equal 76.92% and 1.29×.
King (13): higher or equal means another king: 7.69% and 12.87×. Lower or equal is certain and gives 0.99×.

Note the ends. A certain choice gives a multiplier below 1, so you lose a little by taking it. That is why many versions let you skip such a card instead.

A worked example where each of the thirteen values is equally likely on the next card. The lower the card showing, the greater the chance of «higher» and the smaller the multiplier for that choice.

Skipping a card

Most HiLo variants have a button for skipping the card that is showing. You get a new card without guessing, and your multiplier stands still. That is useful when the card is an ace or a king, where one choice is certain and the other very unlikely.

Skipping does not change the house edge. You only avoid a step where the choice is a poor one for you. Some versions limit how many times you can skip in a row, and the limit is then stated in the information window.

A worked example: three correct cards in a row

Let us follow a round with 1 USDT staked and a 1% house edge per step.

The first card is a three. You choose higher or equal: chance 11/13, multiplier 1.17×.
The next card is a ten. You choose lower or equal: chance 10/13, multiplier 1.287×.
The next card is a five. You choose higher or equal: chance 9/13, multiplier 1.43×.

The combined multiplier is 1.17 × 1.287 × 1.43 ≈ 2.15×. Cash out now and you get around 2.15 USDT. The chance of getting through all three steps was 11/13 × 10/13 × 9/13 ≈ 45.1%.

With no house edge the combined multiplier would have been 1 / 0.451 ≈ 2.22×. The difference comes from the house edge being taken off at every step: 0.99 × 0.99 × 0.99 ≈ 0.970. After three steps you are therefore paying around 3%, not 1%.

The house edge grows with every step in HiLo

This is the most important thing to understand about the game. Every new card you guess on adds its own house edge. At 1% per step it looks like this:

1 step: you get back on average 99%.
3 steps: around 97%.
5 steps: around 95.1%.
10 steps: around 90.4%.

A long chain can give a large multiplier, but the combined cost rises with every card. Cash out early and you pay less house edge per round; go far and you pay more. That does not mean short chains win, only that each round costs less on average.

A worked example. You play 50 rounds with 2 USDT staked. If you always cash out after one step, the expected loss is around 1% of 100 USDT, that is 1 USDT. If you always go five steps before cashing out, the expected loss is around 4.9% of the same amount, almost 5 USDT — but then you also win far less often, and the wins you do get are larger. Choose the length of the chain deliberately before the round starts, not in the middle of a good run where it is easy to carry on one card more.

The relation between the return, the house edge and the swings over many rounds is set out in the walk-through of the return percentage. A game with similar step-by-step logic, but with tiles and mines, is described in the guide to the grid.

Seed checking of the cards

House games of this kind usually use a server seed, a client seed and a nonce. The hash of the server seed is shown before you play, and each card is worked out from the three values. When the server seed is later revealed, you can recalculate the cards and compare them with the round history.

The check shows that the cards were not altered after you began. It says nothing about how large the house edge is per step or about the account rules. The whole course of the check is in the explanation of the seed and the hash.

Before you play with coins

The game itself is fairly similar at the operators that offer it, while the account rules vary. Before a first deposit you should know when an ID check can start and which amount triggers it. Bitcasino.io mentions €2,500 or the value in crypto (cl. 6.6). At Wild Fortune the period for documents is two weeks (cl. 8.4 and 9.3). The operators are compared on such points in the overview with files.

Decide on a loss amount and a number of rounds before you start. If you notice it becoming hard to stop, you can contact Hjelpelinjen (hjelpelinjen.no), which offers free help.

Frequently asked questions

Which card is best to guess on in HiLo?

No card gives a better average, because the multiplier always follows the chance and the house edge is taken off at every step. Cards in the middle, such as a seven, give roughly equal choices in both directions. An ace and a king give one certain choice with a multiplier below 1, and there it is usually better to skip the card.

Why is the win lower than the chance suggests over several cards?

Every step has its own house edge. At 1% per step you get back on average around 97% after three correct cards and around 90.4% after ten. The combined multiplier is therefore a little lower than if you worked out the chance for the whole chain at once with no house edge.

Can earlier cards help me guess the next one?

Not in versions where each draw is independent. Then every value has the same chance every time, whatever came before. If the game uses a deck that empties, the chances change after each card, and that is stated in the information window. The cards are decided by the seed values in any case, not by patterns.