This is the 1st in a series of craps posts aimed at players who want to start winning more often. I’m including everything you need to know about craps to get the best odds of success. Most of the information in the posts in this series is not aimed at beginners. You should probably already understand the basics of craps before digging too deep into this series. The idea is not to provide how to play craps posts but to provide new information and ideas that might take your existing craps game to the next level.

• What Are My Chances Of Winning At Craps
• Chances Of Winning At Blackjack

Craps Is a Negative Expectation Game

The best bet in the casino is when you lay odds in craps. The article suggests betting $10 on the pass line. Sure, the house edge will be 1.4%.

Yes, craps is a “negative expectation” game. But what does that mean, exactly? Gamblers and mathematicians like to talk about bets in terms of their “expected value.” The expected value of a bet is a simple formula, too:

(The amount you stand to win X the probability of winning) – (The amount you stand lose X the probability of losing) = Expected value of a bet

You bet $2 on a coin flip, but if you win, you only get $1. You have a 50% chance of winning $1, which amounts to 50 cents in expected value. But you also have a 50% chance of losing $2, which amounts to -$1 in expected value. Subtract one from the other, and you get an expected value of -$0.50.

It should be obvious that if you flip a coin repeatedly long enough under those terms, you might get lucky in the short run, but you’ll go broke in short order in the long run. (“In the long run” just means “eventually.”) All casino games design their odds of winnings and payouts to provide you with a negative expectation, by the way. That’s how the casinos stay in business.

In some games, the expectation is the same no matter what. In other games, like craps, you can choose from an entire all-you-can-bet buffet of wagers. Some of these wagers have a bigger negative expectation than others. One of the subjects I’ll cover in this series of posts is which bets are better and which bets are worse.

The action at the craps table starts when a player makes what's called the 'come-out roll'. The basic two bets are the 'pass' the 'don't pass' bets. If the shooter rolls a 7 or an 11, you win if you made the pass bet. If the shooter rolls a 2, 3, or 12, you win if you made the don't pass bet, and you lose if you made the pass bet. Pass line win probability = 244/495 (244/495)^3 = 0.119771609 exactly 3. Mustangsally: Maybe I'm missing something, but I get different results from what you show. Suppose (for simplicity) that it was a coin flip with p=0.5 instead of 244/495. To get at least one win in a row would be P=0.5. To get at least two in a row is P=0.5^2, etc.

Why I Love Craps and Why You Should, Too

Blackjack has its fans, and I understand why. But craps is my game, and if you have the right personality, it’s probably your game, too. It’s fun, scary, exciting, suspenseful, and the most entertaining game in any casino which offers it. One of the reasons it’s so great is this buffet of bets I just talked about, by the way.

Other players like to play a close to even game with an even-money payoff. Those players will bet on the pass line and take as big an odds bet as they can. If you can find a casino offering you the option of betting 10X odds, the house edge for all the money you have in action on that combination of bets is only 0.184%.

The house edge, by the way, is just another way of expressing the expected value. In this case, it’s the amount of money the casino expects to win from each bet over the long run. If the house edge for a bet is 1%, the casino expects to win $1 on average every time you bet $100. With a house edge of 0.184%, your expected loss on a $100 bet is only 18.4 cents—less than a quarter!

What I Hate about Craps, Though

The large variety of bets is a 2-edged sword. It’s a feature but also a drawback. With such a large number of bets to choose from, it’s easy to choose bad bets—wagers with a high negative expectation. In fact, when it comes to craps, there are far more bad choices you can bet on than good ones.

But if you choose the wrong bets—the wagers with the highest house edge—you can lose your entire bankroll faster than you ever thought possible. Lots of players make those bets, too, and the casinos even encourage their employees at the craps table to hustle those bets and encourage players to make them.

