Reader Darrell asks in comment:

Pass player with max odds and 2 come bets vs don’t pass player with max odds and 2 come bets….

Even though they should be close to even with similar outcomes, it seems i would need to have a larger initial bankroll if I am a don’t player….is that correct RG?

Feels like the don’t player has to put more.money up front …..If the table conditions are choppy, example….point is made, 2nd point not made, 3rd point made, etc….Feels like the pass player can weather out the storm better…

for some resson, I can’t bet don’t pass with max.odds…

Convince me otherwise….

This is a common question in gambling circles. I’ll attempt to answer the question with a mathematically justifiable answer, rather a common sense guess.

If you want to skip over my explanation and go the final answer, scroll down to TL;DR.

**METHOD USED**

To answer the question, I used a risk of ruin calculation. Simply stated, risk of ruin is the probability, expressed in percentage, that the player will win a certain amount before he loses everything (an event called ‘ruination’).

Before you say that most craps players leave the table before ruination, that fact isn’t relevant. Whether a player leaves at 100% 50%, or 25% loss, the calculation is the same; it’s just prorated for the level at which the player leaves the table.

I am looking for whether the Don’t Pass or Don’t Come (DP/DC) has a higher or lower risk of ruin than the Pass/Come (PL/C).

For example, if the risk of ruin numbers for DP/DC and PL/C are similar at 100% loss (meaning the players lose their entire bankroll), then they should be the similar if players decide to leave at 50% loss.

*A Qualifier to the Question*

When I say ‘similar’, I mean that the risk of ruin numbers should be in close proximity given the fact that the DP/DC has a slightly lower house edge than the PL/C.

The final numbers will not be exactly the same because the DP/DC has a house edge of 1.36%, compared to the PL/C house edge of 1.41%. The relevant question is whether one side of the bet requires a *noticeably *larger bankroll to play, having discounted the slightly lower house edge of the DP/DC.

**THE PLAYERS, GAME, AND CONDITIONS**

*The Players*

Let’s say we have two players: Light and Dark. You can probably guess how they will bet. If you can’t, stop reading and skip to tl;dr or read my article on dark side betting.

**The Bankroll**

Both players have $10,000 as their bankroll and play at max odds, betting minimum $10 line bet.

*The Goal*

For purposes of risk of ruin, we need to establish a win goal. Both players will have a goal of winning 20 units.

*The Game*

The max odds is 10x. We are going to use a higher house edge than 2x so that if there is a larger bankroll requirement, the requirement is magnified and easier to notice.

Using 10x, on the PL, we will have an average house edge of .184% on a bets resolved basis for the flat + max odds.

On the DP/DC, we will have an average house edge of .124%% on a bets resolved basis for the flat + max odds.

Remember that the naked DP/DC bet (meaning without odds) is slightly a better bet than the naked PL/C bet, which is why the above numbers are different. Despite their difference, they’re close enough for now.

**The Bets**

In order to keep the math simple, let’s just say that Dark player and Light player only make one bet per point.

I know what you’re thinking, ‘no one makes only one pass line bet’. That’s true, but we are looking for a comparison baseline. The same figures will apply if the players make three PL +C bets or three dark side bets. The proportions just change on each side, but the numbers relative to the light and dark side remain similarly juxtaposed.

These are the bets, below. I will list out the odds bets because there are sometimes questions about what is the actual max odds on the darkside.

Light Player

- $10 Pass
- Max odds point of 4 or 10
- $100

- Max odds on point of 5 or 9
- $100

- Max odds on point of 6 or 8
- $100

Dark Player

- $10 Don’t Pass
- Max odds point of 4 or 10
- $200

- Max odds on point of 5 or 9
- $150

- Max odds on point of 6 or 8
- $120

*The Definition of ‘Max Odds’ on the Dark Side*

On the PL/C, if ‘max odds’ is 10x, that’s understood to be 10 times the PL bet. So if the player is betting $10, then his max odds is $100. Simple enough to understand.

