Stacked symbols: why they make wins rarer but bigger
Stacking a symbol on a reel strip cuts how often it shows but fills more rows when it does. On an invented 30-stop strip, 60% of windows fall to 26.7%.
From one-armed bandit to video slot: a short history
Four dates show how slots changed: the 1890s Liberty Bell, 1963's Money Honey, the 1976 video slot and the 1984 virtual reel patent, with the odds each allowed.
How a random number generator picks each spin
A slot spin starts with a pseudo-random number generator: a seed, a state, and a rule that turns each number into a reel stop. A 16-stop worked example.
Turbo and auto spin: what speed changes and what it doesn't
Faster spins mean more spins per hour, not better or worse odds per spin. In an example, 4 times the spin rate uses 4 times the coins per hour at the same RTP.
Left to right: why a ways win must start on reel one
In a ways slot a symbol pays only if it runs unbroken from reel one. Counting examples show how one missing cell turns 81 ways into none.
What a multiplier does to a ways-to-win payout
A multiplier scales the pay per way, not the number of ways. Worked through with hypothetical pay values: one cell, the whole win, and stacked multipliers.
Reel strips and stops: where a slot's reels land
A reel strip is an ordered list of stops. One random number picks a stop per reel, and a symbol's chance is its count over the strip length. A 20-stop example.
Near misses: why a symbol just off the line counts for nothing
A symbol one reel short of a ways-to-win line pays nothing. With invented odds, four matching reels in five miss 60% of the time. The sums are shown.
Hit frequency: why most slot wins are smaller than the bet
A made-up slot hits on 43.6% of spins, yet only 13.6% return more than the stake. Hit frequency and RTP are different numbers, and the sums show why.
Scatter symbols: the odds of three on five reels
If each reel shows a scatter with probability 0.2, three or more across five reels turn up 5.79% of the time. Here is the binomial maths, step by step.
How a pick bonus works, and why the picks are already decided
In most pick bonuses the prize is drawn by the RNG when the bonus triggers, and the taps only reveal it. A worked example shows the expected value and why choice cannot help.
Slot RTP and volatility: what each number measures
Three toy slots all return 96% yet behave very differently. RTP is the long-run average; volatility is the spread, and the maths shows how to tell them apart.
Why a slot is never due: independent spins explained
A 1-in-100 feature misses 100 spins in a row 36.6% of the time, and after any drought the expected wait is still 100 spins. Here is the maths of independence.
How a wild changes the count on a ways-to-win slot
A wild adds one to a symbol's count on its reel, so the ways total jumps as a product. It can also bridge an empty reel and lengthen the run.
What 243 ways to win means, and how it differs from paylines
243 is 3 to the power of 5, every left-to-right path through a 5×3 grid. Wins are counted by multiplying symbol counts on adjacent reels.