Casino Advantage. What it is and how to calculate it
Most players who venture in to a casino have heard about the casino's advantage, or house edge. Unfortunately, the majority know very little about how that advantage is calculated or what in fact it means.
To state it simply, the casino advantage is the edge the house has over the player. If a bet has a 5 percent casino advantage, (CA), then over a long period of time; the casino on average will keep 5% of the amount wagered. This average percent take is the casino's way of generating the funds needed to pay the overhead and turn a profit.
The casino creates this advantage by not paying off a winning wager at true odds. For example, at a typical roulette wheel the odds against a number winning are 37 to 1. If a player wagers one chip on a number and wins, the payoff is less than the true odds. In this case, 35 to 1 instead of 37 to 1. The casino's edge or advantage is two chips for every 38 chips wagered (more about how to calculate the casino advantage later).
The casino advantage varies not only from game to game but also differs even within the same game, depending upon the type of bets available. If you are serious about winning, then you ought to limit your play to those games and wagers with the smallest house edge.
Games which give the player the best chance at winning are those games with a minimum casino advantage: Blackjack (with proper playing strategy), Craps, Baccarat, and Single Zero Roulette Wheel.
To calculate the casino advantage in dollars, simply multiply the total amount wagered by the advantage. If a player makes 200 two-dollar bets on the $1 insignia on the Wheel-of-Fortune, a player stands to lose on the average $44.00 (200 x $2.00 = $400 total amount wagered x 11.1% casino advantage = $44.40). Always remember the casino advantage calculation is based on the total amount wagered; the longer you play (increasing your amount wagered), the more you will lose
Shown below are easy calculating procedures for the majority of the casino games.
Roulette.
A typical roulette wheel has 38 numbers (0, 00, 1 thru 36).
To calculate the casino advantage for a winning number bet, we must first establish the odds against any number to win on one spin of the wheel. This is simply the ratio of losses to wins, on any one spin of the wheel, or in this case 37 to 1. The casino advantage is calculated as follows:
True Odds: 37 to 1
Casino Payoff: 35 to 1
Assume 1 chip wagered on each winning and losing decision, then a player will lose 37 times x 1 chip = 37 chips win 1 time x 35 chips (payoff) = 35 chips
net loss = 2 chips
CA = chips lost/ total chips wagered = 2/38 x 100 = 5.26%
The casino advantage for all other wagers (except one) in roulette is the same (5.26%). Some players find this hard to believe. So let's prove it by calculating an example. Assume a player makes a six number bet that pays off on a win at 5 to 1.
True Odds: 32 to 6
Casino Payoff: 5 to 1 or 30 to 6
A player will:
lose 32 times x 1 chip=32 chips
win 6 times x 5 chips=30 chips
Net lost =2 chips
CA = 2 chips/38 chips x 100 = 5.26%
One roulette wager has a higher casino advantage than all others. It's the five number bet 0, 00, 1, 2, 3. Let's calculate what the advantage is.
True odds: 33 to 5 Casino payoff: 6 to 1
A player will:
lose 33 times x 1 chip=33 chips
win 5 times x 6 chips=30 chips
Net lost = 3 chips
CA = 3/38 x 100 = 7.89%
Craps.
The same rules can be used to calculate the casino advantage for every craps wager. In order to calculate the true odds for a winning wager, it is necessary to refer to the Dice Probability Chart. As the chart shows, when two dice are rolled, there are only eleven different numbers possible (2 thru 12) which occur in thirty-six combinations.
Dice Probability Chart
No. Combinations Ways to Make 2 1,1 1 3 1,2; 2,1 2 4 1,3; 3,1; 2,2 3 5 1,4; 4,1; 2,3; 3,2 4 6 1,5; 5,1; 2,4; 4,2; 3,3 5 7 1,6; 6,1; 2,5; 5,2; 3,4; 4,3 6 8 2,6; 6,2; 3,5; 5,3; 4,4 5 9 3,6; 6,3; 4,5; 5,4 4 10 4,6; 6,4; 5,5 3 11 5,6; 6,5 2 12 6,6 1
By using this chart, it is easy to establish the true odds for a winning wager, and then to calculate the casino advantage.
Any Seven Wager is a popular bet amongst Craps players. This is a one roll bet in which the player wagers that a 7 appears on the next roll of the dice. If it does, the payoff is 4 to 1. To establish the odds against winning, simply refer to the Dice Probability Chart. A seven, which is a winner, can be rolled in six different combinations. For every 36 dice rolls, a player stands to lose on 30 dice combinations and win on only 6.The true odds of the seven being rolled versus any other combination is 30 to 6.
True odds: 30 to 6 (or 5 to 1)
Casino payoff: 4 to 1
A player who wagers on each event will
lose 30 times x 1 chip = 30 chips
win 6 times x 4 chips = 24 chips
Net loss = 6 chips
CA = 6 chips/36 chips x 100 = 16.7%
A bet with a casino advantage this high should be avoided.
The Number Bets is another popular bet amongst the high rollers. A player can wager, on any of the point numbers 4, 5, 6, 8, 9, 10, that the number will repeat before a 7 is rolled. A player can either make a place bet on these numbers or a buy bet. Let's calculate which is a better bet.