The confusion comes from the dark side. For example, if max odds is 10x, what is ‘max odds’ on the Don’t Pass bet? The answer depends on the point, but ‘max odds’ is determined by what the DP/DC player can *win* on the odds.

So if the max odds is 10x, and the dark side player bets $10 on the DP/DC, then he is allowed to lay odds of

- $200 on the point of 4 and 10
- $150 on the point of 5 and 9
- $120 on the point of 6 and 8

Each win will result in a $100 payment to the dark side player.

If you notice, it’s like the player and the casino have switched rolls. It can be seen as the casino is betting…

- $100 on the point of 4 and 10
- if the casino wins, the player will pay the casino $200

- $100 on the point of 5 and 9
- if the casino wins, the player will pay the casino $150

- $100 on the point of 6 and 8
- if the casino wins, the player will pay the casino $120

I bring this up because if the dark side player only bets $100 on the DP odds when the point is 4 or 10 (for example), then he is not betting 10x, rather he is only betting 5x, and his expected loss as a proportion of his total action would be higher.

On a side note for craps novices, the house retains the advantage because on a come out roll of 12, the house pushes (ties) and does not pay the darkside player. Just think of it this way: if you – a single player – were to bet on both the Pass line and the Don’t Pass line, if a 12 rolls on the come out, the house will take your Pass Line bet, but not pay your Don’t Pass bet. That’s how the casino makes money.

Anyways, back to the original topic…

**THE ANSWER **

Let’s get to the answer…

**No Odds, Just Flat Betting**

Just out of curiosity, let’s see if there is a difference without odds.

If we were to just calculate the risk of ruin (thought a risk of ruin calculator) based merely upon the PL/C and DC/DP without odds, it would be an easy calculation.

Let’s say both players have 100 units, meaning they’re flat betting $100. In that case…

- The light side player has a risk of ruin of 44.62%
- The dark side player has a lower risk of ruin at 43.66%.

Notice that both numbers are very similar. The difference is attributed to the fact that the dark side has a slightly lower house edge.

If you play with no odds on either side, both dark and light side have roughly the same bankroll requirement.

**With Odds**

Very few line bettors play without odds, so let’s factor in odds to our equation.

*Pass Line*

Here are all the possible outcomes on the pass line, with odds:

- Player wins on come out
- 22.22%

- Player loses on come out roll
- 11.11%

- Player wins on point
- 27.07%

- Player loses on point
- 39.60%

This means that approximately 66.66% of rolls allow the player to bet the odds, thus exposing more money on the odds.

*Don’t Pass*

Here are all the possible outcomes on the DP line, laying odds:

- Player wins on come out
- 8.33%

- Player loses on come out roll
- 22.22%

- Player wins on point
- 39.60%

- Player loses on point
- 27.07%

- Player pushes
- 2.7%

The dark side player will have the option to lay odds 66.66% of the time.

This means that both light and dark side will be risking additional money on the odds at the same rate 66.66% rate.

We will need the above distribution to figure out the following…

**The Average Unit Bet with Odds**

Using the above figures and conditions, let’s stipulate that each player’s average bet will be their ‘unit’. By average bet, I mean that sometimes, the flat bet will win or lose and not require an odds bets, while sometimes, the players will require odds. All those bets can then be averaged out into an average bet using the percentage the outcomes I listed above.

Under that stipulation, our Lightside player will have an average per bet of $76.67 at 10x max odds.

Our Darkside player will have an average per bet of $110.00 at 10x max odds.

In other words, to calculate the risk of ruin for our players, the definition of a ‘unit’ for Light player is $76.67, while a ‘unit’ for Dark player is $110.00.

If we plug in those unit figures to our risk of ruin calculator, and keep the total unit count at 100, then the risk of ruin remains identical for both players (of course it would), with the only difference resulting from the lower house edge on the DP/DC.

But notice the difference…

100 units for the light side player is comprised of a total bankroll of $7,667.

100 units for the darkside players is comprise of a total bankroll of 11,000.

Simply stated, if both Light and Dark players want to play with the same probability of ruin, win goal, and length of time for bankroll, then Dark player needs to bring along 43% more than the light side player on a 10x game.

