The Importance of Knowing How to Calculate the House Advantage

E xcept for the Free Odds bet, every other craps bet has a built-in house advantage (i.e., casino advantage) over you.  How does the casino get its advantage, and how do we calculate it?  More importantly, is there any way to flip it to give us the advantage over the casino?

The fact is that craps is a negative-expectation game designed for us to lose.  No matter what betting system or pattern we use, it’s mathematically impossible to switch the advantage over to us.  Forget the nonsense you read on other websites and forums about using some weird combination of bets that will guarantee you’ll beat the craps out of the casino.  The mathematical fact is that no betting system, no matter how logical it might sound, will ever change the negative expectation so the advantage turns in our favor.  For example, we see it all the time, some joker who thinks he has the game figured out, makes a $10 Pass Line bet and a $1 Any Craps bet (also known as a “craps check”).  His thinking is that his hedge bet protects his $10 Pass Line bet.  (A hedge bet is one or more bets intended to protect another bet, in this case the $1 craps check.)  To him, it’s worth a $1 investment against the $10 Pass bet in case the shooter rolls a 2, 3, or 12 on the come-out roll.  (We’ll learn about all the bets and craps lingo, such as “come-out roll,” in other articles.)  If the shooter craps out on the come-out roll, he loses the $10 Pass Line bet, but wins $7 for the Any Craps bet.  So, he continues on his merry way totally oblivious to the fact that making the $1 Any Craps bet actually increases the house advantage.  It’s a simple mathematical fact, the more bets and wacky combinations of bets you make, the more you add to the casino’s advantage.  The casino loves this kind of player.  The stickman will shout, “Good craps check, sir,” and the dealer will lean close to the guy and quietly say, “Nice play, sir, you’re the only one at the table who knows what he’s doing.”  In reality, he’s a clueless loser.

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Let’s look at how the casino gets its advantage over us.  You don’t need a math Ph.D to understand the fundamental concept.  A simple comparison of two common craps bets is all we need.  You must understand this concept before ever thinking about playing craps for real money.  Let’s look at the Place 6 bet and the Big 6 bet.

With both of these bets, we bet the number 6 against the number 7.  If a 6 appears, then we win.  If a 7 appears, then we lose.  All other numbers are meaningless so we ignore them and roll again.  From another article, “Basic Math of Craps,” we know there are 36 possible outcomes when rolling two dice.  To keep it simple, suppose we roll the dice 36 times and the outcome for those 36 rolls is a “perfect distribution” where, in those 36 rolls, the number 6 appears five times and the number 7 appears six times.  (If you need to review the other article, “Basic Math of Craps,” then do it now before continuing with this lesson.)  When we bet the 6 against the 7 over 36 rolls with a perfect distribution, we make a total of 11 bets.  (As we learned in the article, “Basic Math of Craps,” there are five ways to roll a 6, and six ways to roll a 7.  Therefore, 5 + 6 = 11 bets.)  For those 11 bets, we win five times when the 6 shows, and we lose six times when the 7 shows.  Remember, for the sake of simplicity, we’re assuming a perfect distribution over the 36 rolls, so each number will appear exactly as many times as there are ways to roll it.  Again, if you’re a bit confused, go back and review the article, “Basic Math of Craps.”  We also learned that the casino takes a certain percentage of profit out of every possible bet except the Free Odds bet.  Instead of paying true odds when we win a bet, the casino makes its profit by screwing us and paying “casino odds,” which are a little less than the true odds.  Given these basic assumptions, let’s take a closer look at the Place 6 bet and the Big 6 bet.

The casino odds for the Place 6 bet are 7:6, which are a little less than the true odds of 6:5 (remember, the casino pays us casino odds when we win, not the true odds).  This means for every $6 Place bet we make and win, we win $7.  Because the odds are 7:6, our Place bets should be made in any multiple of $6.  For example, instead of betting only $6 to win $7, we can bet $18 to win $21.  For our 36-roll example, suppose we bet $6 on each of the 11 bets.  Remember, with a perfect distribution, we know we’ll make a total of 11 bets when betting on the 6, and with those 11 bets, we’ll win on five rolls and we’ll lose on six rolls.  Therefore, our total bet investment over the 36 rolls is $66 (i.e., 11 bets x $6 per bet = $66).  Over the 36 rolls, we’ll win five bets when the 6 shows, which means we’ll win $35 (i.e., 5 bets x $7 = $35).  Over the 36 rolls, we’ll lose six bets when the 7 shows, which means we’ll lose $36 (i.e., 6 bets x $6 = $36).  By winning $35 and losing $36, our net loss is $1 over the 36 rolls.  Calculate the house advantage by dividing our $1 net loss by our $66 total investment (1 / 66 = 0.01515, which rounds to 1.52%).  A 1.52% house advantage means if we keep betting the Place 6 over a long period of time, we expect to lose an average of about $0.15 for every $10 that we bet.