More about the House Edge and How the Casino Makes Its Money

The best way to think about how the casino makes its money at craps is to realize that one of 2 things is always happening with a craps bet:

• The casino wins more often than the player on an even money proposition
• The casino gets a cut of our winnings on any bets that you win

These are 2 sides of the same coin. Let me explain how those concepts work to make the casino a fortune:

The most common bets in craps are the pass line bet and the come bet. These are the most basics bets in the game—bets that the shooter will succeed. In the long run, over 495 “rounds,” the casino will win either of those bets on average 251 times. The player will only win an average of 244 of those bets. That’s a difference of 7 bets over the course of 495 rounds of play (7/495 = 1.41%). By taking the odds bet, you can reduce that even further. In a casino where you can take 10X odds, the house edge is reduced to 0.18%, and in a casino where you can take 100X odds, the house edge is reduced to 0.02%.

The Any 7 Bet Is a Great Example

The “any 7” bet is a one-roll bet that the next roll will be a 7. You have 6 ways of making a 7 when rolling 2 dice:

• 1, 6
• 2, 5
• 3, 4
• 4, 3
• 5, 2
• 6, 1

That means the probability of winning this bet is 6 divided by 36. (There are 36 possible outcomes when you roll 2 6-sided dice.) This means you’ll win 1 bet out of 6, which also means that your odds of winning are 5 to 1. If you bet $10 repeatedly on the “any 7” bet, you’ll lose $10 on 5 rolls out of 6, or $50.

The house edge on that bet—the average that you mathematically expect to lose on it—is 16.67%. For every $100 you bet, you’re expected to eventually lose an average of $16.67. That’s a big sum compared to the $1.41 on the pass line bet, or the 61 cents on the pass line bet with 2X odds. This bet is often called “big red.” (I have an ex-girlfriend with the same nickname, but I won’t get into that here.) Since red is the color accountants use for negative numbers on a spreadsheet, this bet is appropriately named. You can analyze any bet in craps this way.

The Field Bet Is another Great Example

Another example is the “field” bet. That’s another one-roll bet, this time that the next number will be one of the following:

• 2
• 3
• 4
• 9
• 10
• 11
• 12

You have a total of 16 ways to make those numbers, out of 36 possible outcomes. That sounds pretty good. Also, most casinos pay out 2 to 1 if you get a 2 or 12. The field bet is still a lousy wager, though. The casino still has 22 ways to win compared to your 16 ways to lose. Even with the doubled payouts on the 2 and the 12, the casino comes out way ahead here. The house edge for this bet is the same as the house edge for an American roulette game—5.26%.

The Hard Way Bets

Some craps players love long odds, though. These guys make “hard way” bets. A popular fictional character who does this is featured in the movie Hard Eight, which I recommend you see if you haven’t already.

You can make the following hard way bets:

• Hard 4
• Hard 6
• Hard 8
• Hard 10

These are called “hard way” bets because you’re betting that the corresponding total will be rolled as doubles—a pair of 2s for a total of 4, a pair of 3s for a total of 6, a pair of 4s for a total of 8, or a pair of 5s for a total of 10. You’re also betting that this will happen BEFORE the shooter rolls either a 7 or the corresponding total the “easy way.” For example, if you bet on “6 the hard way,” if the shooter rolls a 1, 5; a 2, 4; a 4, 2; or a 5, 1.

Right Bettor Wagers, Payoffs, and the House Edge

A “right bettor” is someone who bets with the shooter. (It’s the opposite of a “wrong bettor.”) Basically, all the right bettor wagers are bets that the shooter will succeed before rolling a 7.

Whirl – This is the horn bet and the any 7 bet combined.

It’s actually more complicated than some other craps bets, because the payoffs depend on which number wins. For example, if you roll a 7, the payoff is actually nothing, because it’s treated as a push. (This is a tie where your bet is returned to you without any winnings.) That’s because when you win the any 7 bet, you’re still losing the horn bet.

On the other hand, the 2 or 12 pay off at 26 to 5, and the 3 or 11 pay off at 11 to 5. It’s a complicated bet, and the house edge is high. Don’t bet it. Some casinos and players call it the “world” bet. Your odds of winning are 2 to 1. The house edge is 13.33%.