**TL;DR**

A dark side player needs approximately 43% more bankroll for a 10x game than a light side player.

If the dark side player wishes to maintain the same risk of ruin, win goal probability, and length of time play as the light side player, he must maintain the same unit count as the light side player. The only way for the dark side player to maintain the same unit count as the light side player is to increase his bankroll.

At the same 10x game, the light side player only needs a unit to consist of $76.67, whereas the dark side player’s unit will consist of $110.00.

This larger bankroll requirement is another good reason why the Pass Line is preferable if the player is on a small bankroll. If you’ve ever seen darkside players get wiped out quickly when the table is rolling hot, that’s not your imagination or selective memory. That’s because most darkside players are not aware of the larger bankroll requirement, so they tend to go broke faster and are hit harder than when things go wrong at the table.

The good news for the Darksider player is that if he uses less than 10x odds, his unit cost will be lower, so the bankroll gap between Lightside and Darkside players will narrow. The downside to this good news is that the combined darkside house edge will be higher if the free odds multiple is lower.

There are other metrics that can be used when answering the question posed in this article. You can use win percentage probability or calculate how long your bankroll will last, for example. Regardless of what metric is used, the answer should remain the same: the darkside player needs a bankroll that is 43% larger than a light side player if he is to maintain the same probability conditions at 10x.

Thanks for reading and let me know in the comments if you have any questions or thoughts.

## James says:

Thanks for the detailed description I knew It would be a bigger bank roll for the DS but i didn’t realize it would be quite that wide a margin. I have never tried running the numbers. It’s nice of you to post all your info

I don’t play the DS and thats one of the reasons if it’s running bad i just lay low at the table or take a break.

I am curious of what percentage of time you play the DS.

## Henry S says:

Just a thought: do not put odds on you’re dark side bet. The DC bet is now ahead after getting through the come out roll and adding odds only brings down the Expected Return by providing you true odds on the Odds bet. Thus the combined wager has a lower return than the DC bet alone.

## RoadGambler says:

Henry,

The strategy you mention is a commonly proposed strategy, however, it has a major weakness: the come out roll.

While it is true that the DP/DC bet has an advantage ofter the come out roll, there’s still the issue of the unavoidable come out roll.

To understand why avoiding darkside odds, in favor of a naked DP/DC without odds, is a poor play, think of it this way…

Let’s say you want to bet $5 on the DP. Don’t think of it as a red chip $5 bet. Instead imagine the bet as 500 pennies.

Over the long run, every time that you put down 500 pennies, the theoretical stack becomes 493 pennies, due to the house edge.

Whether you win or lose, whether your DP bet makes it past the come out roll or not, the moment you put down the stack of 500 pennies, it automatically becomes 493 pennies due to the house edge. Remember that the house edge factors in both wins and losses and ALL POSSIBLE EVENTS.

So when the DP bet survives the come out roll, and ends up with a point of 10 (for example) while you may see a 2-1 edge in your favor, in reality, what is sitting in the DP line bet is…you guessed it…493 pennies in the theoretical long run.

Remember, your bet that’s in the DP on the pretty point of 10, at that moment, suffered quite a few hair cuts to get to the point of 10. Just imagine that it had to survive crossing a mine field to get to that moment, and it’s not whole. Its’ brothers had to step on a few mines on the way, and its’ family (your bankroll) is not whole.

You can’t forget the suffering that the DP/DC bet went through to get to that glorious moment where it now has a 2-1 edge. That’s why it’s really 493 pennies.

However, if you put down odds…it’s always 500 pennies theoretically because the house had no edge. The odds THEMSELVES do not suffer a hair cut at any point.

The odds will suffer a theoretical loss, but that’s on the combined bet with the DP before the DP bet is made. That’s why the combined house edge on the DP+odds drops from 1.36% to a mind bogglingly low .125% at 10x (citation Wizard of Odds).

I hope that explanation helps.

## Duffer says:

I’m not a statistics wizard, but I did write a spreadsheet program to compare do side with don’t side with the following settings:

1. Do side: Every roll receives a pass line/come bet plus table odds (take your pick, I used 5X). No place bets, odds only.

