Basically, the house edge is the percentage that the casino should hold as profit on a game. Of course, probability is not a straight line through a set of stationary numbers and this percentage will vary in the short term, but should get remarkably accurate in the longer view. The simplest form of the calculation is what we will look at today with  roulette.

On both American and European roulette tables there are 36 numbers of equal red and black colours. They are arranged into three columns of 12 numbers. The key differences are extra green numbers, a single 0 on the European table and 0 and 00 on an American table. This gives a total of 37 betting square on European and 38 on American. There are a multitude of other betting paces such as ODD/EVEN and RED/BLACK.

The house traditionally pays 35:1 on the numbers, which is 35 chips back in addition to the one you bet. If there were only 36 numbers (rather than 37 or 38) then the game would not offer any advantage to the player or the house as there would be one chip returned for each number available. In the long term, both parties would come out even. Following so far? If we were to play the European table, 36 numbers would pay back, but there are 37 on the table, so one number is the house edge. Likewise on the American table there are two numbers out of 38 for the house.

To calculate the edge, we need to look at the number of unpaid possibilities divided by the return offered if the bet was paid out. If all 37 chips were played on the European table on the numbers, you would walk away with 36. The loss of 1 divided by 37, gives a house edge of 2.7% (2/38 or 5.26% for the American table).

For the RED/BLACK and other even bets, this is the same as the green 0s belong to the house. So if you bet both red and black, you would come back with the same money except when the ball landed on green. OK, so what if we cover the even bets with a “hedging bet” on green. A simple example would be to start at the wheel stopping at 1 and climb through the numbers with the 37th spin going on green 0.

For each of the first 36 bets we receive back 2 chips for each 3 played, which yields a gain to the house of 36. For the last bet which lands on the green, we get 36 chips back for the 3 bet, a gain to the player of 33. The overall gain is to the house in the sum of 3. The player has bet a total of 111 chips, the house has kept 3, 3 divided by 111 is 2.7%.

Roulette does not have a memory, any combination is just as probable as another. All payouts are based on 36 divided by the count of numbers that the play will return on, eg betting on a column of 12 is 36/12 or 3, which is 2 chips returned plus the 1 played, therefore 2:1.

Try this with any combination of betting proposition and you will come back with the same results. In real life if your tables are not performing as specified, put on the thinking cap, but more on that another time.