Theorem 1: If a gambler risks a finite capital over many plays in a game with constant single-trial probability of winning, losing, and tying, then any and all betting systems lead ultimately to the same value of mathematical expectation of gain per unit amount wagered. This is formally stated by game theorist Richard Arnold Epstein in The Theory of Gambling and Statistical Logic as: card counting and handicapping), can alter long-term results.

Strategies which take into account the changing odds that exist in some games (e.g. Mathematically, no betting system can alter long-term expected results in a game with random, independent trials, although they can make for higher odds of short-term winning at the cost of increased risk, and are an enjoyable gambling experience for some people. Betting systems are often predicated on statistical analysis. To be successful, the system must change the house edge into a player advantage - which is impossible for pure games of probability with fixed odds, akin to a perpetual motion machine. A betting strategy (also known as betting system) is a structured approach to gambling, in the attempt to produce a profit.