Casino ede

If a player bets $1 on red, his/her chances of winning $1 is 18/38 since 18 red numbers exist out of  However, his/her chance of losing $1 (i.e., winning −$1) is 20/ Therefore, the expected value may be calculted as follows:

Expected Value = (1)(18/38) + (−1)(20/38)

Expected Value = 18/38 − 20/38

Expected Value = − 2/38 = − 1/19

Expected Value = −%

Therefore, the house edge is %.

Example #2:

Calculate the house edge for European Roulette, which contain a single zero and 36 non-zero numbers (18 red and 18 black).

Solution #2:

If a player bets $1 on red, his/her chances of winning $1 is 18/37 since 18 red numbers exist out of  However, his/her chance of losing $1 (i.e., winning −$1) is 19/ Therefore, the expected value may be calculted as follows:

Expected Value = (1)(18/37) + (−1)(19/37)

Expected Value = 18/37 − 19/37

Expected Value = −1/37

Expected Value = −%

Therefore, the house edge is %.

Example #3:

Calculate the house edge for a game played by wagering on a number from the roll of a single die with a payout of four times the amount wagered for a winning number.

Solution #3:

Since the probability of a winning number for a single roll of a die is 1/6, it follows the game has 5 to 1 odds.  However, with a payout of only four times the amount wagered (i.e., 4 to 1) for a winning number, the house edge may be calculated as follows:

House Edge = (true odds − payout odds) / (true odds + 1)

House Edge = (5 − 4)/(5 + 1)

House Edge = 1/6

House Edge ≈ %