Craps Backup Pass Line Bet

• A classic craps hedge consists of utilizing one bet to offset another bet. For example, you place a $5 Pass Line bet and then ask the dealers to give you a one-dollar 'Any Craps' - 2, 3, 12 - in order to offset the possible loss of that Pass Line bet when any of the craps numbers appear.
• This is the most powerful bet in all of craps. In order to play the free odds bet, you must have wagered on the pass line bet or the come bet. If the shooter has not rolled a craps number (2, 3, or 12) or a 7 or 11, then there must be a point number established (4, 5, 6, 8, 9, or 10).

• The Math Of Adding To A Pass Line Bet After The Come Out
• Increasing Your Odds Bet
• How Fast To Double Your Money: Continuous Come (full Odds) Versus Only Pass Line (full Odds)

I’m writing a series of blog posts about casino games and the good and bad strategies for playing those games.

Betting the Pass Line. Do's and Don'ts of the Pass line Bet When betting right (Do, DEWEY or With the Shooter), the player makes a bet before the first roll of the dice (Coming Out) that the shooter will either roll a 7 or 11, or roll any number but a 2, 3, or 12.

Craps is one of my favorite casino games, so I’ve been looking forward to writing this one.

And the beautiful thing about craps is that it’s a game of pure chance. The best strategy is just to choose the bets with the lowest edge for the house and have fun.

But I’ll have some things to say about some of the strategies and systems that other writers promote, too.

They’re mostly bad craps strategies.

Here’s the Only Craps Strategy You Need

When you’re dealing with an entirely random game – like craps – the only strategy that matters is choosing the bets with the lowest house edge and having fun.

I’ll have something to say about shooters and whether they have control over the outcomes later in this post, but for now, let’s just agree that games like craps are purely chance.

In other games that are entirely random, like slot machines, you don’t even really need to decide which bet to place. It’s chosen for you before you sit down.

When playing craps for real money, you have a handful of good bets you can make, but most of the bets on the table are bad. Just skip the bad bets, and you’re all set.

The Bests Bets at the Craps Table

The best bets at the craps table are the pass line bet and the don’t pass bet.

The come and don’t come bets are also great wagers.

I always advise casino gamblers to try to limit their gambling to games where the house edge is lower than 2% — preferably 1.5% or lower.

The house edge for the pass and come bets is the same, 1.41%, which means they qualify.

The house edge for the don’t pass and don’t come bets is even lower, 1.36%, but the 0.05% isn’t worth worrying about. Most people prefer to root for the shooter to succeed.

The other bet to think about at the craps table is the odds bet. This is a bet you can only place after making one of the 4 bets I already mentioned and when the shooter has set a point.

This is one of the only bets in the casino that has no house edge. It’s a break-even bet, but it can be expensive.

It can also drive the effective house edge on the money you have in action down to almost nothing.

Here’s how that works.

How the Odds Bet Changes the House Edge for the Better

If you’re betting on the pass line and the shooter sets a point, you can expect to lose $1.41 for every $100 you bet. That’s on average and in the long run.

If you’re playing at a casino that only allows you to place an odds bet at 1X the size of your pass line bet, you can put another $100 into action.

Your expected loss remains $1.41, though, which effectively cuts the house edge in half, from 1.41% to 0.71%.

If you’re able to bet 2X your original bet on the odds bet, you can lower that even further to 0.36%. (You have $300 in action, but your expected loss is still only $1.41.)

The more you’re able to bet on the odds bet, the lower the house edge for all the money you have in action becomes.

It’s clear why betting on the pass line and taking the most odds that you can is an effective strategy. With the odds bet, you can get the house edge in craps lower than 0.5% at least some of the time at the table, making it an even better game than blackjack.

And what’s more, you don’t have to memorize basic strategy to get the low house edge at craps.

You just need a big enough casino bankroll to make the right bets, and you need enough sense to avoid the bad bets at the table – of which there are many.

Any Strategy that Involves Placing ANY Other Bets at the Craps Table Is a BAD Craps Strategy

There’s a reason gambling experts measure bets according to their house edge. That’s because it’s the single best indicator of how good or bad a bet is.

