What are the Odds?

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While this article is posted in the "So Craps is New to You and You Don't Have a Clue!" sub-board, the fact is the majority of craps veterans don't have a clear understanding of the odds of the game as well. To that end, I'm going to spend some time here over the next couple of months going through some of the more interesting bets at craps and your chances of winning with them. I won't be adding any skews to the calculations - by that I mean I won't go into things like "if your SRR is 1.728 then the odds of you tossing thirteen tens on any give hand are . . . " We're going to look at the base "random" odds on various bets. It's up to you to determine if you have the skills to beat those odds.

What if I told you I could turn $1 into $27,000 in three rolls of the dice? Would you call "bullshit" on that one? It's not complicated. Toss a $1 chip to the stickman and call "Dollar Midnight (12)." Set the dice and toss a twelve. It pays $30 - $1. Parlay that bet and toss a second twelve. It pays $900. Parlay that bet and toss a third twelve. It pays $27,000. Holy Freshman First Semester at Harvard (tuition only - excluding room and board), Batman. So here's how you arrive at that number. The payoff on the $1 bet on the twelve is $30 to $1. Toss three twelves in a row and parlay the first two bets and it looks like this: 30 X 30 X 30 - 27,000. Now, what are the odds that you'll actually THROW three twelves in a row. Well, there is one twelve out of thirty-six combinations of the dice, making the odds 35 - 1. So we do the math on this one the same way: 35 X 35 X 35 = 42,875. That means you would essentially burn $42,875 trying to win $27,000 one time. It's like going camping and using $15,875 in dollar bills as fire starters.

Have you ever seen a shooter toss three 12's in a row? I've seen it several times. In fact, on one occasion I personally tossed six consecutive 12's on a come-out series where I was betting and setting for the Horn numbers. What are the odds of that? LOL. My calculator wants to go into ERROR mode. It's somewhere around 1 in 1.83 billion, as I recall. How many of those hits did I parlay? Not a one.

For those of us who play craps - it is without a doubt the greatest game in the casino. You can make money faster on a hot table than in any other game in the house. But you can also lose money faster.

Let's talk some more about odds and betting. But first - the dreaded 36 possible combinations of the dice discussion.

Each die has six sides. Each side is numbered with 1 thru 6 pips or spots. Let's say the left die is green and the right die is red - simply so it's easier to track what's happening in this explanation. Now let's get the total number of sides on the dice. Six on each die, so 6 X 6 is 36. That's 36 possible outcomes. They are:

1-1, 1-2, 1-3, 1-4, 1-5, 1-6
2-1, 2-2, 2-3, 2-4, 2-5, 2-6
3-1, 3-2, 3-3, 3-4, 3-5, 3-6
4-1, 4-2, 4-3, 4-4, 4-5, 4-6
5-1, 5-2, 5-3, 5-4, 5-5, 5-6
6-1, 6-2, 6-3, 6-4- 6-5, 6-6

Now, it you look at these combinations you'll notice a couple of things. First off, some numbers can only be rolled one way. These numbers are 1-1, 2-2, 3-3, 4-4, 5-5, and 6-6. The hard four, hard six, hard eight and hard ten are displayed in the hardway box on the layout. Typically the hard four and ten pay 7 - 1 and the hard six and eight pay 9 - 1. Why do they pay different amounts? Because there are two ways each to roll the easy six or eight, knocking off the hard six or eight, but there's only one way each to roll the easy four or ten. Hence the different pay outs. Hardway bets stay up until the number you have wagered is knocked off either by an easy way rolling or by the seven.

The 1-1 and 6-6 are displayed in the prop box area. Variously called aces, post holes, snake eyes, midnight, all the spots we got, high-low, etc., these are one roll bets. Their fate is decided on the next roll of the dice. Hence the higher odds.

Now, the rest of the numbers are "easy way" numbers. That means there are two or more ways to roll that number. The three and eleven are proposition bet numbers. The three can roll 2-1 or 1-2. Some of you are going to be confused by that so think back on that green die - red die I mentioned above. The green die rolls 2 and the red die rolls 1. Then on the next toss the green die rolls 1 and the red die rolls 2. Or just look at that chart above. On the first line you'll see 1-2. on the second line you see 2-1. So there are 2 ways out of 36 possible combinations that add up to three and two ways that add up to eleven. Instead of paying $30 - 1 like the two or twelve craps as mentioned at the top of the page - the three and eleven pay $15 - $1.

