Hold & Win: respins, sticky symbols and jackpots

Hold & Win is a bonus in which prize symbols stay on the screen while the empty cells respin. In Treasures of Horus six golden scarabs start it with three respins; each new scarab resets the count to three, and at the end every scarab pays, with a GRAND for a full screen. It comes once in 102 spins and pays 30.4 bets on average.

Scarabs land on every reel, one by one or in stacked pairs, and each shows its prize as soon as it lands. In the base game those prizes are only a promise: they pay when six or more scarabs share the screen. Most spins come nowhere near.

Five scarabs, one short, land once in 38 spins, so for every bonus you will see two or three of these near things. They mean nothing: in the base game scarabs do not stay, and the next spin starts from an empty screen with the same 1 in 102.

Once the bonus starts, the scarabs lock in place and every other cell empties. On each respin every empty cell, independently, has a 1 in 18 chance to turn into a new scarab. With nine empty cells that is half a new scarab per respin on average, and a 40% chance of at least one.

The counter is what keeps the bonus alive. It starts at three, drops by one after an empty respin and jumps back to three after any respin that brings a scarab. So a bonus that keeps finding scarabs can run for a long time, and the average one plays 6.6 respins and finishes with 8.8 scarabs. The other side: in 22% of bonuses not a single new scarab lands, and three empty respins end it with what was there at the start.

How did we get exact figures for something so branching? A bonus is fully described by two numbers — how many cells are full and how many respins are left. From each such state we know the probability of every next state, so we followed the probabilities step by step until every path ended. The result agrees with 100 million simulated spins within the simulation’s own margin of error.

Take the most common bonus, the one that starts with six scarabs. An average scarab is worth 3.02 bets in the base game, so 18.1 bets are on the screen from the first moment. New scarabs, 2.6 of them on average at 3.31 bets each, add 8.6. The GRAND contributes 3.0: a thousand bets times its 0.3% chance. Together, 29.8 bets.

Compare that with free spins. Hold & Win pays much more evenly: half of all bonuses land between 20 and 35 bets and nearly nine in ten between 15 and 50, only 9% pay less than 15 and only 3.4% pay more than 50 without the GRAND. The free spins of Book of Thoth pay under 15 bets in 22% of bonuses and over 100 in 18%. Same average return, very different ride — that is volatility, and it is why the Hold & Win machine keeps a purse alive longest of the three.

Here is a Hold & Win board with the machine’s own rules: 15 cells, three respins, a 1 in 18 chance per empty cell, and scarab prizes drawn with the same weights the game uses, shown at a bet of 100. Start with six scarabs and play a few bonuses, then try starting with ten and see how much more often the screen fills.

In real-money halls the top Hold & Win jackpots are often progressive: a slice of every bet feeds a pot that grows until somebody hits it. Ours are fixed multiples of your own bet — MINI 10, MINOR 25, MAJOR 100 and GRAND 1,000 bets. Nobody’s bet pays for anybody else’s jackpot, the return is exactly the same at 100 debens and at 50,000, and there is never a “better moment” to play because a pot looks big.

In numbers: a MINI shows up in 7.2% of bonuses, a MINOR in 2.0%, a MAJOR in one bonus in 400 and the GRAND in one bonus in 314 — once in 32,016 spins.

• Chasing the sixth scarab. Five scarabs on the screen do not carry over. The next spin is a fresh 1 in 102.
• Raising the bet “because a bonus is coming”. Nothing is coming; the bet only scales the prizes, not the chances.
• Counting on the GRAND. At 1 in 32,016 spins it is a pleasant surprise, not a plan. It adds 3 bets to an average bonus, a tenth of its value.
• Thinking a long bonus is a lucky machine. A long chain of respins is luck inside one bonus; it says nothing about the next one.