Craps - Odds Bets

The player should always leave the odds on regardless of how many come bets are active. When considering the options, looking at the probability of winning alone is not enough. Yes, with one come bet the odds of losing the come bet are greater than winning, however the potential win is greater than potential loss. The reason the player should always leave the odds on are because it is a bet with zero house edge. By turning the odds off the player is making the overall game more heavily weighted towards the bets with a house edge, thus increasing the overall ratio of the expected loss to the total amount bet.

This is similar to a question I got last week. Yes, it is true that there are ten ways to roll a 6 or 8, and six ways to roll a 7. However, one must not look at the probabilities alone, but weight them against the payoffs. The place bet on the 6 and 8 pays 7 to 6 odds when fair odds would pay 6 to 5. By making six unit place bets on the 6 and 8, and taking the other down if one wins, the probability of winning 7 units is 62.5% and the probability of losing 12 units is 37.5%. If the player must cover both the 6 and 8, then the place bet is the way to go. This rate of return isn't bad but could be better. For the player who puts a priority on minimizing the overall house edge, the best strategy is to make combinations of pass, don't pass, come, and don't come bets, and always take the maximum allowable odds.

For other readers, let me explain that a put bet is making a pass or come bet after a point has already been established. The player may choose the point to be established on the put bet. While the player can make an odds bet immediately on top of the put bet, the opportunity to win on the initial roll is lost. The effect is the same as making a place bet or buying odds, but the house edge is different depending on the multiple of odds allowed. In the case of 20 times odds the house edge of the put bet on the 4 and 10 is 1.59%, on the 5 and 9 is 0.95%, and on the 6 and 8 is 0.43%. At this high level of odds allowed, which is much greater than the norm, all put bets are better than the corresponding place or buy bets. This option should never be taken at a casino that offers less than 5 times odds. At 5 times odds exactly, the put bet on the 6 and 8 is slightly better than the place bet. At 10 times odds or greater, all put bets become better than their corresponding place or buy bets. I shall add something to my craps section about the put bets, thanks for the idea.

A put bet is like a come bet made after a point has already been established. I don't recommend put bets because the value from come bets comes from the first roll, before any point is established. On a the first roll of a come bet the probability of winning is 22.22%, and the probability of losing is 11.11%.

However, if you must cover other points quickly, the odds are generally equal or better on place bets and buy bets on the 4 and 10 (assuming commission paid only on a win). Only if you can get 10x odds, and take them, do put bets become a better value than the better of place and buy bets. Since so few places offer 10x or better odds, it is safe to say to just avoid put bets completely.

The better system is to bet on the don't pass only and take full odds. Yes, betting on both does increase you chances of winning on any one bet. However you are suffering a higher combined house edge by betting on both the pass and don't pass and it will cost you in the long run.

You should leave them on. It is best to have as much on the odds as possible. Turning the odds off is like temporarily removing the odds bet.

Yes, it was luck. It helped that you stuck to the low house edge bets. However, next time, make the line bets with odds only, and don't bet the field, especially if it pays 2 to 1 only on both the 2 and 12.

The house edge is the same regardless of how many come bets you make assuming you always take the maximum allowable odds and leave the odds turned on during a come out roll. How many come bets you make should be a matter of personal preference.

As long as you are backing up your pass and come bets with full odds, it doesn't make any difference how many come bets you make. However, it does reduce the overall house edge to keep the odds on your come bets working on the come out roll.

I went to casinos in Berlin and Hamburg last year and didn’t see craps at all. Let’s consider rule change 3 first. My craps appendix shows the probability of winning the pass line bet as 244/495. Under the German rules it will be marginally higher. The probability of rolling a 2, 3, or 12, and then an 11 is ((1+2+1)/36)*(2/36)=1/162. So the house edge will be 1/162 less. From the craps appendix we see the normal house edge is 7/495 =~ 1.41%. The German house edge is 7/495 - 1/162 = 0.80%. The combined house edge under full double odds is 0.57%, and 0.43% when laying the odds. So clearly the US rules are favorable.

A put bet is like a come bet on a particular point. In other words the put bet does not get the benefit of winning on a 7 or 11 on the first roll, but the bet immediately gets "put" on the point of the bettors choice. The bettor may also immediately take odds on the put bet. Put bets are generally not a good idea because the player is twice as likely to win as lose on the first roll of a come bet, and the player is voluntarily forfeiting that roll with a put bet. However if the odds allowed are high enough a put bet, backed up with maximum odds, can have a lower house edge than a place or buy bet. My craps section states how high the odds need to get for this to happen. My craps advice in general is to stick to the line bets (pass, don’t pass, come, and don’t come) and backed up the odds.

You are of course quoting me from my March 24 column. This is a good and fair question. I should point out that taking or laying the odds in craps does not help the player to win more, only to bet more at no additional expense. The reason I encourage craps players to bet on the odds is that it is the cheapest bet on the table and is truly a craps bet. All odds, as well as place, buy, and lay bets win if one number is thrown before another. This is a very fundamental aspect of the game. It only makes sense for the player to make the bet with the lowest house edge. Refusing the odds in craps to bet on something else instead is like refusing a free coffee refill in a restaurant and instead buying another cup.

