There are thirty-seven numbers, giving us odds against any one number of 36:1. In order for the bet to be fair, the payoff needs to be the same: 36 to one. In this way, you would on average lose your bet thirty six times, then win back those thirty six losses on that one occasion in thirty seven when your number hits.

Alas, in casinos the world over the payout on any single winning number comes in at only 35 to one. If you risk a dollar on one of the numbers and it wins, you're paid $35. There being thirty seven numbers in total, if you were to bet a dollar on all of them you'd end up losing $36 and winning $35, for an overall loss of one dollar. One dollar (your loss) out of thirty seven (your overall initial wager) works out at 2.7 percent, and so 2.7 percent is the house edge on this particular bet - for more information on the mathematical calculations involved in the house edge, see the mathematical expectation page.

The house edge is the casino's average profit in relation to the player's overall initial wagers. If you wager a thousand dollars over the course of an evening on a European roulette table you will either win or lose in any one session, but your average loss - assuming you always play those single-number bets - is going to be that 2.7 percent, or $27. Again, sometimes you'll win, sometimes you'll lose - and rarely will you lose exactly $27. However, the house edge of 2.7 percent ensures that, over time, you will average out at -$27 for $1000 in wagering. Or -$270 for $10,000. Or -$2700 for every $100,000 - all of which explains why casinos like their roulette tables so much.

This is not chance; this is cold, calculated fact. That you might win does not change the fact that you

The same consideration governs every game in the casino. The calculations that produce the house edge numbers are very complex in some cases, but a number there always is, and that's the vital number that tells you how much you

It's very rare to find a casino game with a negative house edge, or an advantage which lies with the player. The great Deuces Wild full pay game is more or less extinct these days, as are good single deck blackjack games. However, that doesn't mean that wagers with negative house edges don't exist; they do. Unfortunately, they invariably come as subsequent wagers in a game that already has a standard house edge - you have to “pay” to get to them. Here are some examples of these bets.

After the initial bets are placed on the table, assuming the player doesn't win or lose outright with a 2, 3, 7, 11, or 12, he can wager on a repeat of his number (called the “point”), on subsequent rolls of the dice,

The probability of each combination is listed in the table below:

Combination | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|

Probability | 3/36 | 4/36 | 5/36 | 6/36 | 5/36 | 4/36 | 3/36 |

...and here are the

Combination | Payoff |
---|---|

4 or 10 | 2:1 |

5 or 9 | 3:2 |

6 or 8 | 6:5 |

The chances of rolling a 7 are 6/36, which is exactly double the chances of rolling a 4 -

Since these are the

Just to check, let's run those figures through the “expected value” formula on the mathematical expectation page:

(2 × 3/36) + (-1 × 6/36) = 0 |

The expectation is 0, or 100% return.

The same is true of all the other odds bets.

Video poker machines, both on land and online, offer the option of “doubling up” on a winning hand, with wins paid at even money.

The machine deals one card at random, and the player must then select one of the other four unseen cards. If the chosen card is higher, the double-up bet wins.

The table below lists the card ranks along with the number of chances that each has of winning and losing:

RANK | WIN | LOSE |
---|---|---|

2 | 0 | 12 |

3 | 1 | 11 |

4 | 2 | 10 |

5 | 3 | 9 |

6 | 4 | 8 |

7 | 5 | 7 |

8 | 6 | 6 |

9 | 7 | 5 |

10 | 8 | 4 |

J | 9 | 3 |

Q | 10 | 2 |

K | 11 | 1 |

A | 12 | 0 |

If you draw a 2, the lowest card, you have no way of winning. Draw an ace on the other hand, and you can't lose.

Adding up both “win” and “lose” columns gives a total of 78; as such, over the course of drawing all 13 ranks, you have 78 ways to win and the same number of ways to lose, giving us true odds of 78:78, or 1:1.

Since the even-money payoff matches the true odds, this is another “fair” wager with no house edge.

The blackjack “double down” bet is unique in the casino in as much as it actually

The player looks at his two cards and the dealer's one exposed card, and takes a decision as to whether or not to double his initial wager and accept just one more card.

As with all blackjack wagers - apart from the natural blackjack paying 3:2 and “insurance” paying 2:1 - the double-down bet pays even money. However, the true odds of the bet always favour the player, on average by approximately 3:2, giving the player the spectacular return of around 120% on his double-down wagers.

There is one big caveat to these three bets: each one requires a

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