Payout Rules And House Advantage

Payout rules and house advantage

Most casino bets pay less than a mathematically fair exchange would require. In a fair wager the probability-weighted net results add up to zero. Trim the winning payment, leave every probability untouched, and the player's expected value turns negative. No rigged dice are needed.

A die as the simplest case

This is the cleanest way to see where the house advantage in casino games comes from. Bet $1 on one face of a fair six-sided die. The face comes up one time in six, so a fair payment is $5 profit per win: five losses of $1 against one win of $5, average zero. Now suppose the payment is cut to $4. Over six rolls the player collects $4 once and loses $1 five times, a net loss of $1 across $6 staked. The average cost is one sixth of every stake, about 16.67%, and the die was never anything but fair.

Other pricing tools

A reduced payout is only the most visible method. Commissions deducted from selected wins do the same job in a less obvious way. So do rules that hand a tied result to one side, or that settle certain outcomes at half the stake. Each one shifts the average without touching the randomness of the draw.


Two checks follow from this. Confirming that outcomes are generated randomly answers one question. Calculating what the payout schedule returns on average answers a different one, and a game can pass the first while scoring badly on the second. A comparison that quotes only the headline payout and ignores commissions, tie rules and partial losses is incomplete, and usually flatters the game.