Hawkplay Standard Deviation: How Much a Slot's Results Spread

Standard deviation is a measure of how far a set of results spreads around its average. For a slot player it answers the question RTP cannot: two games can return the same average and still feel nothing alike. This page explains the term from a statistics reference, then puts three example slots through it with pesos. Once you can read the idea, the slot machine free play basics on the pillar page make more sense.

What standard deviation means

Wikipedia defines standard deviation as a measure of the amount of variation of the values of a variable about its average. A low standard deviation says values sit close to the average, and a high one says they are spread over a wider range. It is the square root of the variance, and unlike the variance it is in the same unit as the data.

The same reference gives a small example of three populations that share one average.

Same average, very different spread, and that is exactly the situation with slots.

A worked example with three slots

The table below is an example with round numbers, not data from any game. Each slot is shown over five spins at a ₱100 stake, and all five return figures average ₱100.

To get Slot C’s figure, subtract the average from each result (-100, -100, -100, -100 and +400), square them, average the squares (40,000) and take the square root (₱200). The same steps give about ₱7 for Slot A. A is a steady slot and C is a rare-big-win slot, even though their averages match.

Why RTP alone is not enough

RTP is an average over a very large number of spins, and the house edge meaning against swings is its mirror image: 100% minus RTP. Neither number says how bumpy the road is between spins. Standard deviation does.

Gates of Olympus 1000 publishes an RTP of 96.50%, a very high volatility rating and a top win of 15000x. Mahjong Ways publishes 96.92% with medium volatility and 25000x. The RTP figures sit within half a point of each other, yet the volatility ratings say the first spreads its results far wider, and that spread is what standard deviation measures.

How standard deviation shows up in a slot’s info screen

Studios give you volatility, not a standard deviation figure. The slice titles on this site carry a volatility label and a top win, and Yellow Bat prints Yellow Bat star ratings for volatility on every card of its games list. Read them this way:

1. Low volatility with a modest top win: results cluster, like Slot A.
2. High volatility with a high top win: results scatter, like Slot C.
3. Same RTP on both: the average is the same, the ride is not.

Pair the label with hit frequency meaning beside standard deviation, the share of spins that pay anything. A low hit frequency usually goes with a larger spread, so a count from a 100-spin demo run is a rough check on the label.

Where the normal curve stops helping

For a normal bell curve, about 68% of values fall within one standard deviation of the average, 95% within two and 99.7% within three. Slot results are not bell-shaped: most spins pay little and a few pay a lot. Use the idea of spread, and skip the percentages when you read a slot.

Using it on the lobby

Try the idea on a pair of Western titles: the cowboy slots on the lobby compared put a high-volatility 5000x slot beside a medium-volatility 2500x one. Run 100 spins on each at one stake, count the paying spins and note the largest win, then compare the scatter yourself.