The casino odds for the Big 6 bet are 1:1, or even money.  This means if we bet $6 on the Big 6 and win, we win $6.  Let’s use the same example as we did for the Place 6 by rolling the dice 36 times with a perfect distribution, but this time we bet the Big 6 instead of the Place 6.  As with the Place 6, our total bet investment is $66 over the 36 rolls (i.e., 11 bets x $6 = $66).  Over the 36 rolls, we’ll win five bets when the 6 shows, which means we’ll win $30 (i.e., 5 bets x $6 = $30).  Over the 36 rolls, we’ll lose six bets when the 7 shows, which means we’ll lose $36 (i.e., 6 bets x $6 = $36).  By winning $30 and losing $36, our net loss is $6.  Calculate the house advantage by dividing our $6 net loss by our $66 total investment (6 / 66 = 0.0909).  As you can see, the house advantage for the Big 6 bet is a huge 9.09%.  A 9.09% house advantage means if we keep betting the Big 6 over a long period of time, we expect to lose an average of about $0.91 for every $10 that we bet.

Remember, the casino screws us by not paying us the full true odds when we win.  Instead, they pay lesser casino odds, which are just enough for them to make a sweet profit but not so much to keep us from walking away.  Let’s compare the results of the two types of bets.  Over a long period of time making only $6 Place bets, we expect to lose about 15 cents for every $10 we bet.  And if we make $6 Big 6 bets over a long period of time, we expect to lose about 91 cents for every $10 we bet.  If we bet the same amount regardless of the bet (i.e., we either make $6 Place bets, or we make $6 Big 6 bets), which do you think is the better and smarter bet?  Yes, you’re absolutely correct!  Obviously, for the player, the $6 Place bet is a much smarter bet than the $6 Big 6 bet.  Unless you own stock in the casino where you’re playing, losing 15 cents for every $10 that you bet is a lot better than losing 91 cents.  Why would anyone bet $6 to win $6 with the Big 6 that pays even money at 1:1, when they can bet the same $6 to win $7 with the Place 6 that pays 7:6?

You can see how much more the casino profits from the Big 6 than the Place 6.  The casino loves the Big 6.  That’s why it has a big area on the table for you to bet it.  It’s a pretty bet, right in front of you to grab your attention.  It calls to you, entices you to lean over and put down your chips.  When the table crew sees a player make a Big 6 bet, they know they’ve hooked a live one.  Suddenly, you see the dealer and stickman offer the player suggestions for making other stupid bets.  Oblivious and ignorant, the player willingly tosses his chips on the table.  This is why it’s so critical to understand the house advantage, how it’s calculated, and why it makes certain bets much better than others.  We’ll learn about the house advantages for all the various craps bets in another article.

houseedgeI know what you‘re thinking, “If we can’t beat the house advantage, why play at all if we’re just going to lose?”  It’s because of another simple concept in the world of probabilities and statistics.  Smart players play because of the wonderful thing called “distribution variance.”  The example above assumes a perfect distribution, which seldom occurs anywhere in nature.  It takes a long time for the odds to balance out for the casino to make a profit.  The casino is extraordinarily patient.  Thousands of players play every day of every week of every month of every year.  Over that long period of time with so many players, the odds follow their natural path to maintain equilibrium, which gives the casino their gobs of profit.  But in contrast, when we go on our Vegas vacation, we play for only a few hours, which is mere blip in time.  During those fleeting blips of time is when “variance” creeps into the equation that enables us to turn the table on the casino.  Variance is our only weapon against the casino, so it’s very important to you as a player.  We’ll learn all about variance in another article, but for now, just know that variance is the phenomenon that causes the familiar hot and cold streaks with the dice.  Understanding variance and how to use it to our advantage makes us the kind of player the casino fears most.

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Author
Written by John Nelsen in partnership with the team of craps pros at crapspit.org.
  • Peter.

    What happens to come bets when the passline point wins?

    • crapspit

      For details on Come bets, including details about your question, please refer to our article on Come bets. The sample Come-bet scenario in that article helps make it easy to understand. Here’s a summary