2 – This is a one-roll bet that the next number rolled will be a 2. The odds of winning are 35 to 1, but it only pays off at 30 to 1. The house edge is 13.89%. This is also called “snake eyes.”

12 – This is a one-roll bet that the next number rolled will be a 12. The odds of winning are 35 to 1, but it only pays off at 30 to 1. The house edge is 13.89%. You’ll notice that the odds are the same as for the 2 bet.

Hop (doubles) – The hop bet isn’t listed on the table. It’s one of those “secret” craps bets. A hop bet is a wager that the dice will fall on a specific combination. In this case, we’re looking at doubles, so a 4 on the hop (doubles) would be a bet that the dice would land on 2, 2. (Yes, this is the same as a 4 the hard way.)

There are 2 big differences between betting on the hop and the hard way. A bet on the hop is a one-roll bet—you win or lose on the next roll. A normal hard way bet stays in action until it’s won or until the total is rolled (or a 7 is rolled.) That’s the 1st difference.

The 2nd difference is that the hop bet has a different payout. The odds of winning a hop bet are 35 to 1, but it pays off at 30 to 1. The house edge is 13.89% on this one, too.

Horn – This is a bet that the dice will land on 2, 3, 11, or 12. The odds of winning are 5 to 1. The payoff depends on the specific total, though. A 2 or 12 pays off at 27 to 4. A 3 or an 11 pays off at 3 to 1. The house edge on the horn bet is 12.5%.

Hop (not doubles) – This is a bet on a specific combination, like 4 on the hop that consists of a 3 and a 1. Since you don’t have to roll doubles, you have twice as many ways to win on the hop if you don’t choose doubles. This makes the odds of winning 17 to 1, and the payoff is 15 to 1. The house edge is 11.11%.

3 – This bet, like the hop bet that isn’t based on doubles, has odds of 17 to 1 of winning. The payoff is also 15 to 1, and the house edge is also 11.11%. This bet is also called “ace deuce.”

11 – This is the same as the bet on 3, but it wins if you roll an 11. The odds are the same as for a bet on 3.

Any Craps – This is also called the “3 way.” It’s a bet that the dice will land on 2, 3, or 12. The odds of winning are 8 to 1, and the payoff is 7 to 1. The house edge is 11.11%. Any craps is a one-roll bet.

Hard 4 – This is a bet that the dice will come up 2, 2 before coming up with a total of 7 or another total of 4 not comprised of doubles. The odds of winning are 8 to 1, the payoff is 7 to 1, and the house edge is 11.11%.

Hard 10 – This has the same odds of winning and same payoff odds as a hard 4, but you’re betting on the dice coming up 5, 5 instead of 2, 2.

C&E – This is a combination of the any craps bet and the yo bet. The any craps portion of the bet pays off if you hit 2, 3, or 12. The yo bet pays off if you hit an 11. The overall probability of winning is 5 to 1. The payout is 3 to 1 if the craps numbers come up, but it’s 7 to 1 if the 11 comes up. The house edge is 11.11%

Hard 6 – The hard 6 is the same as a hard 4 or a hard 10, but there are more ways to lose. (There are more ways to roll a 6 than there are ways to roll a 4.) The odds of winning are 10 to 1, but the payoff odds are 9 to 1. The house edge is 9.09%.

Hard 8 – Almost everything I wrote about hard 6 applies to hard 8, too. The only difference is that you’re betting on the dice coming up 4, 4 instead of 3, 3.

Big 6 – This is just a bet that the shooter will roll a 6 before rolling a 7. The odds of winning are 6 to 5, and the payoff is even money. The house edge is 9.09%.

Big 8 – This is just a bet that the shooter will roll an 8 before rolling a 7. The odds are the same for big 8 as they are for big 6.

Place 4 – This is a bet that the 4 will come up before the shooter rolls a 7. The odds of winning are 2 to 1, and the payoff is 9 to 5. The house edge is 6.67%.

