How to Win at Craps: Calculating the Casino Advantage
Contrary to what you've probably read in books and other websites, the game of craps was designed for the casino to win
and you to lose. No ifs, ands, or buts. Over time, you will lose. The fact is, no matter what craps bets you combine and
betting patterns you use, you can't and won't overcome the casino advantage. No hedge-bet method (i.e., combination of
craps bets and bet amounts) will ever change the negative expectation to result in an advantage for you. The best you can
hope for is to minimize the casino advantage and maximize your fun. The knowledgeable player knows he's supposed to
lose, so he plays for the fun and excitement of it. He hopes, but doesn't expect to win. The secret to craps is to find the
optimal mix of variables that allows you to walk away with something left in your pocket and be happy that you didn't lose it
all. The secret to craps allows you to play longer, lose less, and leave in a good mood. You might even leave a winner,
making your gambling vacation even sweeter.

Let's learn craps and take a fundamental look at how the casino gets its advantage over you. When you understand the
math and the fact that casinos pay less-than-true odds (i.e., they pay casino odds that are worse than true odds), you'll
understand why you can't beat the casino over the long term. The following simple comparison between two bet types
demonstrates two fundamentals that you must fully understand before making any craps bets. Let's look at the Place 6 bet
and the Big 6 bet.

With these two craps bets, we bet the number 6 against the number 7. Knowing there are 36 possible combinations for two
dice, let's assume we experience a "perfect distribution" where, in 36 rolls, the number 6 appears five times and the number
7 appears six times. When betting the 6 against the 7 over 36 rolls, we make a total of 11 bets (i.e., we win five times
when the 6 appears and we lose six times when the 7 appears; therefore, 5 + 6 = 11). It's important to understand that
the casino takes a set percentage out of every possible bet (except the free Odds bet). So, instead of true odds, they stick
it to the player by paying casino odds, which are less-than-true. Given these basic assumptions, let's look closer at the
Place 6 and the Big 6.

The Place 6: To get the full Place odds (i.e., casino odds of 7:6, which are less than the true odds of 6:5), let's assume we
bet $6 on each of the 11 bets. (The 7:6 odds means for each $6 bet that we win, we win $7.) Therefore, our total bet
investment is $66 (i.e., 11 bets x $6 per bet = $66). We win five bets when the 6 appears; therefore, we win $35 (i.e., 5 x
$7 = $35). We lose six bets when the 7 appears; therefore, we lose $36 (6 x $6 = $36). By winning $35 and losing $36,
our net loss is $1. We determine the house advantage by dividing our $1 net loss by our $66 total investment, which
results in a 1.52% house advantage (i.e., 1 / 66 = 0.01515, which equals 1.52%). A 1.52% house advantage means we can
expect to lose an average of about $0.15 for every $10 that we bet.

The Big 6: This is an even-money bet (i.e., casino odds of 1:1), which means if we bet $6 and win, we win $6. Like the Place
6, our total bet investment is $66 over a 36-roll perfect distribution (i.e., 11 x $6 = $66). We win five bets when the 6
appears; therefore, we win $30 (i.e., 5 x $6 = $30). We lose six bets when the 7 appears; therefore we lose $36 (i.e., 6 x
$6 = $36). By winning $30 and losing $36, our net loss is $6. We determine the house advantage by dividing our $6 net
loss by our $66 total investment, which results in a whopping 9.09% house advantage (i.e., 6 / 66 = 0.0909, which equals
9.09%). A 9.09% house advantage means we can expect to lose an average of about $0.90 for every $10 that we bet.

Although each bet is the same amount (i.e., $6), which do you think is the good bet and which do you think is a stupid bet?
Yes, very good! See how easy this is? (Remember, don't fear the math.) The $6 Place 6 is a much smarter bet than the Big
6. I don't know about you, but I'd rather lose an average of only $0.15 for every $10 bet than an average of $0.90 per $10
bet. Wouldn't you? This simple example demonstrates two fundamentals you must fully understand: 1) Over time, you
cannot conquer the casino advantage and beat the casino, and 2) Certain bets are better than others because of their
lower casino advantage.

If the casino has a built-in advantage that you can't beat over time, why do knowledgeable players bother to play craps at
all? If we're all doomed to lose, why play? Two reasons: 1) The tremendous fun and excitement we have at a craps table,
and 2) The phenomenon called "distribution variance." We rarely experience a perfect distribution in the relatively short time
that we play because variance sneaks into the equation. Understanding variance and how to use it to your advantage is a
prerequisite to playing craps smartly. (Refer to the lesson on Variance.) As my dad always said, "Knowledge is money, and
more knowledge is more money."