Expected value is a fixed mathematical figure that describes what a bet returns per unit wagered when repeated across a large number of rounds. Every position on a roulette layout has a payout ratio and a probability attached to it. Adding the probability of each outcome and the sum of those products gives the expected return. This calculation applies to every position on the roulette board and produces consistent results.
Two outcomes exist for any single roulette bet. Either the wager wins and receives the stated payout, or it loses, and the full unit is forfeited. Expected value captures both outcomes in a single number. A negative figure means the average return per unit is a loss over the long run. On standard roulette btc layouts, every bet type produces a negative expected value because payout ratios are set below the fair return that probability alone would require.
Do the formulas apply to inside bets?
A straight-up bet on a single number on a European single-zero wheel carries a probability of 1 in 37, since the wheel holds thirty-seven positions. The payout is 35 to 1. A fair payout for a 1 in 37 probability would be 36 to 1, returning the original unit plus 36 units of profit. At 35 to 1, the payout falls one unit short of the fair return.
Applying the formula: the win outcome contributes 1/37 multiplied by 35, which equals 35/37. The loss outcome contributes 36/37 multiplied by negative 1, which equals negative 36/37. Adding those two produces negative 1/37, which equals approximately negative 0.027, or negative 2.7% per unit wagered. Split bets cover two positions and pay 17 to 1. A fair return for 2 in 37 would be 17.5 to 1. The same one-unit shortfall applies proportionally, and the formula produces negative 1/37 again. Street bets covering three positions, corner bets covering four, and six-line bets covering six each carry the same result through the same structure. The payout ratio adjusts with each bet type, but the expected value figure does not change on a single-zero wheel. Every inside bet type produces a negative 2.7% per unit.
Double zero wheel shifts result
A double-zero wheel adds one additional pocket without changing any payout ratio. Thirty-eight positions now sit on the wheel, but a straight-up win still pays 35 to 1. A fair return for a 1 in 38 probability would be 37 to 1. The shortfall widens because the payout gap now spans two units instead of one.
The formula on a double-zero wheel: the win outcome contributes 1/38 multiplied by 35, which equals 35/38. The loss outcome contributes 37/38 multiplied by negative 1, which equals negative 37/38. The sum is negative 2/38, which equals approximately negative 0.0526, or negative 5.26% per unit wagered. Dozens and columns covering twelve positions still pay 2 to 1 on a thirty-eight-position wheel, and the formula produces negative 2/38. Even-money bets covering eighteen positions still pay 1 to 1, and the formula again produces negative 2/38. Every standard bet type on a double-zero wheel produces the same expected value of negative 5.26% per unit, a figure nearly double the single-zero equivalent.
