Provably fair Hi-Lo game: rules, odds per card, house edge and how to verify a round

A provably fair Hi-Lo game is the simplest card game in a crypto casino's originals section: one card is face up, you call whether the next one will be higher or lower, and every correct call grows your multiplier until you cash out or miss. Every card comes from seeds you can check afterwards. This guide covers the rules, the card draw, the odds and payout for every card, the house edge, how to recompute a round in our verifier, and which audited casinos run Hi-Lo.

How Hi-Lo works

A round starts when you place your bet. The game deals a start card, and you choose one of two calls:

• Higher or same: the next card ranks equal to or above the current one.
• Lower or same: the next card ranks equal to or below it.

If you are right, that card becomes the current one and your multiplier rises; cash out, keep going or skip. If you are wrong, the stake is lost.

Rank order runs from ace (lowest) to king (highest). Thrill's published method gives the values directly: ace 1, two to ten at face value, jack 11, queen 12, king 13. Suits do not matter.

The two edge cards change the buttons. On an ace, "lower or same" can only mean another ace, and "higher or same" would always win, so the game offers Higher and Same instead. On a king it offers Lower and Same. Thrill lists exactly these bet types: Same or Higher on an ace, LowerOrSame or HigherOrSame on two to queen, Lower or Same on a king.

Skipping swaps the current card for the next one without a call and without changing your multiplier.

Not every Hi-Lo plays like this. Gamdom's HiLo adds bets on colour, card ranges and a 99x Joker, each paid as its own bet, so check the in-game rules first.

How each card is drawn from the seeds

Before the round, the casino commits to a secret server seed by showing its hash. You hold a client seed, and each bet has a nonce. The game feeds these into a keyed hash (HMAC) and turns the output into one number per card.

There are two schemes that our verifier can recompute:

• Stake-style floats (Stake, Shuffle). HMAC-SHA256 keyed with the server seed over client seed:nonce:round. Each 32-byte output gives eight random floats of 4 bytes each. A card is the float times 52, rounded down, used as an index into a fixed list that runs 2♦ 2♥ 2♠ 2♣, then the 3s, and so on up to the aces. Shuffle's game events article shows Hilo generating 52 floats per round this way, with the example indexes 22, 34, 9, 29 and 44 becoming 7♠, 10♠, 4♥, 9♥ and K♦.
• Thrill. HMAC-SHA512 over client seed:nonce:cursor, with the cursor moving on by one for every card. Each hash gives a whole number from 0 to 51 that indexes Thrill's ordered deck. Thrill's own list runs ace to king in hearts, diamonds, clubs and spades.

Every card is an independent draw from 52, which is what Shuffle means by an "unlimited card deck". The same card can come twice in a row, and tracking cards, skipped or not, changes nothing.

Hi-Lo odds and payout for every card

Because the deck is infinite, the chance of each call depends only on the current card. With v as the card value, Thrill publishes these formulas:

• Higher or same: (14 minus v) / 13
• Lower or same: v / 13
• Higher (on an ace): (13 minus v) / 13, which is 12/13
• Lower (on a king): (v minus 1) / 13, which is 12/13
• Same: 1/13

The fair multiplier for any call is 1 divided by its probability. A casino keeps its edge by multiplying that by the RTP. At a 99% RTP, the first call pays:

Figures are before any on-screen rounding. A 4 looking up is the same bet as a 10 looking down, and on a 7 both calls win 7 times in 13 because "or same" counts the tie for either side.

Where the house edge sits

What matters is how the multiplier grows after the first call. Thrill's formula applies the RTP once: the first multiplier is RTP / probability, and each later one is the last multiplier divided by the new probability. Multiply it out and a run of any length pays RTP divided by the chance of the whole run. Your expected return per round is the RTP, whether you cash out after one call or ten.

A game that applied the RTP on every call instead would charge the edge again at each step. At 99% per step, five calls would return 95.1%, ten calls 90.4%. You can tell which method a game uses from its own numbers: at a 99% RTP, two calls on an ace (12/13) then a 3 (11/13) should show 1.0725 times 13/11, about 1.2675x, if the edge is charged once, or about 1.2548x if it is charged twice.

