Ember Circus

1. 01

   Draw k is int(k, W), W = 317 being the sum of the symbol weights; the symbol is the one whose weight range the value falls in. Weights, in the order Ringmaster, Fire breather, Juggler, Torch, Hoop, Ticket, Spark, Match, Rope, Flame, Big top: 12, 16, 20, 24, 28, 44, 48, 52, 56, 8, 9.

2. 02

   The first 15 draws fill the grid column by column, top to bottom. A wild drawn on reel 1 or 5 becomes the last low symbol.

3. 03

   Each cascade refills the cleared cells with further draws: columns left to right, top to bottom.

4. 04

   Ways from the right take no draw: in free spins each symbol is counted again from reel 5 leftwards, unless it already reached all five reels from the left.

5. 05

   Free spins run the same way on the same stream; a bought feature has no spin before it, so its draws begin at k = 0 with its first free spin. The whole spin, feature included, is reproducible from one nonce.

float(k) and the rest of the notation are defined in the byte stream.

5 reels × 3 rows, 243 ways, left to right. Winning symbols clear and new ones fall in; each cascade in a spin climbs 1× → 2× → 4× → 8×. Wilds land on the three middle reels.

In free spins every way pays from the left and from the right: a symbol on 3 or more consecutive reels counted from reel 5 pays as it would from reel 1. A way across all five reels is paid once. About one free spin in 3 pays a way from the right.

3, 4 or 5 scatters on the first drop of a spin award 10, 15 or 20 free spins; 3, 4 or 5 on a free spin add that many again, up to 60 free spins in all. The feature can be bought for 18.13× the bet with 10 free spins, for 27.18× with 15, or for 36.26× with 20. Each price is what those spins return on average, less the house's share: no tier is a better buy than another.

Bought, the three return 96.30%, 96.29% and 96.29%, as measured (each give or take 0.15 points at most); most buys return less than they cost.

When two scatters are in view, the reels still turning stop more slowly. That is decided only by the reels that have already stopped and happens every time two are in view, whether a third comes or not: it says nothing about what the turning reels will show.

One spin, feature included, pays at most 8,000× the bet: a spin that reaches it stops there and is paid exactly that.

The return printed here was measured, not derived: 96.33%, give or take 0.10 points, over 60 million spins. 36.5% of spins pay something; the free spins come about one spin in 124 and pay 15% of the return.