Book of Thoth

Book of Thoth is a five-reel, ten-line slot built around free spins. Three books anywhere give ten of them, and a special symbol drawn at the start fills whole reels whenever it lands. The machine returns 95.20%: 62.09% from ordinary spins and 33.11% from free spins, which come once in 187 spins and pay 62 bets on average.

Reels 1 and 2 have 36 stops each, reels 3 to 5 have 35. Every strip carries one book, one Thoth, two pharaoh’s masks, two Anubis, four scarabs (three on the last three reels), five each of A, K, Q and J and six tens. The same strips spin in the free spins.

Your bet is split over ten lines, so at 100 debens each line carries 10. A line pays matching symbols in a row from the leftmost reel: Thoth, the mask and Anubis from two, everything else from three. The book does two jobs. On a line it is wild and replaces any symbol. Anywhere on the screen it is a scatter: three books pay 2 bets, four pay 20, five pay 200, and three or more start the free spins.

Books on a line count as the symbol next to them, so a book, a book and a mask on the first three reels pay as three masks. Only the best combination on each line pays, the lines add up, and the scatter pays on top.

1. Three or more books anywhere pay their scatter win and open 10 free spins at the same bet.
2. Thoth leafs through his book and picks the special symbol: one of the nine symbols other than the book, each with the same chance of 1 in 9.
3. Each free spin pays its lines as usual. On top of that, if the special symbol shows on enough reels — two for Thoth, the mask and Anubis, three for the others — it fills those reels and pays on all ten lines for that many symbols. The reels do not have to be next to each other.
4. Three books during the free spins add 10 more, up to 100 free spins in one bonus.
5. A round, meaning the spin plus all its free spins, pays at most 5,000 bets. Once that is reached, the remaining free spins are not played.

An ordinary spin is worth 0.62 bets on average. A free spin is worth 5.87, almost ten times more, and that difference is the whole reason the machine is so quiet the rest of the time. The mechanics in more detail, with the maths of retriggers: how free spins work.

Here is the surprise. The humble ten is the best special symbol, and Thoth, the one everybody cheers for, is the worst on average. The ten sits on six stops of every strip, so it fills reels in half of all free spins. Thoth sits on one, so it expands in only one free spin in seventeen.

What Thoth has is reach. Four reels of Thoth pay 1,000 bets in a single free spin and five reels pay 5,000, the cap. About one Thoth bonus in 390 contains such a spin. So the ten pays the rent and Thoth buys the lottery ticket — and since the choice is Thoth’s, not yours, it all averages out to the same 62 bets.

Ordinary spins: we went through all 36 × 36 × 35 × 35 × 35 = 55,566,000 reel positions with the game’s own line rules. Free spins use the same strips, so for every special symbol we calculated exactly how often it shows on two, three, four or five reels, and how many free spins a bonus lasts with retriggers: 10.56 on average. Only the 5,000-bet cap needed a simulation. In 6 million bonus rounds it was hit 26 times, which costs the return 0.0002%. A check run of 100 million full spins gave 95.33% ± 0.08%, within the noise.

Seven spins in ten pay nothing at all, and the bonus is a lumpy thing: more than half of all bonuses pay under 50 bets, while the average of 62 is held up by the few that pay hundreds. That makes Book of Thoth the most volatile of the three machines, with a standard deviation of 8.45 bets a spin.

In our 20,000 test sessions with 10,000 debens at 100 a spin, the median one ended after 362 spins — the shortest of the three machines — and yet in 31.5% of them the purse doubled at some point. And any 500 spins in a row have a 7% chance of passing without a single bonus.

• Bring enough for a dry spell. With 10,000 debens at 100 a spin the median session lasts 362 spins — about two bonuses’ worth of waiting. If you want a fair chance to see the free spins, lower the bet rather than hope.
• Two books and a slow third reel mean nothing. The extra spin time is a show; the result was decided before the first reel stopped.
• You cannot pick the special symbol. Thoth draws it at random, 1 in 9 each, so over many bonuses they all blend into the same 62-bet average.
• The bet does not change the odds. The return is 95.20% at every stake, and the 5,000-bet cap is measured in bets, so it scales with you.