Armed with this knowledge you can calculate the probabilities of each number rolling. I'll fill you in with the totals:

The 4 and 10 will roll three ways each
The 5 and 9 will roll four ways each
The 6 and 8 will roll five ways each
The 7 will roll six ways

Now here is where a lot of people go wrong when building betting strategies. They attempt to combine wagers into a single bet, screw up on the odds calculations and cost players a ton of money. Let me explain. We'll take a $10 game and utilize place bets on the six and eight at $12 each. There's a system that's been sold for many years that claims to beat the odds at craps. The strategy recommends Place betting the six and eight only. It claims you have 10 ways to win versus 6 ways to lose, giving you something like a 1.67% positive expectation (10/6). You have 5 ways to win on the six and 5 ways to win on the 8. But the system seller forgets to mention that you have a total of $24 action ($12 each on the six and eight). Result? Every time the seven shows you're going to lose $24. Now let's plug in the numbers:

5 wins at $14 = $70
6 losses at $24 - $144
Net = minus $74

So much for THAT systems.

There are other ways we step out of bounds from time to time when calculating "odds." For example, let's say I wanted to know what the odds were that the four, five or six would roll on the next toss. There are three ways to roll the four, four ways to roll the five, five ways to roll the six. That's twelve of thirty-six combinations, so it looks like the answer should be 3 - 1 against, but the correct answer is 2 - 1 against. That's because three is the sum of all possible outcomes. That includes the possibility that it will happen - or that it won't happen. When we say the odds are 1 in 3 we're also saying that there's two ways of the event not happening versus one way of it happening.

Thoroughly confused? Don't sweat it. Even the old farts hanging around here are struggling with some of this. I'll let you mull that over a bit (and check my math . . . after all, I'm one of the old farts I mentioned) and in my next post I'll talk about things like the odds of a particular number showing on the next roll.

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Okay, let's revisit the odds calculation for a minute. Let's say there are 24 ways to roll a box number out of 36 possible numbers, 6 of which are Sevens. What are the odds you'll roll a box number on the next toss of the dice?

Hint. I threw that six ways to make a seven in there to jack with you. I did not mention that there are six other combinations not mentioned - the 2, 3, 11, and 12.

Figure it out yet?

There are 24 ways to roll a box number versus 36 possible combinations. Set that up as a fraction and you come up with 2/3 after you reduce it. Translated - two out of three times you'll roll a box number. So what are the odds you'll roll a box number?

2 to 1 in favor of you rolling a box number. Remember, out total "universe" of numbers is 36. There are 24 ways to roll a box number. So on average you will toss a box number two times - and some other number the third time.

Am I saying the same thing - just differently?

Uh . . . yeah. But if you're going to do odds calculations you have to be working with apples and apples, not apples and oranges.

Let me go through some common bets and state the odds two different ways:

All Points (box numbers) . . . . . . . . odds are 2 out of 3 . . . . . . . . odds for/against are 2 - 1 for
Inside Numbers (5,6,8,9) . . . . . . . . odds are 1 out of 2 . . . . . . . . odds for/against are EVEN

Now let me stop right there for a minute before some of you go frolicking down the "I can't lose with inside bets" trail. Let's take our lowest level correct bet on a $10 game - $44 inside. On any win you collect $14. On any seven you lose $44. That means you have to get four hits on your numbers and win $56 to get ahead. Three hits will pay you $42 and you're still a $2 loser if the seven shows. That "EVEN" odds thing means you have a 50/50 chance of winning/losing that bet on the next toss. But it has nothing to do with the size of the bets and whether or not you'd win or lose money.

