Ask the Wizard: Craps

I still say hop bets, like the yo-11, are the way to go. Using chips, you could keep track of how many cards of each face are left in the decks.

With 26 unseen cards, if any one face had 6 left in the deck, you would have a 43.1% advantage on a hard hop bet (two of the same face), assuming it paid 30 to 1. With only 5 left, the house would have a 4.6% advantage.

The easy hops are even more exploitable. If the two dice sides in majority have at least 10 left combined, both with a minimum of 3 left, out of 26 unseen cards, then make an easy hop bet on those two numbers. If two numbers have 5 left, you will have a 23.1% advantage. If one has 4 and one has 6, you will have an 18.2% advantage. If one has 3 and one has 7, you will have a 3.4% advantage. All this assumes easy hop bets pay 15 to 1.

None of the above takes into consideration the $1 fee. As long as you are making large bets, it won’t make much difference. November 6, 2008

According to the the Bone Man at NextShooter.com, here is where and when you can find the tubs:

One Tub at Wild, Wild West (probably open only evenings, weekdays, and on weekends).
One Tub at Ellis Island (probably open only evenings, weekdays, and on weekends).
One Tub at Circus Circus in West Casino section, hardly ever open unless on busy holiday. November 6, 2008

You’re welcome. Thanks for the kind words. In my experience, most players make proposition bets for the dealers. For example, a "two way yo" bet is split 50/50 between the player and dealers. To make this bet, a player will hand or toss the bet to one of the dealers and say "two way yo." However, all the proposition bets are sucker bets, which will cut down the value of the tip by up to 16.7%. As you said, I prefer to give the dealer the tip directly, as opposed to betting it. Before a come out roll I will try to get a dealer’s attention and then put the tip in front of him, saying "for the dealers." I don’t like making pass line tips for the dealers, because I’ve been goaded into tipping extra on the odds, which was more than I intended to offer. If you must make a bet for the dealers, I would put it on the field, saying loudly "dealers in the field."

To answer your second question, dealers are only obligated to share cash tips. Anything else they may keep for themselves. I asked about this at the Venetian and the floorman said dealers may accept personal gifts up to $100 in value. Acceptable gifts can be things with a close to cash value, including gift certificates and unresolved sports tickets. It was quietly added that if a player gave a dealer an envelope, nobody other than the player and dealer would ever have to know what was in it. Should you decide to give a specific dealer a tip I would suggest being discreet about it, putting it in an envelope, and away from the table.June 2, 2007

I didn’t know they had a buy bet in Crapless Craps. The following table shows the house edge of place and buy bets, assuming there were no rounding of winnings. In your example of a $30 buy bet on 2 or 12 the winnings would be 6*$30-$1=$179. So the expected return is [(1/7)*$179 + (6/7)*-$30] / $30 = -0.0048, so we’re very close. December 13, 2006

In the October issue of Casino Player magazine, Frank Scoblete wrote an article on controlled dice shooting where you state you lost $1800 to Stanford Wong when he rolled only 74 sevens in 500 rolls. Why did you bet on such a small sample (500)? A person who claims to be able to control the dice should be willing to demonstrate their skill with a least 50,000 rolls. Am I wrong in thinking that 500 rolls is such a small sample that just about anything could happen? - Gerald from Alexandria

My webmaster Michael Bluejay had the cover story in that issue. They asked me to write for them again but I have been too busy. Regarding your question, I lost the $1800 to another gambling writer, not Stanford. I would have preferred more rolls but there was an obvious time contraint. Assuming one throw per minute it would take 34.7 days to throw the dice 50,000 times. I wasn't the one who decided on 500 but it seemed like a reasonable compromise between a large sample size and time. You are right that 500 is too few to make a good case for or against influencing the dice, but 500 throws is better than zero. Nov. 9, 2005

I'm walking through a casino and see a craps table with a shooter winning lots of money. I feel lucky and want to place a bet. What can/should I do? Do I have to first make a pass line bet? Can I make a come bet? Can I make either bet with odds? Or, do I wait until the next round of play? -- Todd from Chicago

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, because you'd lose the ability to win with a 7 or 11 on the come-out roll. However, you could make a come bet right away and still have the chance of winning on a 7 or 11. Sept. 25, 2005

If you have reason to believe that the seven is weighted and is coming up more than it should, does that favor the don't or the pass side of craps? - Haig from Englewood

