Although concise and not as in-depth as my book, this article shows you how the casino gets its advantage over the player. My book, The Secret to Craps: The Right Way to Play, clearly and logically explains all aspects of the math, distributions, variances, calculating odds, and everything else you need to know to become a truly knowledgeable craps player. When you understand the math and the fact that casinos pay less-than-true odds, you understand why you can't beat the casino over the long haul. The following simple comparison between two bet types demonstrates two fundamentals that the player must fully understand before putting money on the table. Let's look at the Place 6 and the Big 6.
With these two bets, we bet the number 6 against the number 7. Knowing there are 36 possible two-dice combinations, 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 (my book explains the easy math for calculating how many times a number appears in a 36-roll perfect distribution). 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 screw 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), 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 x $6 = $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 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 betting investment is $66 over a 36-roll perfect distribution (i.e., $6 x 11 = $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 $0.91 for every $10 bet.
Although each bet is the same amount (i.e., $6), which do you think is the better bet and which do you think is the stupid bet in terms of the player? Yes, very good! See how easy this is? (Don't fear the math. My book explains it in simple terms.) 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 $0.91 per $10 bet. This simple example clearly demonstrates two fundamentals the player must fully understand: 1) Over time, the player cannot conquer the house advantage and beat the casino, and 2) Certain bets are better than others in terms of the player because of their lower house advantage.
My book, The Secret to Craps: The Right Way to Play, teaches you the math in an easy-to-understand method similar to the example above, but with more detailed explanations. You'll also learn the house advantage for every bet on the table so you know which to make and which to avoid.
So, if the casino has a built-in house advantage that no one can beat over time, why do knowledgeable players bother playing? If we're all doomed to long-term failure, why play? Two reasons: 1) The incredible fun and excitement that we experience 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 our advantage is a prerequisite to learning the secret to craps. And that secret, my friend, is clearly explained in my book. So, what are you waiting for? The $25 price tag is a small price to pay for the knowledge you'll gain from this book. Knowledge is money. And more knowledge is more money.