hizi.engine, the no-code game-engine builder on the hizi.io Game-Studio Operating System, adds Match, a new Original. A pool of numbered balls is shuffled into numbered slots and the player bets on how many land back in their own slot - exactly that many, or at least that many. The odds behind every bet are exact combinatorics, the payouts are derived from them, and the RTP holds whatever the player picks. Match is live inside hizi.engine now, exclusively for studios on hizi.io.
A 300-year-old puzzle
Match is built on the hat check problem, a probability puzzle first published in 1708. A hundred guests leave their hats at a coat check. The attendant loses the tags and hands the hats back at random. How likely is it that nobody gets their own hat?
Most people guess close to zero. The real answer is about 36.8%, and it barely depends on the size of the crowd: for any pool beyond a handful of items the probability settles at 1/e, where e is Euler's number. The puzzle has a second twist. It is impossible for exactly 99 of the 100 guests to get their own hat back, because the one hat left over can only belong to the one guest left over. Exactly N-1 matches never happens, for any N.
Those two facts, one counter-intuitive and one absolute, are what make the mechanic work as a game. The player's gut and the real odds disagree, and the game lives in that gap.
How Match plays
The player sets three things: the number of balls in the pool, the bet mode and the target. Exactly wins on exactly that many matches, At least wins on that many or more. Multiplier, win chance and the amount to win are shown before the bet is placed. The balls drop into their slots, matches light up, and the round resolves in a single call. A Match Road keeps the history of recent draws, the way a baccarat road does, so streaks are visible at a glance. The impossible target is simply not on the board.
The Match prototype: 5 balls, Exactly 1 and At least 2, with the Match Road tracking the last 50 draws.
The prototype above is a reference frontend. On the platform a studio builds its own presentation on the hizi SDK; the engine provides the bet list, the odds and the outcome.
The math does the work
With five balls there are 120 possible arrangements. 44 of them have no ball in its own slot, so a bet on zero matches wins 36.67% of the time. Every multiplier is the configured RTP divided by the probability of the bet, so the house edge is identical on every line. At a 98% RTP the five-ball table looks like this:
| Target (exactly) | Ways (of 120) | Win chance | Multiplier |
|---|---|---|---|
| 0 matches | 44 | 36.67% | 2.67x |
| 1 match | 45 | 37.50% | 2.61x |
| 2 matches | 20 | 16.67% | 5.88x |
| 3 matches | 10 | 8.33% | 11.76x |
| 4 matches | 0 | impossible | not offered |
| 5 matches | 1 | 0.83% | 117.6x |
Match on 5 balls at 98% RTP. At least bets sum the lines above the target.
Volatility is in the player's hands. On the same five balls and the same RTP, At least 1 is a 63.33% shot at 1.55x, while exactly 5 is a 1-in-120 shot at 117.6x. The general formula behind every line counts the ways to pick which k balls stay put and derange the rest:
The same formula runs at any pool size, and the top end grows factorially: on ten balls a perfect match is a 1-in-3,628,800 event and pays 3,556,224x at 98% RTP. A studio sets the ball range and the RTP per configuration, and every multiplier follows from them; there is nothing to tune by hand. The full derivation, including the payout matrix for pools of 3 to 12 balls, is in the Match math primer (PDF).
Built into hizi.engine
Match ships as a game type in the hizi.engine builder, next to slots, plinko, mines, keno, bingo, crash, roulette and blackjack. The studio configures the ball range, the bet modes and the RTP. The engine generates the bet list with the exact win probability and multiplier for every line, draws the arrangement on the certified RGS behind every hizi game, and returns the result with the matched slots, ready to animate. The frontend never shuffles anything itself, and rounds can run as provably fair. The frontend contract is documented at docs.hizi.io.
Robert Lenzhofer, CEO of hizi.io, said:
"Crash, mines and plinko all do the same trick: a simple picture of a simple probability. Match turns that around. The picture is simple, but the probability is one that breaks people's intuition, and that gap is the game. The odds are exact, the payouts follow from them, and the RTP does not move whatever the player picks. We built it once, inside hizi.engine, and every studio on the platform can ship it."
About hizi.io
hizi.io is a self-service Game-Studio Operating System for real money games (iGaming) and the evolution of the hinterzimmer.io RGS. Part of THE SPIEL GROUP, hizi.io lets game studios, operators and aggregators rent a complete, certified Remote Gaming Server - backoffice, no-code game engine, billing, hosting, compliance and aggregator connectivity - month to month, with public pricing and online T&Cs. More at hizi.io.