The fewer the sevens the greater the odds favor the pass line bet. The following table shows the house edge according to the percentage of sevens, assuming the probability of all other numbers is proportional to the fair probability. Sept. 25, 2005

House Edge in Craps According to Seven Probability
Seven Probability	Pass House Edge	Don't Pass House Edge
15.000%	-0.666%	3.499%
15.333%	-0.202%	3.024%
15.667%	0.237%	2.574%
16.000%	0.652%	2.148%
16.333%	1.044%	1.744%
16.667%	1.414%	1.364%
17.000%	1.762%	1.005%
17.333%	2.089%	0.667%
17.667%	2.395%	0.349%
18.000%	2.682%	0.051%
18.333%	2.949%	-0.227%

Hi, if person A makes 1000 consecutive bets on the pass line without backing up his bet, and person B makes 1000 consecutive bets on the pass line and he takes 100X odds whenever possible, doesn't each person lose the same amount of money? - Blake Haas from Thousand Oaks

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%. Aug. 28, 2005

I realize that decisions per hour in games like blackjack and craps can depend heavily on factors like the number of other players at the table, the hand shuffle vs. machine shuffle, shooter and dealer speed. Still, I was curious if you could give me a rough approximation of how many decisions per hour an individual can expect at a mostly-full craps table and a blackjack table with both a hand shuffle and machine shuffle. This would help me estimate my expected loss per hour and weigh it against the comps I am being offered.

The following tables show the number of hands/tosses per hour in blackjack, craps, and roulette. The source of the tables is Casino Operations Management by Jim Kilby. Aug. 28, 2005

Hands per Hour in Blackjack
Players	Hands per hour
1	209
2	139
3	105
4	84
5	70
6	60
7	52

Rolls per Hour in Craps
Players	Rolls per hour
1	249
3	216
5	144
7	135
9	123
11	102

In craps 29.6% of total rolls are come out rolls, on average.

Spins per Hour in Roulette
Players	Spins per hour
1	112
2	76
3	60
4	55
5	48
6	35

Thanks for the great site. You recently stated that the average craps shooter lasts approx. 8.5 throws. I normally bet the pass with full odds followed by come bets with full odds. Does it make more sense to quit making come bets after, say four throws given the long term probability that the thrower will seven-out in only three to four more throws? Thanks, Fred

You're welcome, thank you. The dice do not have a memory so after four throws you do not get any closer to sevening out. You could roll 1000 non-sevens and still be no closer or further away from a seven than you were the first throw. There is no optimal number of come bets, just make as many as you find the most fun. Dec. 13, 2004

Is the combined house edge in craps of 0.014% (taken from your chart) on don't pass and laying 100x odds the lowest house edge of any casino game? And, does 0.014% casino edge mean that for every $100 you wager you will lose 1.4 cents?

There are still video poker games that with proper strategy pay over 100%. I've also seen a blackjack game at the Fiesta Rancho and Slots-a-Fun in Las Vegas that had a basic strategy advantage. As I argue in my sports betting section betting NFL underdogs at home against the point spread also has resulted in a historical advantage. So 100x odds in craps is still one of the best bets out there, but not the very best. Yes, 0.014% means that per $100 bet you lose 1.4 cents on average. Dec. 5, 2004

In one of your answers you state that the average number of rolls for a shooter in craps is 8.522551. How is that number obtained? - Steve S., Long Island, NY

First, if the probability of an event is p then the expected number of trials for it to occur is 1/p. Let's call x the expected number of rolls per shooter. The probability that any given round will end in one roll (with a 2, 3, 7, 11, or 12) is 1/3. If the player rolls a 4 or 10 on the come out roll the expected number of additional rolls is 4, because the probability of rolling a 4 or 7 is (6+3)/36 = º. . Likewise If the player rolls a 5 or 9 on the come out roll the expected number of additional rolls is 3.6 and for a 6 or 8 is 36/11. Assuming a point was thrown the probability of it being a 4 or 10 is 3/12, a 5 or 9 is 4/12, and a 6 or 8 is 5/12. So the expected number of throws per round is 1+(2/3)*((3/12)*4 + (4/12)*3.6 + (5/12)*(36/11)) = 3.375758. Next, the probability that the player will seven out is (2/3)*((3/12)*(2/3) + (4/12)*(3/5) + (5/12)*(6/11)) = 0.39596. The probability that player will not seven out is 1 - 0.39596 = 0.60404. So...

x = 3.375758 + 0.60404*x
0.39596*x = 3.375758
x = 8.52551 Nov. 28, 2004

Why is it better to make Come bets with odds than to make Place bets? My math indicates that you make more on a place bet when betting equal units. On 4, to instance, if I were to place $10 I'd win $18. On the come bet I would only win $15 ($5 on the initial bet and $10 on the odds). The other advantage to place bets is that I get to choose which numbers I want to bet and that I win the first time that it is rolled. Am I missing something?