Place 10 – The odds are the same as for the place 4 bet, but you’re betting on a total of 10 coming up before the shooter rolls a 7.

The Field – I wrote about the field bet earlier in this post. It’s a bet that the dice will land on 2, 3, 4, 9, 10, 11 or 12. The odds of winning are 5 to 4, and the payoff is even money, unless you roll a 2 or 12. If you roll one of those, you get a 2 to 1 payoff. The house edge is 5.26%.

Place 5- This is a bet that the 5 will come up before the shooter rolls a 7. The odds of winning are 3 to 2. The payoff is 7 to 5. The house edge is 4%.

In the next post in this series, I’m going to look at some more of your betting options. That’s right. Craps has so many betting options that I can’t cover them all in a single post. More importantly, I’ll start offering some advice about which bets you should actually be placing on a regular basis.

For now, take this away from this post: Craps is a negative expectation game, but if you stick with the right bets, the house edge is so low that you can often walk away a winner. The larger number of bets available at the craps table is one of the more confusing aspects of the game. The casino makes its money from craps by making sure they’re going to win more often than you do or by paying you at odds lower than the odds of actually winning. Depending on the bet, the house edge can be as low as 0.18% or as high as 16.67%.

Chart on the possibility of each number being rolled.

When playing online Craps, it is important to understand the probability of each dice combination being rolled. Once you know what the probability is, you can work out what the house edge is on particular bets. The odds paid to you, the probability of your bet being successful and the house edge are all important factors in how lucrative Craps will be for you.

Why Use a Craps Probability Chart?

The more information that you have at our disposal, the better decisions you can make. A more informed and smarter Craps player has a much better chance of winning on a regular basis. Whether you are a seasoned online craps professional or a casual players, a craps probability chart is crucial to understanding the probability of each dice roll result. With this knowledge, you can make smarter bets at the craps table.

For example, you can see on our craps probability chart that the most common number to come up after a dice roll is a seven. This is the reason that most craps professionals will recommend the pass line as the smartest bet you can make when formulating a solid craps strategy. On the other hand, you can easily see that, according to our craps probability chart, the most uncommon dice roll results are two (or snake eyes in many circles) and 12. Taking this into account, making a bet on two or 12 would likely not be the best bet that you could make.

How to Use a Craps Probability Chart

Obviously, there is nothing to stop you from printing out our craps probability chart and posting it by your computer any time that you are playing craps online. However, by reading our extensive section on the rules and etiquette of craps in offline casinos, you will also find that there are no rules preventing you from printing out the craps probability chart (or copying it on paper with a pencil) and bringing it with you to your favorite offline craps casino.

Every time you are considering a bet, you can consult the craps probability chart to see if the odds match up to the amount of your bet. However, a craps probability chart is simply a tool and cannot alone formulate your entire craps strategy. Some situations require a great deal more information than a craps probability chart before determining whether or not the bet is wise. For more information, you can consult our craps strategy section if you are unsure how to discover the total odds of a bet being successful. For now, memorizing the craps probability chart is your first step towards becoming a craps professional.

The game of craps is a wonderful opportunity to enjoy an energetic casino experience. The high enthusiasm for the game is mixed with the lure of “tempting fate” with the chance of betting on dice rolls. Players and onlookers rejoice together when the shooter hits the point and satisfies several bets, or lament together when the “dice” are against them.

In addition to this, part of what craps offers interested gamblers is a simple way to work the odds of the casino to a player’s favor. Winning at craps is entirely about learning the true probabilities of certain dice rolls occurring and making sure a player has money on the rolls with the best probability. The surest way to win in craps is to maximize bets with good odds and avoid bets with very poor odds.

Dice Probability

The essential starting ground for craps odds and probabilities is with the dice roll itself. Since bets are made based on the potential outcome of the dice, knowing how often, or how infrequently a number combination will occur is the foundation for betting odds in craps.