As I pointed out in the last column some video poker games allow the player to make a double or nothing bet with no house edge. The reason I am not as forceful about taking this bet is that it does not follow the flow of video poker. The video poker player is generally not there to make a mindless even money bet. Gambling should be thought of as entertainment, for which the player should expect to pay for. If the player doesn't get any entertainment value out of the double up feature then he shouldn't pay for it, even with no house edge. So my advice to the video poker player is make the double up bet if you enjoy it, otherwise don't.

There are 4 ways to roll a 5 (1+4, 2+3, 3+2, and 4+1) and 6 ways to roll a 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). So the probability of rolling a 5, given that a 5 or 7 was rolled, is 4/(4+6) = 0.4. The expected value of the place bet on 5 is (0.4*$4.50 + 0.6*-$3.00)/3 = 0. So you're right there is no house edge on the 5, or the 9. On the 4 and 10 the expected value is ((1/3)*$5.50 + (2/3)*-3)/3 = -0.0556. In other words the house edge is 5.56%. I take it this is only true of $3 bets, the casino rounding the winnings up from $4.20 to $4.50. As I reported in the last issue the player can gain an advantage in blackjack if the dealer pays $4.00 for a blackjack on a $2.50 bet.

It depends on how the games are played. If optimal strategy is compared to optimal strategy then craps is better. By betting only the line bets and taking maximum odds the combined house edge in craps is well under 1%. The best you can do is baccarat is bet on the banker at a house edge of 1.06%. However it wouldn’t surprise me if the actual house edge in craps is higher, due to all the sucker bets players make.

Thanks for the kind words on my Travel Channel appearance. For those of you who missed it the show was titled Sucker Bets. The dealer was right. In general bets are turned off on a come out roll in which a seven would cause the player to lose. I guess they don’t want some players to sour the mood of the table by rooting against a 7 on the come out roll. Since a 7 would cause the odds on the don’t pass to win they are left on.

Let’s say you have a $10 don’t pass bet and the point is a 4. You have a 2/3 chance of winning the bet, so the expected value is (2/3)*$10 + (1/3)*-$10 =$ 10/3 = $3.33. Now consider adding a $40 odds bet on top of it. Now you have a 2/3 chance of winning $30 and a 1/3 chance of losing $50. The expected value of both bets combined is (2/3)*$30 + (1/3)*-$50 = $10/3 = $3.33. So either way your expected gain is 3 dollars and 33 cents. With the don’t pass alone the player edge is $3.33/$10 = 33.33%. With the don’t pass and odds the player edge is $3.33/$50 = 6.67%. So, yes, the player edge as a percentage drops by making the odds bet. However that player edge is effective over more money. The way I think gamblers should view the house edge is as the price to pay for entertainment. If you want to pay as little as possible then taking or laying the odds is getting entertainment for free.

I get challenged a lot on my support for come bets with odds. Those against come bets are always quick to say a number has to hit twice with a come bet and only once with a place or put bet. That is not a good way to look at it. First of all with come bets you have a 8/36=22.22% chance of winning on the first roll as opposed to only 11.11% of losing. You get no such advantage on the first roll of a place or bet bet. Even if you do roll a point number it can be any number. In other words there are six point numbers that can win on a come bet, and only one on a place or put bet. Ultimately the reason the come bet with odds beats place or put bets is the house edge is less.

Thanks for the compliments. As you know I strictly look at the expected value of a bet. However, if taken to an extreme it doesn’t make sense at some point. If you made the proposition to me in your example I would only bet about $200 on it, although it has a 100% player advantage. The reason is if I won I would win $2,000,000 and I don’t really need more than that. However in craps a 2 to 1 win is not going to change my lifestyle if I win. 2 to 1 in craps is not a big long shot so I say get aggressive on the odds. If you’re uncomfortable with bets that have a low probability of winning you might take up betting the don’t pass and laying odds.

Yes, you are. You are forgetting that a come bet wins on the first roll 22.22% of the time and loses 11.11% of the time. So you are missing the extra value of the first roll of a come bet. However if you had a crystal ball that told you that the first roll would result in a point number then you would be right.

Yes. I can just imagine the follow up question to be why I recommend taking the odds if doing so doesn’t help to win more. What I suggest is betting less on the pass so that your need for action is mostly met by a full odds bet. For example if you are comfortable betting about $90 per bet, and the casino allows 5x odds, then I would drop the pass line bet to $15 and bet $75 on the odds. That will lower the overall house edge from 1.414% to 0.326%.

First, it doesn’t make any difference that the shooter is making lots of money. Your odds are the same on an ice-cold table. The past does not matter. However if you are going to play then wait patiently for a come out roll. Never make a pass bet after a point has been established.