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. Sept. 23, 2004

I'm getting ready to go to Vegas and it has been a few years since I have been there, I know Binion's used to be the best place to play craps, however I understand since the Harrah's takeover that it no longer holds true. Could you please tell me the best places to play craps are?

I don't think the takeover had any effect on the craps at Binion's Horseshoe in Vegas. Although they used to offer 100x odds they ended that long before the federal marshals shut them down earlier this year. The best odds in Vegas can now be found at the Casino Royale (between the Venetian and Harrah's), which offers 100x odds. Sept. 23, 2004

What is your opinion of Card Craps as played by many of the casinos in the San Diego area?

In California dice alone can not be used to determine the outcome of a game. To get around this law many casinos use a hybrid of cards and dice called Card Craps. In this game there is a deck of 7 cards, one each numbered one to six, plus a joker. Using a die two of the seven cards are drawn randomly from the shoe. If the first card is a joker then there is no action on craps bet (although there is joker bet). Otherwise the first simulated die roll is whatever number is on the card. If the second card is the joker then the second simulated die is whatever number was on the first card. Otherwise it is whatever number is on the second card. Mathematically speaking the odds are the same as regular craps. However it is a ridiculous commentary about California gambling laws. May 5, 2004

Mr. Wizard, great site. You are the one true expert on the internet. Because the odds in dice are based on the probability of winning as compared with the payout, I question whether it makes sense to take odds on bets that have a low a probability of winning. For example, the odds on the 4 and 10 are 2 to 1. Is it really a good bet to back up the pass line when the 4 or 10 shows. If someone offered a payout of 10,000 to 1, with the odds of winning 5000 to 1 (and you could only make one bet), it would appear to be a good bet, but the chances of winning are so slim that in reality it is probably a suckers bet. Is there any validity to what I am saying?

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. Feb. 27, 2004

You say the house edge on the pass line bet in craps is 1.414%. Is there any coincidence that this number is the square root of 2?

Just a coincidence I assure you. The exact house edge in craps is 7/495, which by definition must be a rational number. In fact I would argue the house edge in all casino games must be a rational number because there are a limited number of possible outcomes in all games, resulting in a house edge of a perfect fraction. 2 is not a perfect square thus the square root of 2 must be irrational by definition. Therefore the two numbers can not be equal. To be specific the house edge on a $100 pass line bet would be $1.41414141... The square root of 2 is 1.4142135623731... Feb. 27, 2004

Mr. Wizard, you're site is great. I think you may be the only honest expert on the internet. My question is this. I know how odds are calculated in craps but I cannot shake the feeling that once a player gets up multiple bets, either through placing them or betting the pass line and making successive come bets, that the odds shift dramatically into the houses favor. It only takes one seven to wipe out all the bets at one time. In order to win, you must hit each number and after it is hit, a seven would wipe out the remaining numbers.

Thank you for the kind words. I still say that the house edge is not dependent on the number of come bets you make. Yes, it is depressing to establish one come point after another and then lose everything on a seven. However there are other times when the shooter takes ages before rolling a seven and you win lots of come bets along the way. Dec. 2, 2003

Could you provide some details about the mechanics of "buying in", for example, at a crap table? Do dealers take cash only? If so, and I wish to make a substantial buy-in, does this mean I must arrive at the casino carrying nothing but cash (a risky action in LV)? What about travelers' checks? Can I make advance arrangements for credit with the casino Cashier's Office? If so, how does that work exactly? Get specific, please.