What the edge actually is depends on the operator, and few publish it for Hi-Lo:

• Thrill uses RTP as a variable in its formula but does not state the value.
• MetaWin's Originals hub lists Hi-Lo at a 97% RTP, a 3% edge.
• Gamdom puts its HiLo in a group of Originals with an RTP of "around 99%".
• Stake and Shuffle show the multiplier for each call in the game; neither publishes a Hilo RTP on the pages we read.

If nothing is stated, multiply the shown multiplier by the probability above: 1.0725x on a two means 99%.

Is there a Hi-Lo strategy?

No call or cash-out pattern changes the expected return, because every call is priced at the same RTP. What you choose is variance:

• Safe calls (an ace going higher, a king going lower) win 92% of the time, but the first pays 1.0725x and each one after it only multiplies the total by about 1.083. Reaching 2x takes nine of them, and the chance of nine in a row is about 49%.
• Long shots (a "same" call at 12.87x) hit 7.69% of the time.
• Skipping a 6, 7 or 8 does not improve your odds, it only lets you wait for a card where one side has more cards. The next card is just as random as the one you skipped.

Max wins cap long runs: Thrill lists a $500,000 max payout for HiLo, and Winna sets a $400,000 max win and forces a cash-out when continuing would exceed it.

How to verify a Hi-Lo round

Here is a worked round with made-up seeds on a Stake-style game:

1. SHA-256 of the server seed gives 16e21271...8128c1f9, matching the hash shown before play.
2. HMAC-SHA256 over amber-fox-19:0:0 starts fbd843b2. As a float that is 0.983769, and 0.983769 x 52 = 51.2, so index 51: the ace of clubs. That is the start card.
3. The next floats give indexes 28, 5, 44, 38 and 12: 9♦, 3♥, K♦, J♠ and 5♦.

Played out: on the ace you call higher (9 wins), on the 9 lower or same (3 wins), on the 3 higher or same (king wins), on the king lower (jack wins), on the jack lower or same (5 wins). At a 99% RTP with the edge charged once, the five calls pay 0.99 / (12/13 x 9/13 x 11/13 x 12/13 x 11/13), about 2.344x. The chance of that exact run was about 42%.

Open this check in our verifier and set the cards to 8.

For your own rounds:

1. Note the hashed server seed before you play, then rotate your seed pair after the round.
2. Copy the client seed and the round's nonce from your bet history.
3. In the verifier, pick the casino (Stake, Shuffle or Thrill), choose Cards and paste the seeds.
4. Set enough cards to cover the start card, every call and every skip, and compare. At Thrill the nonce starts at 1.

For the general method, see how to verify a provably fair bet.

Which audited casinos run Hi-Lo

These audited casinos list Hi-Lo among their provably fair originals:

Spribe's HiLo, offered at Wild.io and 1win, is a third-party game with its own fairness system, not a house original. For blackjack on the same card draw, see provably fair blackjack; for the rest of a full set of originals, see Stake Originals explained.

Bottom line

Provably fair Hi-Lo is pure probability: 13 ranks, an infinite deck, and a multiplier of 1 divided by your chance, less the edge. Where the RTP is charged once per round, no cash-out point costs more than another. Know the edge, verify a round now and then, and set a loss limit first; our responsible gambling page has the tools.

Sources

• Thrill: provably fair game event (HiLo values, bet types, probability and multiplier formulas)
• Thrill: Thrill Originals (HiLo bet and payout limits)
• Shuffle: provably fair game events (Hilo floats, card list, unlimited deck)
• Gamdom: Gamdom Originals (HiLo rules and RTP group)
• MetaWin: Originals hub (stated RTPs)
• Winna: max bet and max win limits on Winna Originals
• Card schemes as recorded in our casino audits and implemented in our verifier; odds, multipliers and the worked round computed by us