Normal Distribution

The normal distribution, often visualized as a bell curve, is the probability distribution that describes how results cluster around the average in many random processes. In gambling, the distribution of outcomes over many bets approximates a normal distribution centered on the expected value, with the spread determined by the standard deviation.

For a gambler making many bets, the normal distribution allows you to predict the range of likely outcomes. After 1,000 even-money bets, approximately 68% of the time your results will fall within one standard deviation of the expected loss. Approximately 95% of the time, results will be within two standard deviations. This provides a framework for determining whether your actual results are within normal expectations.

The shape of the distribution depends on the game's volatility. Low volatility games produce a narrow bell curve with results tightly clustered around the expected value. High volatility games produce a wider bell curve with results spread over a broader range. Both distributions are centered on the same expected value (determined by the house edge), but the experience of playing them is very different.

Casino revenue projections rely heavily on normal distribution mathematics. By knowing the house edge and the expected volume of play, casinos can calculate with high confidence what their revenue will be within narrow bounds. An individual player's experience is just one draw from this distribution, which is why personal results can vary so widely from the mathematical expectation.