I remember my first trip to a casino I didn't know how to actually get chips to play with and purchased them at the cage and walked them to the blackjack table. The proper way to buy in at the table is simply to lay your cash on the table and at the appropriate time the dealer will exchange the cash for chips. However if you wish to play for amounts too uncomfortable or unsafe to carry in cash you can wire funds to the casino in advance. Then all you have to do when you get there is ask the pit boss for chips and he will have you sign something, stating you are buying chips against your cash account. To get off topic a bit I think it is time the United States Treasury should start making $500 bills, making it easier to carry large amount of money. A 500 Euro note already exists, which is worth $598 U.S. dollars at the time of this writing. Dec. 2, 2003

I have a craps question. If I make a $100 pass line bet and then a $100 come bet every roll, what is my average action per roll? For example, I bet $100 on the come-out. The dice show a 4. I bet $100 come bet ($200 total on the layout). A five is rolled. I bet another $100 come bet ($300 on the layout). A seven is rolled. My total action was $100+$200+$300=$600, or average of $200 per roll. What is this number for the long run using this betting pattern? Essentially I am looking for my average bet. Thanks.

Good question. Let's think of this in units as opposed to $100 bets. You will always have a bet on the pass or come. On any given roll the probability there is an old pass or come bet on the 4 is 3/9. This is the probability that by looking back at old rolls you will find a 4 before a 7. Likewise the probability of having a bet on 5 is 4/10 and on 6 is 5/11. So the average overall bet is 1+pr(4)+pr(5)+pr(6)+pr(8)+pr(9)+pr(10) = 1+3/9 + 4/10 + 5/11 + 5/11 + 4/10 + 3/9 = 3.3758 units. This average will not true at the beginning, while you are getting in to the game. It will only apply after all point numbers and the 7 have already been rolled at least once. June 27, 2003

At the craps table, I've observed that 80% of the people bet one the pass line. From what you say, the don't pass line has a slightly lower house edge. So why don't most people bet accordingly? - Dan from Ottawa, Canada

Most player probably don't know the don't pass is a slightly better bet. Even those that do probably bet the pass bet because it feels better to be part of a group than to go against it. May 26, 2003

According to the Las Vegas Advisor the record for the longest time a single shooter held the dice in craps is held by Stanley Fujitake, who once held the dice for three hours and six minutes at a downtown casino before sevening out.

(1) What are the odds that Mr. Fujitake could have accomplished his feat, assuming typical craps speed?

(2) What are the odds that this happened in Vegas since 1950?

- Veggie Boy

Yes, this happened at the California casino. There is a plaque in the side of the building mentioning it. For those who don't know, in craps the same person throws the dice until he loses a bet by throwing a seven. If the player loses on a come out roll he still keeps the dice.

According to Larry Drummond of nextshooter.com the number of throws per hour ranges from 60 to 120, depending on how crowded the table is. I would assume during this famous roll the table got crowded, so we'll assume only 60 rolls per hour, or a roll a minute. So Mr. Fujitake threw the dice 186 times. From my craps appendix 2 we see the average number of throws per pass line bet is 3.38. So he went about 55 pass line bets. The probability of either winning a pass line bet or losing it on the come out roll is 60.4%. Subtracting one pass line bet (the losing one) the probability of winning 54 is .604⁵⁴ = 1 in 664 billion.

The average rolls per shooter is 8.54, so assuming 90 rolls per hour an craps table would have 10.54 shooters per hour. To make a very rough guess I'll assume that the average number of active craps tables in the United States at any given time since 1950 is 200. So that would be 53*365*24*10.54*200 = 979 million shooters, but let's just say a billion. So the chances of a roll this long in 53 years is 0.15%. However I tend to think the pace of this legendary roll was much less than 60 rolls per hour, making the probability of going over 3 hours much more likely. May 5, 2003

I've just starting learning the game of craps. In craps, the Don't Pass is a better bet for the player than the Pass Line bet. But the few times I've played in the casinos, most people seem to be betting the Pass Line and not the Don't pass. I'm either not correct on the odds b/t the two bets or is there some reason most players are taking the Pass Line bet over the Don't pass line bet?