A pair of standard six-sided dice offers thirty-six possible number combinations that can occur with each roll. First, players need to understand that craps, and dice probabilities are literally roll by roll. Mathematically, what makes craps a game of chance is that every time the shooter picks up the dice, the exact same overall odds apply. There are not cumulative effects roll by roll, so the gambler’s fallacy of “what hasn’t occurred in a while is more likely to occur soon” cannot apply to craps, though many players bet like it will.

In reality, the dice odds stack in a pyramid that symmetrically pairs combinations of numbers, which have the same odds of occurring. The most frequently rolled number is a seven, which a player can mathematically expect to see once in every six rolls. This high probability is due to the fact that seven has the highest possible number of dice combinations to form it between the two dice.

The craps dice odds and probabilities list as follows:

• 2 and 12 have only one way they can be formed on two dice, thus carrying odds of 35 to 1 (a one in thirty-six chance of being rolled).
• 3 and 11 have two possible formations, so the odds of these appearing are 17 to 1.
• 4 and 10 each have three potential combinations, improving the odds of showing either of these to 11 to 1.
• 5 and 9 have four possible formations each, thus holding odds of 8 to 1.
• 6 and 8 are the second most frequently rolled combinations, with five possible ways to see a six or eight on the dice. The odds of either are 6.2 to 1.
• 7 has six possible formations, the most possible and gives it 5 to 1 odds of showing.

These odds are calculated by taking the number of possible formations out of thirty-six, reducing it to it’s lowest denominator and placing it in odds terms. For example, the four has three ways of being formed on the dice, thus a 3 in 36 chance of occurring or, reduced a one in twelve chance of being rolled. In odds terms one in twelve becomes 11 to 1. Understanding and remembering the dice odds is the basis for effective betting in craps.

The chance factor comes in with the fact that even though these odds are mathematically true over dozens and hundreds of rolls, and can be trusted to show in these ratios over a larger sample, they won’t “perfectly” occur with human shooters. Thus a shooter who gains six rolls can sometimes roll all six without showing a seven. This is what brings the element of risk and excitement to craps betting.

Making Good Odds Bets

There are three groupings of bets that have the best odds and the lowest house edge that a craps player can come by. These are the bread and butter of a craps player’s existence, and the wisest and winningest craps players use these bets like clockwork to maximize their odds of taking home cash, not just laying it down on the table. These are the most commonly used bets, as well.

On the right bettor side are the pass bet and the come bet. Pass bets are made during the come out roll; come bets are made after the shooter has established the point. Both of these are sweeping bets that the shooter will roll seven or eleven or a point number before rolling craps, 2, 3 and 12, the low frequency numbers. Pass bets and come bets parallel each other. Both of these bets have true odds of 251 to 244. The house edge, or casino advantage on these bets is one of the lowest at 1.41 %, which means bettors placing pass or come bets have a very good chance of winning this bet.

The wrong bettor partners to the pass and come bets are the don’t pass and don’t come bets. These bets go against the shooter (and thus are sometimes disliked by players), betting that the shooter will hit craps before hitting his point or seven. The house edge on these wrong bets actually drops further to 1.36%, and the odds of these bets showing are 976 to 949.

Free Odds Bets

The free odds bets that go with these are even better from an odds standpoint. The best bets to make in craps, free odds bets multiply a pass or come bet (or a don’t pass or don’t come bet). The advantage of these is the house edge gets lowered to almost zero, meaning players have a good chance of winning these bets at their actual mathematical odds. The odds bets have to be made in conjunction with the main pass/come and don’t pass/don’t come bets. On the right bettor side for pass and come odds bets, making this bet is called “taking the odds.” On the wrong bettor side, odds bets with don’t pass and don’t come bets are called “laying the odds.”

The pass odds and come odds bets have actual odds 2 to 1 on four and ten, 3 to 2 on five and nine, and 6 to 5 on six or eight. The payout ratios for these odds bets match the odds ratios for each number. On the don’t pass/don’t come odds side, the true odds are 1 to 2 against four and ten, 2 to 3 against five and nine, and 5 to 6 against six and eight. Again, the payout ratio when one of these bets wins is the same as the odds of occurrence.

