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Expected value of a casino wager

What does a bet actually cost on average? The question sounds simple, and the arithmetic behind it is simple too. List every possible outcome of the wager, attach a probability to each, and record the net amount won or lost in each case. Multiply result by probability, add everything up, and the sum is the expected value. When that sum is negative, the player pays an average price for every round played.


Take a wager with a 2% disadvantage. Over 500 units of betting the expected loss is 10 units. Nobody loses exactly 10 units in a given session, of course. The figure is an average over a very large number of repetitions, not a deduction applied to each individual result. Short samples wander far from it.


Where does the percentage come from? From the full rule set. Payout ratios, commissions on winning bets, tied hands that return the stake, and the choices a player is allowed to make all enter the calculation. Two games sharing a name can carry different prices once one of those details changes, so a comparison is only informative when it names the exact bet and states which rules apply.


Average cost is one thing; the spread of results is another. A wager with a small expected loss can still swing wildly if its big payouts arrive rarely. The [https://casinohouseedge.com/ casino house edge] describes the price of repeated participation, while variance describes how bumpy the road to that average will be. The first number is silent on which way a single evening will go.