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The house edge


A house edge, a player edge or any imbalance which gives one side an advantage over the other comes into being when the payout on a bet doesn't match the odds of the bet. For example: take a look at the European roulette table:

European Roulette table layout


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 will lose, at an average rate of 2.7 percent, if you play those inside numbers on a European roulette table. It's set in stone, immutable, and in no way dependent on whether or not the roulette gods are smiling at you on a particular day. This is the “crystal ball effect” of gambling without the crystal ball: decide how much you're going to wager and you can work out your average return.

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 will lose, on average, for however much wagering you indulge in. The lower the house edge, the less you lose. If the house edge is bang on zero, you're average loss is zero. And finally, in ultimate casino heaven, if you can find a game with a negative house edge, you will win on average.


Bets with a negative house edge


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.


“Taking odds” in Craps


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, before a 7 combination is rolled. The six possible “point” numbers are 4, 5, 6, 8, 9 and 10. This wager on a repeat of the number is called “taking odds”, because the payoff on the bet matches the true odds of the bet.

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


Combination45678910
Probability3/364/365/366/365/364/363/36


...and here are the payoffs for the six combinations:


CombinationPayoff
4 or 102:1
5 or 93:2
6 or 86:5


The chances of rolling a 7 are 6/36, which is exactly double the chances of rolling a 4 -3/36. Looking at the above table, you can see that the payoff on a 4 combination is 2:1.

Since these are the true odds of the bet, 7 having two times the probability of the 4, this is fair wager with no house edge.
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.


The video poker “double up”


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:



RANKWINLOSE
2012
3111
4210
539
648
757
866
975
1084
J93
Q102
K111
A120


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”


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

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 preceding wager to enable the subsequent no house edge bet to take place, and that initial wager almost always does have a house edge - casinos offer few free lunches.


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