First I would take a taxi to the Hard Rock, the closest major casino to the airport. I’m not sure how much odds the Hard Rock allows in craps but I would guess 3-4-5. If that is the case then bet 1/7 of your bankroll on the don’t pass bet, or $275 to round down. If a point is established then lay the maximum on the odds, or $1650. If you win you’ll be a lot closer to your goal, the amount will depend on the point. Win or lose bet the lesser of 1/7 of your bankroll and 1/7 of how far you are from $4000. If you get close to either extreme just get it over with and bet everything if you’re low, or whatever you need to close the gap on $4000 if you’re high, and forget about the odds. Four hours should be enough time. However don’t dilly dally. The lines at security can get pretty bad. If your outbound flight is in terminal C be sure to ask an agent about the secret entrance.

Yes, there was a story taped in which some frat boys at UNLV were trying to parlay $1,000 into $5,000 to buy a high end television. They sought out my advice on how to best achieve this goal quickly. I was limited to the games at the Golden Nugget. The Nugget has 10x odds in craps, which I felt offered the opportunity to achieve the goal. It was my strategy on each come out roll to bet min(bankroll/11, (5000-bankroll)/21), subject to convenient rounding, and take the maximum odds. This way we would never go over $5,000 after a 4 or 10 win, would always have enough to take full odds, and would risk the maximum amount if we didn’t have enough to get to $5,000.

For the first bet, this formula would call for a pass line bet of $90.91, but I rounded it up to $100. Then a point was rolled, I think a 6 or 8. On the second roll the shooter sevened out. So the entire grand was lost in two rolls. It apparently didn’t make for very entertaining television and that story never made the air.

Two questions I can anticipate being asked would be (1) why did I have them bet the pass as opposed to the don’t pass, and (2) why didn’t I bet $91 on the line and $910 on the odds, adding the extra dollar out of my own pocket. To answer the first question, I think that for purposes of going for a quick big win the pass line is better. While the overall house edge is less on the don’t pass, I felt it would have taken more rolls to achieve the $5,000 goal, thus exposing more money to the house edge. To answer the second question, there is not much difference between 9x odds and 10x odds and I thought it would look better on television to be betting only black chips, at least to start.

I agree. I don’t recommend making put or place bets, because as you said, the odds are better making a line bet and then maximum odds. However, some people absolutely must bet on the points directly. If that is a given, I advocate making the best bet between the place, buy, and put, which I explain in greater depth in my craps section.

That is a good question. Here in Vegas it varies by casino. I would say that most of them exclude odds in comp calculations, others only count odds up to a point, like 2x, and some count the full amount. I would love to name names but casinos are protective of their comping policies and much of what I know was given “off the record.”

We can see from my analysis of the Fire Bet that the probability of a shooter making all six points is 0.000162435. So, the value of the promotion per shooter is $4,000 × 0.000162435 = 0.649739.

The next question to be asked is what is the expected loss per shooter. The house edge on the pass line bet is 7/495 = 1.414141%. The tricky part is how many pass line bets will a shooter make, on average.

There are four possible states the shooter can be in. Let's define each one as the expected number of future pass line bets for that shooter.

• A = Come out roll
• B = Point of 4 or 10 made
• C = Point of 5 or 9 made
• D = Point of 6 or 8 made

Here are the equations showing the probability of each state leading to the next state.

A = 1 + (12/36)*A + (6/36)*B + (8/36)*C + (10/36)*D
B = (1/3)*A
C = (2/5)*A
D = (5/11)*A

A little algebra results in A = 2.525510, the number of pass line bets made per shooter.

So, the expected loss per $5 shooter is $5*2.525510*0.0141414 = 0.178571.

The expected amount bet by the shooter is $5*2.525510=$12.627551.

Finally, the expected return is the expected win divided by the expected bet: (0.649739-0.178571)/12.627551 = 3.73127%. So the house edge is -3.73%.

Unless life changing amounts of money are involved, I disapprove of hedging, per my seventh commandment of gambling.

I'm going to ignore the fact that if you hit the 5 you could hedge more to lock in an even larger win, and just look at this as if it ended after a 5 or 7. At this point your net will will be $785 or $50. You should start by taking down the odds bet. That will change the scenario to winning $755 or $70. Then you should lay the odds on the 5. Let b represent your lay bet against the 5. If you lose the bet, you’ll have $755-$b. If you win the bet, you’ll have $70 + (19/31)×$b. So, equate the two sides, and solve for b:

755-b = 70 +(19/31)×b
685 = (50/31)×b
b=424.7

That will lock in a win of $330.30. So, if rounding were not an issue, then lay $424.7 against the 5. However, rounding always is an issue, so I would lay $403 against the 5 ($390, plus $13 commission on possible win of $260).

Compared to 5X odds, that lowers the overall house edge from 0.326% to 0.269%. I don’t see why they would allow the extra odds bet on the 6 and 8, because a 5X bet at $75 would pay an even $90. However, as long as they did, I would take advantage of the extra odds, as long you are comfortable with the additional risk.

I asked a former table Vegas game manager about this. He said that the portion of the odds bet over the allowed multiple of the line bet would be paid at place bet odds. This question was raised and discussed in the forum of my companion site Wizard of Vegas.