That is a good question. It is obviously more fun to go with the crowd than against it. The question is why does the crowd favor the pass line? Perhaps it is just tradition. Maybe when people first started playing craps in private games the don't pass wasn't even an option. March 7, 2003

The Kelly strategy for betting requires a positive edge to be effective. I play craps and I give the house less than a 1% edge. Once a week I get comps of $62. I gamble only 1 1/2 hours and my total betting doesn't reach $3000. Theoretically I earn approximately $30 per session. Would the Kelly strategy be helpful to me? - Jerry Tatz from Del Ray Beach, USA

Unless bankroll preservation is very important to you then Kelly betting won't help. I would just flat bet. Nice strategy to milk the comp system. Jan. 11, 2003

I have two friends that have a bet on which game (craps or baccarat) have the best odds for the player. Could you help me settle this. They are both casino workers and are sure they are right. - Charline from Las Vegas

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. Sept. 24, 2002

Before I ask my questions I just want to say your site is phenomenal! I have two craps questions I was hoping you could answer:

1) Your preference is to count the come out roll of 12 in the calculation of the house edge on the don't pass. If one was to choose NOT to count it, would the house edge on the pass line combined with full double odds be exactly equal to that of the house edge on the don't pass line combined with full double odds?

2) Does the overall house edge against player x go up if player x places come bets (which will be backed up with full double odds) after betting the pass line with full double odds? i.e. player x with just a pass line with full double odds = house edge .572%, player x with same bet but places two come bets with full double odds = house edge (.572%)x(3)? - Jay Sparks from Hamilton, Ontario

Thanks for your kind words. Here are my answers.

1. If we define the house edge as the expected loss per unresolved bet (not counting ties) then the house edge on the don't pass would be 1.40%, just barely less than the 1.41% on the pass line bet. If the player can bet more money on the don't pass side, which is the case in real but not Internet casinos, then the combined house edge favors the don't side more the greater the multiple of odds allowed.

2. Assuming the player keeps his odds on during a come out roll then the overall house edge does not change if the player adds come bets, backed up with the odds. However if the player keeps the odds off, which is the default rule, then the overall house edge will actually go up slightly by adding come bets. Dec. 4, 2001

Will you be doing a risk of ruin analysis for Craps? The only analysis I have found online to date seemed to be flawed. - Brian E from Raleigh, USA

I wasn't planning on it. There are so many betting patterns in craps that one analysis would only fit a small percentage of craps players. Aug. 6, 2001

Hi, I'm from Germany and it's difficult to play craps here. I finally found a place where it is possible. But they changed the rules:

1. you may only bet the "right way"
2. it's not allowed to make odds-bets after establishing the point
3. if the come out roll is craps (2, 3, 12) the bet is deferred and if the next roll is 11 you get your money back, otherwise it's lost.

I wonder which effect it has on the house edge? - Toter Mann from Munich, Germany

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. July 18, 2001

When reading literature about the formula casinos use to determine comps, the only formula I ever see used as an example is a formula for blackjack. Assuming the casino determines your average bet by your spread, what formula is typically used by casinos to determine expected craps losses, which in turn, determines available comps. - Tim Patton from San Antonio, Texas

I asked my friend Larry Drummond, a craps dealer and webmaster of Next Shooter for help on this question. Larry can be a bit abrasive but is a good source of hard to find information on craps. Here is what he said, "Comps for craps vary from Casino to Casino and from Boxman to Boxman. A player should get to know the Boxman. The Boxman sets the players average bet and tracks the TIME that a player is at the table. It is easier for the Boxman to track action for COMPS. if the player is consistant in their wagering pattern. Now, I ask you... if a player goes $52 or $54 across after a Point is established with a $5 flat bet on the Pass Line. Is that a $57 or $59 average?... Or a $5 average with a whole bunch of other INDIVIDUAL bets? The answer is... IT DEPENDS ON HOW WELL YOU KNOW THE BOXMAN and HOW MANY TIMES TO YOU ATTEND THIS PARTICULAR CASINO." Larry added in another e-mail the following, "In addition to the information I already sent to you... ODDS on Pass Line and Come bets are often NOT included in the AVERAGE for comps. Same with LAYING ODDS on the Don't Side... as in the long run this should be a WASH. But... If a smart boxman wants someone who is spending big bucks on ANY 7, the worst bet on the table... he would probably average the ODDS and the LAYS to keep the sucker coming back to the casino... you can re-word this to make it a little more palitable for your site... In addition... A good boxman will COMP to the MAX if he sees that the PLAYER is 'Betting for the Boys'. June 6, 2001

In craps, does the house edge change if you make a don't pass bet then remove it if the point is 6 or 8? What if you remove it if the point is 6,8,5,or 9? - Jon Moriarty from Danville, New Hampshire

