Hi-Lo Odds
A hi-lo call has two numbers attached: the chance that it wins, which comes from the deck, and the multiplier the game prints on the button, which comes from the game. The first is the same in every title with the same rules, and this page gives it for all thirteen cards. The second is the game's to choose, and the last section shows how to turn it into the return the game is actually offering.
The tables assume the ace is high. A game that ranks it low simply swaps the ace's row for the 2's and shifts every other card one step, and the page says where. For how a round runs and what the buttons do, see the how-to-play guide.
Fresh Deck: Every Card
Each card is drawn from a complete deck, so the showing card is still in the pack and every rank has the same chance on every call. A fair multiplier is the total return per unit staked that leaves the house no margin; the matching rank is counted as a loss here. With the ace low, read the ace's row as the 2's: from a low ace a higher call wins 92.31% of the time and a king becomes the card no higher call can beat.
Dealt-Down Deck: Every Card
The showing card has been removed and the other fifty-one remain, which is the position on the first call of a dealt-down deck. The match is rarer and every directional call a little likelier than from a fresh deck. Later in such a deck the figures depend on everything already dealt, and the table no longer applies.
When a Match Wins
Some games fold the matching rank into both calls, labelling the buttons accordingly. From an 8 the higher call then wins 53.85% of the time instead of 46.15%, and its fair multiplier falls from 2.1667 to 1.8571. From a 2 the higher-or-same call cannot lose at all, which is why such games print a multiplier of one on it, or refuse the call and offer only lower.
A separate Same button, where offered, is a bet on the match alone. From a fresh deck it wins 7.69% of the time whatever the card, so its fair multiplier is 13; from a dealt-down deck the chance on the first call is 5.88% and the fair figure 17. A printed multiplier can be compared with those directly.
From a Printed Multiplier to a Return
Multiply the multiplier on a button by the chance of that call and the answer is the share of the stake the call returns over time. A game that prints 1.625 on lower from a 10 returns everything, because that is the fair figure in the first table; a game that prints less returns the shortfall to itself. The same arithmetic runs backwards: a game that states its return in the rules has, in effect, told you every multiplier on every button, since each is the fair multiplier scaled down by that percentage.
The key number: Return per call equals the printed multiplier times the chance behind it; a 10 showing with 1.625 on lower is a game keeping nothing.
That is also why one hi-lo title cannot be cheaper on one card than another. Where every button is priced at a single return, a long shot from the middle of the deck and a near-certainty from its end give up the same share of the stake; the long shot just does it in fewer, larger steps. A title whose stated return is higher is cheaper on every call at once.
Chains of Calls
A chain of correct calls returns the product of its multipliers, and its chance of coming off is the product of the chances. Both multiply the same way, so a chain priced at one return per call is priced at the same return overall, no matter how long it runs. Stopping after two calls or after six does not alter what was given up on each; it alters only how much of the accumulated win is exposed to the next card.
The exposure is the point to keep in view. By the fourth or fifth call the running win is several times the stake, and a single wrong card takes the whole of it, which is a far larger swing than any single call carries. Players who bank often see smaller wins more frequently; players who run long chains see larger wins rarely. The game keeps the same share of each either way.
The rule: Banking early leaves the game's share untouched and only trims the sum the next card can take away.
Why No Single House Edge Is Quoted
Blackjack, baccarat and roulette each have a house edge that follows from fixed rules and fixed payouts. Hi-lo does not, because the payouts are whatever the studio decided to print, and two titles with identical decks and identical rules can sit at very different returns. The honest figure for a hi-lo game is therefore the return its own help screen states, read in the knowledge that it is the game's choice rather than a law of the cards.
The chance tables above are the fixed half of the arithmetic, the half that lets a stated return be checked: pick any card, set its printed multiplier against the table, and the product should match the figure the game claims. Where it does not, one of the two is wrong, and the rules screen is the place to look first.
Hi-Lo Odds FAQs
They depend entirely on the card showing. From a 2 with the ace high, higher wins 92.31% of calls; from an 8 either call wins 46.15%; from an ace, lower wins 92.31%. The remainder in each case is the chance of a matching rank.
7.69% of the time when every card comes from a full pack, whichever card is showing. Remove the showing card, as a dealt-down deck does, and the first call carries 5.88%.
At fair value, one divided by the chance of the call. A call that wins half the time is worth a total return of two per unit staked; a call that wins 61.54% of the time, such as lower from a 10, is worth 1.625. A game prints less than that figure, and the gap is its margin.
Only in games that deal a real deck down. Where every card comes from a fresh pack the odds never move. Where cards are removed, the first call is already a little different from the fresh-deck figure and later calls drift further as the deck empties.
With the ace high it is the 8: both calls stand at 46.15%. With the ace low the middle of the deck moves to the 7. Both are the cards a skip button exists for.