Place Bet Odds

The third category of bets that use the dice probabilities to a great advantage are the place bets on the box numbers at the top of the craps table. Essentially, a place bet makes the same assertion as the free odds bet, that the shooter will roll one of these numbers before a seven or craps. The advantage to place bets is they can be made independently and don’t require a pass line bet first. However, the disadvantage is they payout at poorer odds than the free odds bets.

Four of the six possible place bets have a low house edge, making them still some of the better bets to make as far as player advantage. Place bets on six and eight have the third lowest house edge at 1.52%, making them very profitable bets. The odds of winning on place six and place eight bets are 6 to 5 or 45.45%. Payouts are at 7 to 6 odds. For even dollar payouts, player should bet in increments of $6 on these place bets, preventing rounding down by the casino on paying winnings.

Place bets on five and nine are also still lower house edges than most bets on the table at 4%. Players have a 40% chance of winning or 3 to 2 odds, and they payout at 7 to 5 odds. Place these bets in multiples of $5 for even dollar payouts without rounding.

Place bets on four and ten are still decent bets, but the house edge starts to climb–it’s 6.67%. The odds of winning a place four/place ten bet are 33.33% but if it does win, the payout rate is 9 to 5. These bets should also be made in $5 increments for even payout amounts.

Another advantage to place bets is that when a place bet wins, the dealer pays the player’s winnings but leaves the original bet on the table effectively starting another place bet. The player doesn’t have to add money to the bet to continue it. Players can ask the dealer to “turn off” the standing place bet or remove it if they wish.

A few online casinos offer the wrong side version of place bets called place bets to lose. Live casino Star City in Sydney, Australia also allows place bets to lose. These bets flip the bet to lose when the shooter hits the number first, but win if the shooter rolls a seven before the number. The odds of winning these place bets go from 54.55% to 66.67%, rather than under 50% for their right side counterparts. Place to lose on six and eight pay out at 4 to 5; on five and nine they pay out at 5 to 8; and on four and ten they pay out at 5 to 11.

Betting the Field Odds

The field box bets are right in front of the players and can be enticing bets. Their major disadvantage stands in that they are single roll bets, only valid for the next immediate dice roll. The house edge at 5.56% is smaller than many other craps bets, but still starting to be larger than is wise for a player to use often. The payout odd for field bets on three, four, nine, ten and eleven are 1 to 1, even money. For the more rarely rolled two and twelve, the payout odds are 2 to 1. The true odds of betting on the field are 5 to 4.

Odds on Proposition Bets

The proposition bets located in the center of the craps table actually hold the poorest odds for a player, and with high house edges hold great odds for the casino winning. Craps experts consistently advise staying away from these various “sucker bets” that catch novices or people who have not bothered to learn a few key points about playing craps.

Proposition bets are mostly single, next roll bets on specific numbers. The rates of the occurrence for the dice roll is the first basis for the enticingly high payouts, but the house edge factors in on the lesser likelihood that the single next roll will produce that number or combination of numbers.

The list of odds for the main proposition bets is as follows:

• Craps 2 or 12 has true odds of 35 to 1, that single dice combination. The payout odds are 30 to 1, with a huge house edge of 13.89%.
• Single number bets on 3 or Yo (11) carry true odds of 17 to 1, but the casino pays 15 to 1 odds on a winning bet. The house edge is 11.11%
• A Hi-Lo bet matches the odds of 3/11 bets with true odds of 17 to 1 and payout odds of 15 to 1. The house edge is also 11.11%.
• Any Craps bets (looking for 2, 3, or 12) have true odds of 8 to 1, payouts of 7 to 1 and that ever-large 11.11% house edge.
• C-E or Craps-Eleven bets have true odds of 5 to 1. The payouts vary at 3 to 1 for craps (2, 3, 12) and 7 to 1 on eleven. This also carries an 11.11% house edge.
• Any 7 bets have true odds of 5 to 1 with payout odds at 4 to 1. Any 7 has the largest house edge on the table at 16.67%.
• Horn bets carry a higher house edge of 12.5%. The true odds are 5 to 1. Payout odds are 27 to 4 on two or twelve and 3 to 1 on three or eleven.
  World or whirl bets are a variation of the horn bet on 2, 3, 7, 11 and 12. The true odds are 2 to 1. The payout odds on two or twelve are 26 to 5 and on three or eleven are 11 to 5. The house edge is 13.33%.

