Slot machines operate on mathematical principles designed to ensure profitability for casinos while providing entertainment for players. The core mechanism is the Random Number Generator （RNG）, a computer program that constantly cycles through numbers even when the machine is not in use. When a player presses the spin button, the RNG stops at a random combination, determining the outcome. 
The probability of winning is determined by the number of symbols on each reel and the machine\“s programming. Modern slot machines use virtual reels with many more stops than visible symbols, allowing for complex odds calculations. The payback percentage, or return to player （RTP）, is a key mathematical concept representing the long-term expected return. For example, a machine with a 95% RTP will theoretically return $95 for every $100 wagered over millions of spins.
Another important mathematical aspect is the hit frequency, which indicates how often a machine pays out any prize. This is different from the RTP, as a machine can have frequent small payouts （high hit frequency） or rare large jackpots （low hit frequency）. The house edge is the mathematical advantage the casino holds, calculated as 100% minus the RTP. Understanding these mathematical fundamentals reveals that slot outcomes are purely random and predetermined by complex algorithms. |