Field Bet (2,3,4,9,10,11,12) . . . . . . odds are 4 out of 9 . . . . . . . . . odds for/against are 5 to 4 against
Outside Numbers (4,5,9,10) . . . . . . odds are 7 out of 18 . . . . . . . . odds for/against are 11 to 6 against

Remember when you see odd numbers like that 7 in the 7 out of 18 odds that we are reducing fractions. There are 14 ways to roll an outside number out of 36 combinations - which reduces to 7/18.

SEVEN (7) . . . . . . . . . . . . . . . . . . odds are 1 in 6 . . . . . . . . . . . . . odds are 5 - 1 against

The odds on the seven are something you guys who like to hop the sevens on the Come Out should think about. Likewise, those of you who play small Don't Pass bets and still waste money hedging against the seven need to give it some thought.

Six or Eight (6, 8) . . . . . . . . . . . . . odds are 5 in 36 for either . . . . . odds are 6.2 to 1 against
Five or Nine (5, 9) . . . . . . . . . . . . odds are 1 in 9 for either . . . . . . odds are 8 to 1 against
Four or Ten (4, 10) . . . . . . . . . . . . odds are 1 in 12 for either . . . . . odds are 11 to 1 against

The odds are so bad on the horn/prop numbers that I'm not even going to qualify them with numbers. Just stay away from them.

Okay, ALL of the above was about calculating the odds of any given number showing up on the next toss. It was NOT about the odds of a number showing before the seven. Those numbers are going to be a lot more familiar to most of you and are much easier to calculate. You simply take the number of combinations possible to make a number versus the number of ways to make the seven (6 ways).

Six or eight - odds are 6 - 5
Five or nine - odds are 3 - 2
Four or ten - odds are 2 - 1

Of course, the only way you get PAID those odds is if you take advantage of the Free Odds bet - or you pay a commission and Buy the point - which is always the way to go on the four and ten and may be to your advantage on the five and nine as well.

And that's as far as I'm going to get on this today, because I need to do a little research on how to post fractions and mathematical formula on phpbb without having to do it in a spread sheet and converting that into a file php can deal with. More to come.

[stratocasterman]

Danga Heavy...looks like I passed up the chance of about $70G with just a parlayed Horn bet (3 times) the other day with my crazy 11 Horns in one roll! All I got out of it was a 10, 8 & 4 payoff!

"I set a point of 5, then 2,3,12,10,2,11,2,Hard8,3,11,Hard4,2,12,3,SO"

[heavy]

Well, if you were a see a horn bet a horn kind of guy and parlayed the first hit you'd have had a $4 horn when the 2 craps hit. Pays you $12 and up to win again - or parlay to $16. Then the 12 rolls and you get 4X30 or $120. If you parlayed that you would have lost it on the 10, which i why I say only parlay the first hit if you're going to make this play. At no point did you toss more than three horn numbers in a row. You probably would not have been on the first one. Go up on the second one and if it hits - parlay it. If you get a second hit then lock it up. HOWEVER, generally speaking you'll be dollars ahead staying off of the horn numbers.

[London Shooter]

This will be a great series of articles to follow. Hopefully as the short pays relative to true odds on a lot of bets are explored they will lead people to stop bleeding their buyin as much as they do on the more exotic stuff such as the hops, props and bonus bets.

Yes, guilty as charged - see ATS for me, or even "Repeater, Repeater, The Bankroll Eater" as I call it Strangely I do not have a weak spot for the firebet. I guess it's a lot easier to see with the evidence of your own eyes that the thing hardly ever pays out.

The real cost of ATS and Repeater is effectively hidden by the reload on come out 7s.

Incidentally, a parlayed £1 midnight over here in London will return you over £39,000. Still well off the mark of true odds of course but a lot closer than you guys get.

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I've refrained from continuing this thread due to the challenges of posting certain mathematical equations in php.bb format. I've come to the conclusion that my best best is to compose my posts on odds, casino math, et al off-line and then cut and paste it into the forum's software. That's the direction I'm headed today. But first I want to talk about gamblers - not gambling. There are two types of gamblers. There are what I'll call "gamblers in fact," and there are "gamblers in fiction." A fictionalized gambler may be based on a factual gambler - but the fact that his story is fictionalized means it is a lie. Period. If it were not a lie you'd be watching a documentary. And (seriously) those of us who know the behind-the-scenes stories of some of those gambling documentaries you see on the cable channels know that they are heavily embellished as well. At the end of the day I put most factual gamblers in the same boat with factual fishermen. When their lips are moving then odds are they're going to start lying.

