The "expected return on a dollar in Las Vegas" is a complex concept, as it varies significantly depending on the specific game played, the rules of that game, and the player's skill level. Generally, for most casino games, the expected return is less than one dollar, meaning the player is expected to lose money over the long run. This is due to the inherent house edge built into every game. For the vast majority of casino games in Las Vegas, the expected return on a dollar is less than $1.00, typically ranging from approximately $0.90 to $0.99, depending on the game and specific rules. This means that for every dollar wagered, a player can expect to receive back, on average, between 90 cents and 99 cents. The difference represents the casino's profit, known as the house edge. For example, a game with a 5% house edge would have an expected return of $0.95 for every dollar wagered.

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The expected return can be calculated using the formula: $E=\sum (P_i\times R_i)$, where $E$ is the expected return, $P_i$ is the probability of a specific outcome, and $R_i$ is the return for that outcome. For instance, in a simplified coin flip where you bet $1 and win $2 if it's heads (50% chance) and lose $1 if it's tails (50% chance), the expected return would be $(0.50\times \$2)+(0.50\times -\$1)=\$1-\$0.50=\$0.50$. However, casino games are designed with a negative expected return for the player.

House Edge and Game Variations

The house edge is the primary determinant of the expected return. Different games have different house edges:

• Blackjack: The house edge in blackjack can range from as low as 0.2% to 1% or more, depending on the specific rules (e.g., number of decks, blackjack payout, dealer hits or stands on soft 17) and the player's strategy. A player employing perfect basic strategy can significantly reduce the house edge, leading to an expected return closer to $0.998 per dollar wagered in optimal conditions.[1]
• Craps: The house edge in craps varies by bet. The "Pass Line" and "Don't Pass Line" bets have a relatively low house edge of around 1.41% and 1.36% respectively, leading to an expected return of approximately $0.9859 and $0.9864 per dollar.[2] However, other bets on the craps table can have a much higher house edge, sometimes exceeding 10%.
• Roulette: American roulette, with both a single zero and a double zero, has a house edge of 5.26% on most bets, resulting in an expected return of approximately $0.9474 per dollar.[3] European roulette, with only a single zero, has a lower house edge of 2.7%, yielding an expected return of approximately $0.973 per dollar.[3]
• Slot Machines: Slot machines have the widest range of expected returns, often expressed as "Return to Player" (RTP) percentages. These can vary significantly from machine to machine and casino to casino, typically ranging from 85% to 98%.[4] This means an expected return of $0.85 to $0.98 per dollar. High-denomination slots generally have higher RTPs than penny slots.
• Video Poker: Similar to blackjack, video poker can offer very high expected returns, sometimes exceeding 99% or even 100% with optimal strategy and specific pay tables (e.g., "full pay" machines). For example, a "full pay" Jacks or Better machine with optimal strategy can have an expected return of 99.54%, meaning an expected return of $0.9954 per dollar.[5] However, finding such machines and consistently playing with optimal strategy is crucial.
• Baccarat: Baccarat has a relatively low house edge, particularly on the "Banker" bet (around 1.06%) and the "Player" bet (around 1.24%). The "Tie" bet has a much higher house edge (around 14.36%).[6] This translates to an expected return of approximately $0.9894 for the Banker bet and $0.9876 for the Player bet.

It's important to note that these are long-term averages. In the short term, a player can experience significant wins or losses due to the inherent randomness of casino games. The expected return is a statistical measure that becomes more accurate over a large number of trials.

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