You should never remove a don't pass bet after a point is made! Likewise you should never make or add to a pass line bet once a point is made. However if you must make a don't pass bet after the point is made then it is best to do so on a point of 6 or 8, since these have the least chance of winning. May 1, 2001 

Is there a casino that teaches how to play craps? ñ Marty from Houston, USA

There are lots of them. Many casinos give free gambling lessons in the mornings when things are slow. To name just one I know the Silver Legacy in Reno offers lessons. Dec. 24, 2000

I just finished reading your section on strategy for craps with great interest. I understand that better the pass line and come bets with full odds is a good strategy. My question is "does the house edge change at all when playing a strategy of pass line with full odds and making a maximum of two come bets with maximum odds?" In other words; how does time (more rolls) and having more money at risk affect these odds if at all? Or should a person stick with just the single bet with full odds? This seems to be a favorite strategy for most knowledgeable players I have met at the dice tables. -- Jim Marlow of Yakima, USA

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. Nov. 11, 2000

I played craps for the first time the other night and went from $70 to $700 with small bets on the pass odds and field bets. I then lost it all down to $6 because my bets were too large (by the dealers suggestion), and gained it back to $1000 after slowing down. For this being the first time it seems like a very easy game to win if you have patience, was it beginners luck? Chris, Tyler, USA

It was mostly just luck. Given the low house edge in craps it isn't unusual to do well often. I would recommend staying away from the field bet in the future and sticking to the line bets and the odds. Oct. 15, 2000

I'm a floor supervisor at a local casino and was wondering about a strange play. A player was betting both the pass and don't pass at the same time. My question is if he was betting the do side for $10, I would give him an average bet of $10. Now that he is betting both sides, and probably not risking any funds, what would the average bet be? I know if this patron bet both the red and black on roulette, he should get an average bet of both bets on red and black, since the house advantage of 5.26% make both bets a loser over the long run. ñ Ray from Plainfield, USA

I see you have a second question on this topic. I suppose to be fair he should get the same credit as for one bet of $20. However I don't know how much you value craps play. Some bets carry higher house edges than others. For each $20 he bets the casino can only expect to profit 28 cents. So don't let him milk the comp system if you assume the casinos expected revenue to be greater than that. Oct. 5, 2000

Q: Great site. Do programs like Microgaming "learn" to defeat the player? I was under the assumption that the answer is no until I played "Don't Pass" in craps. Out of 39 "hands" 28 were Pass, 10 were Don't Pass and 1 was a 12 on the come out roll. I realize that this can happen, but it made me wonder. I had read elsewhere that the software can "learn". I didn't really believe it. No, I didn't lose a lot, my betting unit is $1. I'm "testing" onliine for myself. - Rosalyn Blanchette from South San Francisco, California

A: No, programs like Microgaming do not learn to defeat the players. Reputable companies like Microgaming do not need to play any dirty tricks to make money but realize that there is more money to be made long-term by offering a fair game. Even if they did want to cheat the players there would be much easier ways to do so.

However there is a lot to be said about computer teaching themselves to play. I'm not an expert but I do know that computers can learn from past experience in games like backgammon and chess to improve their play. Finding the Edge (Edited by Olaf Vancura, Judy A. Collins, and William R. Eadington) has a paper titled 'A Computer Teaches Itself to Play Blackjack' by Olaf Vancura if you are interested in learning more about the topic. June 25, 2000

Q: As a moderate craps player who is of course interested in receiving every "comp" possible, could you give advice on the best betting (craps) strategy. Tried to find it in your GREAT web site. - Ernie from Hernando Beach, Florida

A: Unlike most gambling writers I don't put much emphasis on betting strategies. There is no one right or wrong strategy. They all behave differently in the short run but in the long run you will give the house the same percentage of total money bet. However if getting good comps is a priority for you then bet more when the pit boss is watching. Otherwise just do what is most comfortable for you. May 6, 2000

Q: I made the mistake of making a pass line bet in craps after a point was established. The next roll was a 7 and I thought I won but the dealer said I lost. Can the player make a pass line bet after a point is rolled? What should have happened? -Larry of Detoit

A: Yes, you can make a pass line bet at any time but you never should make one or add to one after a point is thrown. Once a point is thrown the odds of winning drop to 33% to 45% depending on the point. You can not add to a don't pass bet because that would favor the player. In your case when a 7 was thrown all pass line bets lost including yours. What happened is what was supposed to happen. Feb. 12, 2000

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