The house edge is a statistical estimate of how much money you’ll lose as a percentage of your original bet over the long run.

If the house edge is 1.41%, the casino expects to win an average of $1.41 every time you bet $100.

If the house edge is 16.66%, the casino expects to win an average of $16.66 every time you bet $100.

Which bet looks like the better bet for the casino?

And which one looks like the better bet for the gambler?

It shouldn’t be hard to make the distinction.

Even the best of the bad bets on the craps table are inferior to the 1.41% or 1.36% you can get from the pass, don’t pass, come, and don’t come bets.

And trust me on this:

You can have PLENTY of fun sticking with the basic bets at the craps table.

Betting Systems Where You Raise and Lower the Size of Your Bets Are Bad Strategies

The classic example of this kind of betting system is the Martingale System, where you double the size of your bets after each loss. When you do this repeatedly, you eventually win back the money you’ve lost along with a profit of one unit.

The problem with a system like the Martingale is that you’ll eventually run into a big enough losing streak that it will wipe out all those small profits and then some.

Most people underestimate how quickly a bet’s size gets when doubling after every loss.

They also overestimate how likely they are to avoid long losing streaks.

If you double a $5 bet once, that’s $10.

But if you run into a losing streak of 8 bets in a row, you’re looking at having to bet $640 to make up for your losses.

Also, every roll of the dice is an independent event. The odds don’t change based on how many times you’ve won or lost in a row.

You might think the probability of losing that 8^th bet is lower than the likelihood of losing the first one, but the truth is that the dice have no memory. They have the same 6 sides, no matter how many times you’ve lost in a row.

Each bet in craps is an independent event, and any betting system will assume that the odds are changing based on how many times in a row you’ve won or lost.

Money Management Strategies Don’t Hurt Anything, but They Won’t Improve Your Odds of Winning, Either

Money management strategies involve having strict gambling discipline about how much of your bankroll you’re willing to risk before quitting the game. They also require you to stop when you’ve won an arbitrary amount of money.

Money management techniques are often used in conjunction with betting systems.

Here’s an example of a money management strategy in craps:

You decide your bankroll for the session is $250, and you’re playing for $5 per roll of the dice.

Your stop-loss limit is $100, so, if your bankroll drops to $150, you must quit the craps session and go do something else.

Your win goal is $250, so once your bankroll gets up to $500, you must quit the game and go do something else.

This kind of strategy might increase your chances of walking away from the game a winner.

But that’s only because a lot of gamblers will just keep playing until they’ve lost their entire stake. They just don’t generally have a lot of sense about that sort of thing.

The Jury’s Out on Dice Setting or Dice Control

I’ve seen multiple reputable gambling writers express interest and some belief that some craps shooters can influence the probability of specific outcomes. I’m skeptical – in the extreme – but I’ll give it an appropriate amount of credence.

The idea is that you hold the dice a specific way – “setting” the dice – then throw with a minimum amount of force – just enough to hit the back wall and eliminate most of the rolling action.

A controlled shooting expert doesn’t have to be perfect. Instead, they’re trying to be like someone who’s playing darts. They improve the probability enough to change the negative expectation on a bet to a positive expectation.

You can buy books and videos explaining how to get an edge at craps this way, but I can’t imagine the amount of practice and record-keeping required to have any confidence in your ability to change the odds.

Imagine if you spent 1000 hours trying to learn how to control the dice and coming up short. Maybe you just don’t have the knack for it.

That doesn’t sound like a good deal to me.

I’d rather learn to count cards in blackjack.

Conclusion

Those are the best and the worst of the strategies I know of for playing craps in the casino. I know plenty of people who would disagree with every recommendation I’ve made, but the math behind the game doesn’t lie.

