How to Apply the Best Mathematical Craps Strategy

Today’s article is about the best mathematical craps strategy – and why I don’t think it’s the best way to play. 

The general principle is that folks who don’t play much like to think that the best mathematical craps strategy must be the best way to play, but in fact, I believe it’s not.

Once you have read the article, you will know what the numbers say you should do, and what I think is a better way to go.

Let’s get started.

What is the best mathematical craps strategy?

Most people think that the numbers indicate that playing the Don’t Pass and then laying the maximum the casino will allow is the best way to play. (And just to be clear, adding the odds on the Don’t Pass after a point is established is called laying the odds).

While it’s absolutely true that the Don’t Pass and laying the maximum odds is perhaps the best mathematical way to play, there may be a better way to go.

Because the Don’t Pass/Pass Line strategy assumes you’re going to play one or the other.

And the reason you may want to play the Don’t Pass or the Pass Line is because you want to shoot the dice.

But what if you don’t care about shooting the dice?

Are the Don’t Pass and the Pass Line still the best bets?

Are there other bets that are a better mathematical option than the Pass Line or the Don’t Pass? 

Wait, what?

If the table has other players, the only way to shoot the dice is if you have a Pass Line or a Don’t Pass bet.  

If you’re the only player, they may let you shoot with only a Field bet, but with one or more other players, you must have a Pass Line or Don’t Pass bet.

But what if you don’t care about shooting the dice?

What if you only shoot the dice when it’s your turn, and bet the Don’t Pass or Pass Line when it is, but don’t bet that way when anyone else shoots?    

What if you pass the dice when they come to you, and don’t shoot at all?

That’s a legitimate strategy, too, isn’t it?

Is there a better way to play, mathematically speaking, than betting the Don’t Pass with a maximum lay bet, or the Pass Line with maximum odds?

Things that make you go hmmmm . . .

Let’s take a closer look . . . (and btw – House Advantage and House Edge are used interchangeably in this article, and in real life).

The Pass Line and the Don’t Pass

On the Pass Line with no odds, the House Advantage is 1.41%.

And the casino will win $1.41 out of every $100 bet on the Pass Line.

On a Pass Line bet with single odds taken, it’s 0.7%   Yes, that’s less than 1% if you add the same amount as odds as you have bet on the Pass Line. 

And the casino expects to win 70 cents out of every $100 bet.

And a Pass Line bet with double odds taken is 0.47%.  Yes, that’s 47 cents per $100.

And a Pass Line bet with 5x odds?  0.235% - 23.5 cents per $100 bet.

The more odds you take, the lower the combined House Edge goes.

So what does that do to the House Edge?  By adding the odds bet (in some cases up to 100x odds), how does that change the HE on the Pass Line bet?

Does it even change the HA on the Pass Line bet?

And the answer is no, it doesn’t.

Oh, the combined House Edge changes, but the opportunity to roll the point still has the same House Edge.

How much does the combined House Edge change?

Well, it depends. It’s really low at 10x odds, and ridiculously close to zero at 100x odds.

Take a look:

Pass Line bet with 10x odds?

The combined House Edge is 0.128% - that's 12.8 cents per $100 bet.

And at 100x odds, the combined House Edge is 0.014% - 1.4 cents per $100 bet.

As you can see, the more odds the casino allows you to take, the lower the combined House Edge becomes.   

And I have to tell you, the first time (and the only time) I saw anyone taking 100x odds was just so . . . weird.

It was at the opening of the Stratosphere in Las Vegas (and full disclosure, I was part of the opening management team that day).

The shooter had a $5 Pass Line bet, got a point of 4, and then put up a $500 odds bet.

It may be the most disconcerting thing I’ve ever seen on a crap game – and in 35+ years, I’ve seen a lot.

The Casino House Advantage

So how does the casino make any money if their HA is so low?

And why don’t the players lower their Pass Line bet and max out their odds bet?

If you believe the mathematicians, it’s a simple math problem and easy to decide to play that way.

Richard Scheutz at the Stratosphere with a strong background in economics, and the Texas cowboy Benny Binion, who owned the Horseshoe downtown, both came from different ends of the ‘formal mathematical education’ background, but they both knew how the odds worked.

And they knew all about ‘the pendulum’.

Because a typical player making a $5 Pass Line bet isn’t going to bet $500 odds. It’s just too much of his bankroll to bet on one outcome.

And a guy who’s going to bet $500 odds isn’t going to make a $5 Pass Line bet.

From the player’s point of view on the Pass Line, the player has a 22.22% chance of rolling a winner on the Come-Out roll versus an 11.11% chance of rolling a loser.

So our $500 bettor wants more of his money on the Pass Line on the Come Out roll, and isn’t going to mess around with a $5 bet.

The Pendulum

Here’s one of the casino secrets that isn’t well-known to the players but all the guys who work in casinos see it every day.

The player buys in for $100 (pick a number).  Then he’s winning $50, then he’s losing $20, then he’s winning $40, then he’s losing $80, then he’s winning $150, then he’s losing $100.

And the casino has won his $100 bankroll, so he leaves.

And because the casino has a much bigger bankroll than virtually every player, and the player isn’t going to leave if he’s only winning $150 (it’s not enough, right?), the casino ends up winning his $100.

And it happens over and over and over. 

Every day.

Don’t Pass vs Pass Line 

Let’s look at the House Advantage on the Don’t Pass.

In theory, it’s the best bet on a crap game.

It’s slightly less than the HA on the Pass Line at 1.36%.

