Win Cycle Calculator

Defaults are Hit Rate 30 percent, Sessions 10, Spins per Session 500. Submit. Avg. Spins Between Wins is 3.33 (that is 1/0.30), Expected Wins is 1500 (500 × 0.30 × 10), P(At Least 1 Hit / Session) is 100.00% for practical purposes, and P(No Hit / Session) is 0.00% because 0.70^500 is about 10^−78. With a 30% hit rate, a 500-spin session without any paying spin is not a realistic sample path; the interesting output is the 3.33 spacing and the 1500 count.

Lower Hit Rate to 1 percent, keep 10 × 500. Average spacing becomes 100 spins. Expected wins become 50. No-hit probability per session is 0.99^500 ≈ 0.66%, so about one session in 150 would be completely dry at 500 spins. That is the regime where the no-hit row stops being a decorative zero. Lower further to 0.2% (a sparse bonus-like hit if you misuse the field): spacing 500, expected wins 10, no-hit per session 0.998^500 ≈ 36.7%.

Sessions scales the expected-win total only. It does not change spacing or the per-session miss probability. Ten sessions of 500 is the same expected count as one session of 5000, but the no-hit probability is computed per session of 500, not on the aggregate. If you actually play one long sitting, set Sessions to 1 and put all spins in Spins/Session so the miss probability matches the sitting.

Hit Rate here is any success probability you choose to model: base-game pay, bonus trigger, or a custom event. It is not auto-linked to the 25% default in the volatility analyser. 30% was chosen so the default spacing is a clean 10/3 and the miss probability on 500 spins collapses to zero, teaching the geometric formula before the scary tail appears.

Reload 30, 10, 500 to recover 3.33, 1500, ~100%, ~0%. Then move only hit rate down until the no-hit percentage becomes visible. That exercise is the point: at 30% the drought language is folklore; at 1% it is arithmetic.

A win cycle is the waiting time between independent hits in a Bernoulli sequence. If each spin pays with probability p, the mean gap is 1/p spins. Slot marketing talks about “cycles” as if the machine owed a pay after a dry spell. The geometric distribution has no memory: 20 misses do not raise the chance of a hit on spin 21. This calculator’s purpose is to make the mean gap, the expected count, and the empty-session probability explicit for a chosen p, session length, and number of sessions.

Fruit-machine folklore in Britain used “the cycle” as a mechanical story about cams and reels. RNG slots have no cam. Hit rate is a weight table. High hit-frequency titles (25–40%) produce a pay—often a fraction of stake—every few spins, which players read as fairness. Low hit-frequency titles concentrate return in rare events. Both can share the same RTP. The cycle length is about frequency, not about edge.

Limits: independence, constant p, no distinction between a 0.2× dribble and a 200× feature. Expected wins is a mean count, not a cash total. P(no hit in a session) uses (1−p)^n, which for p = 0.30 and n = 500 underflows to zero on any sensible display. That is correct, not a bug. If you wanted bonus droughts, you must type the bonus probability, not 30%.

History: Feller’s volume on geometric waiting times is the mathematical ancestor; the gambling ancestor is every player who said “it has to pay soon.” Casinos do not store a pity timer in certified RNGs for ordinary hits (separate discussion exists around some licensed “must-hit-by” progressives, which are a different object). This tool models the memoryless case only.

Use it to size how long a session must be before a rare event becomes likely, and to stop calling a 3-spin gap at 30% hit rate a drought. Pair it with RTP for cash means and with bonus frequency for feature waits. It will not restore a loss after 50 blanks.

Waiting times for a hit are geometric when spins are independent and the hit probability is constant. If 30 percent of spins return anything counted as a hit, then p equals 0.30 and the mean wait until the next hit is one over p, which is approximately 3.33 spins. Variance of a geometric wait is (1 minus p) over p squared: 0.70 divided by 0.09 is about 7.78, so the standard deviation is about 2.79 spins and the 3.33 mean is tight. At p equal to 0.005 the mean wait would be 200 and the standard deviation about 199, so droughts of several hundred spins would be ordinary. The contrast is the lecture: moderate hit rates do not produce long droughts; rare features do.

Expected count uses linearity, which does not need independence. Each spin is a Bernoulli indicator with mean p. Over five sessions of 300 spins each there are 1500 trials, so expected hits equal 1500 times 0.30, which is 450. Dependence among clustered bonus spins would change the variance of that count, not the mean, so long as the marginal hit probability stays 0.30. The empty-session probability does need independence: the chance that 300 independent misses occur in a row is (0.70) to the power 300. Natural logarithm: 300 times ln(0.70) is about minus 107.0, so the probability is e to the minus 107, on the order of 10 to the minus 46, which any percentage display rounds to zero. Complement, at least one hit in a 300-spin sitting, is therefore indistinguishable from 100 percent on the page.

Worked identities to recover. Hit rate 30 percent, five sessions, 300 spins per session: mean wait 3.33, expected hits 450, empty-session chance tiny, at least one approximately 100 percent. Compare p equal to 0.01 over the same 300 spins: (0.99) to the 300 is about 0.049, so a blank sitting is no longer a fantasy. Compare p equal to 0.30 over 10 spins: (0.70) to the 10 is about 0.028, and the educational shock of the default 300-spin window disappears. Sessions multiply the expected count but the miss probability is computed per session, not Bonferroni-adjusted across five sittings. Probability that all five sessions are empty would be the per-session miss raised to the fifth, which is not displayed.

Assumptions. Constant p. Independent spins for the geometric tail. A hit defined however the rate was typed: any pay, or only a feature, two different meanings. No cash weighting, so ten tiny pays and one bonus count alike. The mean wait 3.33 does not say the bankroll rises; hits can be smaller than the stake while still occurring every few spins. That is why a 30 percent hit-rate game almost never produces a blank 300-spin sitting and can still leak, because the hits are 0.2 times dribbles. Geometric memorylessness is the other caution: having just waited five spins does not shorten the remaining wait.

History of the model is older than slots. Pascal and Fermat treated repeated independent trials; Bernoulli's Ars Conjectandi named the binomial count of hits in n trials, whose mean is n p, matching the 450. The geometric wait is the waiting-time sibling of that binomial. Use the sibling for droughts. Use the binomial mean for expected hits. Do not use either as a cash forecast without a prize table.