Place Bets
No. True odds* Casino Payoff 4 or 10 2 to 1 (or 10 to 5) 9 to 5 5 or 9 3 to 2 (or 9 to 6) 7 to 5 6 or 8 6 to 5 7 to 6
On the 4 or 10 a player will
Lose 10 times x 1 chip=10 chips
Win 5 times x 9/5 (payoff)=9 chips
Net loss=l chip
CA = 1/15 chips x 100=6.6%
On the 5 or 9 a player will
lose 9 times x 1 chip=9 chips
win 6 times x 7/5 chjps=8.4 chips
Net loss=0.6 chips
CA =6/15 chips x 100 = 4.0%
On the 6 and 8 a player will
lose 6 times x 1 chip = 6 chips
win 5 times x 7/6 chips = 5.83 chips
Net loss = 0.17 chips
CA = 0.17/11 chips = 1.5%
Now let's calculate the casino advantage for the Buy Bets. A player who makes a Buy Wager on any of the point numbers 4, 5, 6, 8, 9, 10 will be paid at the true odds, but the casino charges a 5% commission. Thus for every $20 wagered, the player is charged a fee of $1. The casino advantage is simply 1/21 x 100 = 4.76%. All of the Buy Bets have the same 4.76% casino advantage because, on the average, a player will lose 1 chip (the commission) for every 21 chips wagered.
Which is the better bet to make? It should be clear that the lowest casino percentage bet is to Place 5, 6, 8 and 9 and to Buy 4 and 10.
Money Wheel.
The Money Wheel or Big Six Wheel is a popular casino "side game." The typical wheel has 54 spaces around the rim of the wheel surface. The typical bets available and the casino payoffs are as follows:
Bet Spaces on Wheel Payoff $1 Insignia 24 1 to 1 $2 15 2 to 1 $5 7 5 to 1 $10 4 10 to 1 $20 2 20 to 1 Joker 1 40 to 1 Flag 1 40 to 1
Is the casino's advantage the same for all the bets? Let's see:
$1 Insignia
True odds: 30 to 24 (30 spaces can lose; 24 can win)
Casino payoff: 1 to 1 (or 30 to 30)
For every 54 spins of the wheel a player will
lose 30 times x 1 chip = 30 chips
win 24 times x 1 chip = 24 chips
Net loss = 6 chips
CA = 6/54 chips x 100 = 11.1%
On the Flag Bet or the Joker Bet, a player will
Lose 53 times x 1 chip = 53 chips
win 1 time x 40 chips = 40 chips
Net loss =13 chips
CA = 13/54 chips x 100 = 24.1%
Similar calculations will show that the casino advantage for each bet is as follows:
Bet Casino Advantage $1 Insignia 11.1% $2 16.7% $5 25.9% $10 18.5% $20 22.3% Joker 24.1% Flag 24.1%
It should be obvious that all the bets on the Money Wheel have a very high casino advantage. It is not recommended for the serious player.
What we've shown is how a player can calculate the casino advantage for the various bets available in the games of Roulette, Craps and Money Wheel. The calculations for the games of Blackjack, Baccarat and Keno are more difficult because of the nature of the games and require more complex calculations.
Test Yourself.
A player in an Atlantic City casino that wants to wager against a Craps point number has two choices:
either Lay the number or make a Place Bet on the number to lose. The casino payoffs are:
1. Lay Bet. Pays true odds but the player is charged a 5% commission based on the amount of the winning payoff. 2. Place Bet to Lose. The casino payoff is 5 to 11 on point numbers4 and 10; 5 to 8 on the 5 to 9; and 4 to 5 on the 6 and 8.
Which is the better bet to make:
Lay the number or Place number to lose?
Answer. The casino advantage for the Lay Bets are as follows:
4 and 10 (true odds 1 to 2).
A player wagers $40 to win $20 but pays 5% commission on $20 won (or $1 commission).
CA = 1/41 chips (40 plus 1 for commission) x 100 = 2.40%
5 and 9 (true odds 2 to 3).
A $30 bet yields a $20 payoff and $1 commission.
CA = 1/31 chips x 100 = 3.23%
6 and 8 (true odds 5 to 6).
A $24 bet yields a $20 payoff and $1 commission.
CA = 1/25 chips x 100 = 4.00%
For the Place Bet to lose wager, the casino advantage is as follows:
4 and 10. A player will
lose 1 time x 1 chip = 1.00 chips
win 2 time x 5/11 chips = 10/11 or .909 chips
Net loss = 0.09 chips
CA = 0.09 chips/3.0 chips x 100 = 3.0% 3.0 chips
5 and 9. A player will lose 2 times x 1 chip = 2.0 chips
win 3 times x 5/8 chips=1.875 chips
Net loss = 0.125 chips
CA = 0.125 chips/5.0 chips x 100 = 2.5%
6 and 8. A player will
lose 5 times x 1 chip =5.00 chips
win 6 times x 4/5 chips=24/5 or 4.80 chips
Net loss = 0.20 chips
CA = .20/11 chips x 100 = 1.82%
To summarize, the casino advantage for the Place Bet to lose and Lay Bet is:
4 or 10 5 or 9 6 or 8
Place Bet to lose
3.0% 2.5% 1.8%
Lay Bet 2.4% 3.2% 4.0%
Your best bet is to Place the 5,6,8, 9 to lose and Lay the 4 to 10.