The best strategy is to stick with the bets with the lowest house edge and have as much fun as you can.

pass line win probability = 244/495
(244/495)^3 = 0.119771609 exactly 3
you want 3 or more
formula for the sum of a geometric series is a/1-r
where a is the first term
r = the ratio
a = (244/495)^3
r = 244/495
so (244/495)^3 / (1-(244/495) = 0.236202973
But now you want this to end. Multiply the above result by 1-(244/495)
0.119771609
((244/495)^3 / (1-(244/495)) * (1-(244/495))
added my table

at least in a row then lose	Prob	1 in
2	0.242979288	4.1
3	0.119771609	8.3
4	0.059038934	16.9
5	0.02910202	34.4
6	0.014345238	69.7
7	0.007071188	141.4
8	0.003485596	286.9
9	0.001718152	582.0
10	0.000846928	1,180.7
11	0.000417475	2,395.4
12	0.000205786	4,859.4
13	0.000101438	9,858.3
14	5.00017E-05	19,999.3
15	2.46473E-05	40,572.4
16	1.21494E-05	82,308.7
17	5.98878E-06	166,978.8
18	2.95205E-06	338,748.0
19	1.45515E-06	687,214.1
20	7.17286E-07	1,394,143.4

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. To get the answer for exactly n in a row, you need to multiply the 'at least' by the probability of losing on the n+1 try.
For the pass line problem, I think the 0.119771609 figure is for 3 or more, not for exactly 3.
Isn't that correct, or what did I miss?

For the pass line problem, I think the 0.119771609 figure is for 3 or more, not for exactly 3.
Isn't that correct, or what did I miss?

rudeboyoi and Sally both arrived at the same value.
Sally did it differently by starting with 3 pass line wins in a row in 3 trials.
The OP asked a unique question.
Most ask the probability of winning 3 pass line bets in a row. And for 3 trials it is simply p^3
OP wanted to add the probability of 3 *or more* and *followed by a loss*.
Sally's math shows 3 in a row in 3 trials and the OPs Q arrives at the same value. It should.
IF the OP had asked what is the probability of winning 3 pass line bets in a row then losing, we would have p^3 * q or 0.06073
Let us see if OP is happy and replies.
added
average number of trials to see a run of 3 or more pass line wins: 16.466
4 or more: 33.404
5 or more: 67.765
6 or more: 137.475
Multiple streaks of pass line winners.
15 trials about 30 minutes of play at 100 rolls per hour
30 trials about 1 hour of play
Example: 30 pass line trials
about a 90% chance of at least 3 pass line wins in a row at least one time
about a 58% chance of at least 3 pass line wins in a row at least two times
about a 23% chance of at least 3 pass line wins in a row at least three times
here is the losing streaks (miss) for the pass line per N trials

added
average number of trials to see a run of 3 or more pass line wins: 16.466
4 or more: 33.404
5 or more: 67.765
6 or more: 137.475

The Math Of Adding To A Pass Line Bet After The Come Out

You guys are great. Thanks for the detailed responses.
How did you calculate the average number of trials to see a run of 3, 4, 5, 6 or more pass line wins?
How do you define a trial? Would each shooter be a new trial? Or does a new trial begin after any losing pass line bet, in which case a single shooter could have multiple trials that end and start over with a losing pass line bet from throwing 2, 3, or 12 on a come out roll?
If a bettor were to power press the pass line bet with a $100 wager:

at least in a row then lose	Prob	1 in	Bet	Win	Lose
1	0.492929293	2.0	$100.00	$100.00	$100.00
2	0.242979288	4.1	$200.00	$300.00	$100.00
3	0.119771609	8.3	$400.00	$700.00	$100.00
4	0.059038934	16.9	$800.00	$1,500.00	$100.00
5	0.02910202	34.4	$1,600.00	$3,100.00	$100.00
6	0.014345238	69.7	$3,200.00	$6,300.00	$100.00

Does this mean that on average you would be betting about $1600 to win $700 on a press of 3 pass line wins for a net loss of $900?
$3,300 to win $1,500 on 4 pass line wins losing $1,800?
$6,700 to win $3,100 on 5 pass line wins losing $3,600?
$13,700 to win $6,300 on 6 pass line wins losing $7,400?

Increasing Your Odds Bet

How Fast To Double Your Money: Continuous Come (full Odds) Versus Only Pass Line (full Odds)

What's the best way to interpret this expected value for power pressing a pass line bet?