If the casino allows you to take 5x odds, here’s the combined House Advantage calculation for the Pass Line and the Don’t Pass:

• Pass Line bet with 5x odds: combined HA = ((1 * 0.0141) + (5 * 0)) / 6 = 0.235%
• Don’t Pass with 5x lay: combined HA = ((1 * 0.0136) + (5 * 0)) / 6 = 0.226%

As you can see, the Don’t Pass is a marginally better bet for the player than the Pass Line which holds true for any amount of odds the casino allows.  The more odds the casino let’s you take or lay, the lower the combined House Advantage becomes.

What those numbers tell you is that the casino will win 23.5 cents out of every $100 bet on the Pass Line, and 22.6 cents out of every $100 bet on the Don’t Pass.

So when we say ‘marginally better’, we’re not kidding. 

At  0.9 of one cent per $100 bet, it’s marginally better. Yes, that’s less than one penny!

And there’s the rub.

Many players don’t bet the maximum odds because it eats up too much of their bankroll.

They have a solid Pass or Don’t Pass bet, but 5x odds would be just too much, so they don’t bet the full 5 times odds - instead, they bet single or double odds.

And once that decision has been made, there are better options than the Pass Line with odds, and the Don’t Pass with odds.

What are the better options?

Let’s take a look . . .

The table below lists the combined HA for both Pass Line and the Don’t Pass, plus the other options that may be a better mathematical bet.

Please note that the odds and lay bets on the Pass Line and Don’t Pass have 0.00% House Advantage, and if the Field pays triple on 2 and 12 it also has a House Advantage of 0.00%.

This Field percentage is not included in the table because you’re never going to see it.

Bets listed above with a star * - I”ve never seen them bet or offered in any casino.

We have many articles about all the casino table games, slots and many other casino-related subjects in the Chipy Academy. They are all written by experts and are all free.

The Don’t Pass With Odds Strategy

Here’s how you might implement this strategy:

Make a $20 bet on the Don’t Pass.

•  If the shooter rolls a 2 or 3, you win $20. 
•  If he rolls a 7 or an 11, you lose your $20.
•  If he rolls a 12, it’s a push.

But let’s say the shooter rolls a 4.

The most common odds system that the casinos worldwide have adopted is the 3x, 4x, and 5x system.

This means that the player is allowed to bet 3x odds on the 4 and 10, 4x odds on the 5 and 9, and 5x odds on the 6 and 8.

To make the maximum lay bet on the Don’t side, you must bet enough to win 3x the flat bet on the 4 and 10, to win 4x the flat bet on the 5 and 9, and to win 5x the flat bet on the 6 and 8.

And that gets you to having to lay 6x the flat bet on the Don’t Pass if the player wants to lay the maximum odds on the Don’t Pass.

Let’s get back to playing the Don’t Pass.

The shooter has a point of 4, so now you would lay the odds – and if you’re allowed to bet 3x odds that means you can bet enough to win 3 times your $20 Don’t Pass bet. 

The odds of a 4 coming up before a 7 are 2 to 1 against you, so you can bet enough against the 4 to win $60 – and as a Don’t Pass bettor, you are betting that the 7 will show before the 4.

Which means you can lay $120 to win $60 against the 4.

And here’s an example of what the 3x, 4x, and 5x looks like on the Pass Line:

When the casino offers 3x, 4x, and 5x odds, the player gets paid 7x the flat bet as a combined maximum payout on any bet with the maximum odds on the Pass Line.

And as an aside, I don’t know who he was, but I would like to congratulate the guy who came up with the 3x, 4x, and 5x odds system.  It’s a work of art.

Expert’s Advice

So how do you think you should bet, given what we’ve covered so far?

Well, here are a couple of things for you to think about.

The first is, are you going to bet the full amount you can, to take advantage of the maximum odds the casino will let you bet?

Because with no odds, single odds or double odds, you would be better off not playing the Don’t Pass (or the Pass Line) at all, and placing the 6 and 8, and if the casino takes their vigorish after the number hits, you should also buy or lay the 4 and 10.

The House Advantage on those bets is 0.46% for placing the 6 and 8, and 0.42% for the buy or lay bets on the 4 and 10, which is lower than the combined House Advantage for a Pass Line bet with no odds (1.41%), single odds (0.71%), or double odds (0.47%). 

The House Advantage on the Don’t Pass bet with no odds (1.36%), single odds (0.68%) and double odds (0.45%), are also higher than those bets so it makes more mathematical sense to place the 6 and 8, and buy or lay the 4 and 10, because they are still a better mathematical bet than simply betting the Pass Line or the Don’t Pass with double odds or less.

Otherwise, placing the 6 and 8, and if the casino takes it’s vigorish when the bet wins, buying or laying the 4 and 10 is the best way to play.

And then there’s this:

As you saw a little earlier in this article, at 5x odds, the difference between the Don’t Pass and the Pass Line is 0.9 of a penny.  Less than a 1 cent difference per $100 bet.

So my recommendation is to play where the casino has the 3x, 4x, and 5x odds structure in place, and bet the Pass Line, and limit your Pass Line bet to allow you to bet the maximum odds they will allow.

Is it the best mathematical way to play?  No, by as much as 9/10s of a penny. 

And I believe the added entertainment value of being part of the winning crowd is worth way more than 9/10ths of a penny.

And that’s why it makes more sense to play the Pass Line, so you can be part of the winning crowd when the shooter gets hot and everyone is winning.

Except the morose lost souls betting their lonely Don’t Pass bets.

Conclusion

So there you have it – the best mathematical craps strategy isn’t how I play, and for me, it makes a lot more sense (and it’s a lot more fun) to play the Pass Line with the maximum odds.

And as always, may Lady Luck accompany you on you next visit to the casino.