Free spins and the expanding symbol

Free spins are a bonus round of spins you do not pay for, started by scatter symbols. In Book of Thoth three books anywhere give ten, and a special symbol drawn at the start fills whole reels when it lands on enough of them. The bonus comes once in 187 spins, pays 62 bets on average and holds 33.11% of the machine’s 95.20% return.

A scatter pays wherever it lands; lines do not matter. Each strip of Book of Thoth has exactly one book, and it shows in the window on 3 of the 36 stops of reels 1 and 2 and on 3 of the 35 stops of reels 3 to 5 — about one spin in twelve on each reel. For the bonus you need it on at least three of the five reels.

Look at the “two” row. Two books land once in 18 spins, so for every bonus you will see about ten spins where the third book did not come. In our game the remaining reels spin a little longer after two books to build the suspense, but that is theatre: the result was settled on the server before the first reel stopped.

1. Before the first free spin Thoth draws the special symbol: one of the nine symbols other than the book, each with a 1 in 9 chance.
2. Every free spin pays its lines as usual. Books are still wild on the lines and still pay as a scatter.
3. Then the game counts on how many reels the special symbol shows, anywhere in the window.
4. If that is enough — two reels for Thoth, the mask and Anubis, three for the others — those reels fill from top to bottom, and the symbol pays its line pay for that many symbols on all ten lines at once.

Two things surprise new players. The reels do not have to be neighbours: a ten on reels 2, 4 and 5 pays exactly like a ten on reels 1, 2 and 3. And the expansion is paid on top of the line wins of the same spin, so the special symbol can be paid twice — once on its own lines and once as an expanded block.

Three books during the free spins add ten more, up to a hundred in one bonus. Free spins use the same strips as ordinary spins, so the chance of a retrigger is the same 1 in 187 on every free spin. About one bonus in 19 gets at least one retrigger. Working through every possible chain of retriggers gives an average of 10.56 free spins per bonus.

Some machines switch to special, richer reels for their bonus. Book of Thoth does not: all the extra value of a free spin comes from the expanding symbol.

A symbol’s value in the bonus is a trade between how often it expands and how much it pays when it does. The ten has six copies on every strip, is visible on about half of all reel stops and fills reels in every other free spin: small pays, but constantly. Thoth has one copy, needs only two reels, yet still expands in just one free spin in seventeen.

Thoth’s strength is the tail. Four reels of Thoth pay 1,000 bets in a single free spin, five reels pay 5,000 — the round’s cap. About one Thoth bonus in 390 has such a spin. So when Thoth turns the page and shows himself, cheer by all means; just know that on average the ten would have served you better.

An ordinary spin of Book of Thoth is worth 0.62 bets on average, books included. A free spin is worth 5.87: the same 0.62 plus 5.25 from the expanding symbol. Ten and a half of those every 187 spins add up to 33.11% of all bets — more than a third of everything the machine gives back.

The bonus is lumpy, though. 22% of bonuses pay under 15 bets, and more than half pay under 50. At the other end, 18% pay 100 bets or more, one in 311 pays 500 or more and one in 1,933 pays at least 1,000. In 10.7% of bonuses the special symbol never expands at all. That shape is what makes the machine volatile; the numbers behind it are in RTP and volatility.

• “After a long dry spell the bonus is due.” Every spin has the same 1 in 187. One stretch of 300 spins in five passes without a bonus, and one in fourteen goes 500 spins dry, without the machine owing anything.
• “Big bets get stingier bonuses.” The bonus is counted in bets: at 100 debens and at 50,000 it pays the same multiple on average.
• “Thoth is the best special symbol.” He is the most exciting one and, on average, the least paying.
• “Stopping the reels or turbo changes the bonus.” The whole bonus, every free spin included, is drawn on the server at the moment of the triggering spin; the buttons only change how fast you see it.