Now let's talk about different types of factual (real) gamblers. You've seen them all and I'll let you try to figure out which category you fall in yourself. First off, you have the low roller - low stakes player whose bets are so small (when expressed as a percentage of his total bankroll) that if he played every session to his personal loss limit it still would not impact his bottom line significantly. He may or may not fully understand the intricacies of the various games he plays. Odds are he has limited knowledge of odds and how they work. He doesn't like losing, but losing is not something he dwells on. He knows how much time and money he can afford to risk gambling and is able to pull himself away from the game when those limits are reached.

Next you have the compulsive gambler. If you've spent much time at the tables you've probably crossed paths with a few of these guys. They are at their happiest when gambling. His is fueled by his emotions - running from elation to despair on a turn of the cards. The more he loses the larger he bets as he chases his losses. He is like the alcoholic (often he IS an alcoholic) desperate for that next drink. Their loss limit is what they have in their wallet - and may extend to what they can get out of the ATM machine. And while they are essentially random gamblers - even Randy gets lucky sometime and those brief brushes with luck just reinforce his bad behavior.

Last of all you have the professional gambler. Now, this may be a low-level "semi-pro" or a full time player who is backed by a million dollar bankroll and an almost magical comprehension of the math of every game he plays. He may play like the casual gambler - methodically adhering to loss limits, etc., or he may play like the compulsive gambler, spending 12 - 16 hours a day at the tables. But whether he's in the casino, at the track, or playing a private game - he gambles well and manages to make a good living out of it.

Which one of these types of players are you? Are you the player you want to be? Those are the first questions I'd like you to think on while I'm working on this month's CrapsCheque newsletter and some additional material on "the odds."

[Moe Bettor]

I'm a combo. More low roller seeing pro in the distance and slowly crawling towards it.

[220Inside]

Nailed it Nick. #metoo

[London Shooter]

Pro in the day job, casual pretty low roller in the casino.

[SHOOTITALL]

Most of the time I am a low roller but there are times when I am subject to make larger bet or go on tilt. It is easier to control now than it use to be. Gotta keep between the ditches.

[Bankerdude80]

I'm a combo. More low roller seeing pro in the distance and slowly crawling towards it.

Nailed it Nick. #metoo

I as well, striving towards it.

[skasower]

I am a timid gambler even though I have a reasonably large casino budget. I have difficulty viewing myself as any different than the Rollin Randies and so far Bone Trakker confirms that is what I am. Clearly, I need to practice and I am indeed practicing every day since the new year. I know that being completely at the mercy of "random" keeps me from betting more on myself and timidly on others. One observation for those who read my words and think I am overly pessimistic. Last June, I was playing craps with a few of you Axis Gang at Ballys Las Vegas. If you recall, Carrol B. has a mini-monster hand and we all made money. That was an amazing experience and made me a believer (in what I am not sure, but, I have a hard time thinking that Carrol just hit a lucky trend. His tosses were easy from the far corner of the table and he made them look controlled and symphonic. My goal is to keep at it and someday see Bone Trakker announce that I slightly influences something. At that point, I will be more willing to press up my bets and not look like such a timid gambler.

skasower...aka...

[Dylanfreake]

I am a very low roller. For any session , I only put up about 4% of my Total Gambling Bankroll at risk.

I have no desire to attempt to become a professional craps player.

[Cap-n_Lou]

To analogize it to football (American), most of the time I'm Alex Smith of the Chiefs. Low-roller, conservative, cautious, "game manager." But every once in a while I go all Favre. Usually when I'm chasing losses. Even then, though, I will give my alter ego the hook if he's throwing too many picks. The most I've ever lost in a given session is less than $300. The most I've ever won is less than $2,000. When I retire, assuming my savings and investments will support it, I want to up the ante a little. But if I were a betting man (and I am, of course), I'd say I won't. Old dogs, new tricks ...