Big 6 and Big 8

The corner proposition bets of Big 6 and Big 8 have been banned from Atlantic City casino craps tables because the odds make them such poor bets. With a large house edge of 9.09%, bets on Big 6 and Big 8 only payout even money, though the true odds of rolling a six or eight before a seven, like in Place 6/Place 8 bets is 6 to 5.

Hardways Bets

Hardways proposition bets can be ongoing bets, but these are also costly bets to make. The hard four and hard ten bets have an 11.11% house edge and pay 7 to 1 if they win, but only carry an 11.11% chance of winning. Hard six and hard eight bets payout at 9 to 1, but only have a 9.09% chance of winning. The house edge for those two bets is 9.09%. It doesn’t seem like a bet bodes well for a player when the odds of winning equal the odds of the house advantage over the player.

Buy Bets and Lay Bets

For players who like to use place bets but who don’t like the odds, the option exists to buy the points for a 5% house commission that reduces the house advantage to “fair odds.” Some casinos require that commission up front; others take the commission on winnings. Most players will advise staying away from Buy and Lay bets. Paying extra to level the odds is simply not worth it. However, some players do like to use these bets.

Buy bets have a standard 4.76% house edge on all three pairs of bets. The odds are:

• Buy four and Buy ten have 2 to 1 odds.
• Buy five and Buy nine have 3 to 2 odds.
• Buy six and Buy eight have 6 to 5 odds.

What Are My Chances Of Winning At Craps

Lay Bets are the “Place to Lose” or wrong side lay odds commission bets. The lay bet odds are slightly different than the buy bet odds.

Chances Of Winning At Blackjack

• Lay four and Lay ten have 1 to 2 odds with a house edge of 2.44%.
• Lay five and Lay nine carry odds of 2 to 3 and a house edge of 3.23%.
• Lay six and Lay eight have 5 to 6 odds and a 4% house edge.

Overall Craps Odds

Some players ask about their overall chances of winning or losing at craps. Honestly, with most games of chance players will do well to expect to lose more than what they win. Statistically, in a particular session the mathematical odds reinforce the odds of losing are slightly greater than the odds of winning.

The odds of breaking even are about 0.67%.

For a truly big picture perspective on the odds of playing craps, probabilities calculated from simulating 1,000,000 sessions of 100 come out rolls each leave a players odds of winning and losing overall at the following percentages:

• Winning $1 to $25: probability 28.64%
  Losing $1 to $25: probability 30.06%
• Winning $26 to $50: probability 14.43%
  Losing $26 to $50: probability 16.36%
• Winning $51 to $75: probability 3.91%
  Losing $51 to $75: probability 4.64%
• Winning $76 to $100: probability 0.564%
  Losing $76 to $100: probability 0.65%
• Winning over $100: probability 0.0418%
  Losing over $100: probability 0.0422%

With so many calculations for craps odds and probabilities, the best way for a player to utilize this information is to remember the dice probabilities and the most beneficial bets to use. Craps tables list the payout odds for the higher bets as part of inviting players to spend money on bets that the house is more likely to win than the player. Seeing a 30 to 1 payout option makes some folks eager to bet there for the big return, but the savvy player will remember that the odds of that single two or twelve showing up on the next roll are 35 to 1. There are many more useful places to invest those bets. Strong players will use these odds and probabilities on craps to make guided decisions about where best to bet their hard earned money.