2. Don’t side: Every roll receives a don’t pass/don’t come bet plus a lay (equivalent to the odds taken in 1 – in other words $5 odds taken on the do 6 is equivalent to $6 odds laid on the don’t 6). No buying of lays, odds only.

Although obviously the average odds laid is greater than the average odds taken – and hence the overall combined average bet on the don’t side is larger than on the do side – I got the following results on a simulation over 10,000 rolls.

The bankroll fluctuation is precisely mirror-imaged. A bad sequence on the do side is the mirror image of a “good” sequence for a don’t better.

If you consider the “burn rate” being the overall downward trend of a given bankroll, they are essentially identical – 1.41% versus 1.36%.

There did not appear to be a greater downward risk on the don’t side than there is on the do side – according to the simulation. Perfect mirror images. This doesn’t appear to show that a larger bankroll is required. Assuming that a unit on the do side is mirrored by an unit on the don’t – which of course is larger.

It seems counter-intuitive to think that playing the don’ts does not require a larger bankroll* than the dos, but the simulation showed otherwise – at least based on the bets I described above and on long-term results.

So if you have a large enough bankroll for a do side session, it should be just as successful (with regard to not bottoming out, not with regard to winning money) if you choose to go dark side with equivalent don’t odds. Not sure about mixing things up though. I think if you mix them up, the fluctuation actually goes down. In other words you get a pretty tight pattern around the burn rate (a very boring and kind of useless way to play, though).

For what it’s worth, unless I’m misunderstanding something.

*Except for the rare rally of the century, which didn’t show up in my simulation very often. So the moral of the story is the well-worn maxim “Why would anyone play the don’ts?” We all want to be part of that rally of the century. Playing the don’ts takes this opportunity away. Regardless of how rare it may be, why rule it out?

## RoadGambler says:

Duffer,

One of the reasons that I show my logic and work out my answers is so that readers can double check and critique my work.

Good job on your very thoughtful analysis.

I agree that there is a similar, almost mirror like trend for both darkside and light side, with an allowance for the slight difference in edge.

If I may suggest, run the simulation over 1,000,000,000 hands to eliminate the luck factor. Then look at 100 of the most extreme data points.

I think that if you look at the extreme data points for both darkside versus lightside, you may find that the actual dollar figures for the darkside is larger than for lightside, thus suggesting that the darkside requires a larger bankroll.

If you have your simulation, I would like to publish it here, with credit to you. It would be interesting to our readers.

## Duffer says:

RG,

Thanks for the compliment. I agree with your extreme data point comment, but that is an outlier. Reason to have a higher bankroll? Sure. But 95% of the time not actually necessary. I’ll see if I can get a screenshot of the simulation sometime you can post.

A billion rolls? No can do. I only have my garden-variety home computer. Don’t have the computing power.

Aside from that, mathematics requires that there can be no long-term net deviation from the burn rate, be it 1.41% or 1.36%. Which is to say, if you look at the bankroll downtrend, it will fluctuate equally (but not synchronously) about the straight-line house-edge downtrend. The net positive bankroll total above this line – only temporary since the bankroll must come back to it – must (in the billion rolls you mention) exactly equal the net negative bankroll total below the line. In fact, a don’t better spends slightly less money per hour than a do better – his burn line is not as steep downward as a do better.

I would certainly see a lot of those rare rallies in a billion rolls. If a person plays only the don’ts obviously his bankroll is going to plummet straight down in those cases. Nevertheless, the bankroll will – eventually – recover back to the burn line. It must. Even the craps gods know this.

Over those same billion rolls, the net amount above the line must be the same as the net amount below the line. Which is to say that although a spike is not as likely to occur on the upside – i.e. the don’t better’s upside -, the don’t better will have more don’t winners than right-side betters will have do winners. There will be more time spent on the upside, but there will be a higher likelihood of spikes on the downside.

Thus the ultimate point. It is much more fun to experience an upward spike in our bankroll because of an amazing run of luck. And since a don’t better will inevitably experience the same spike – but in the wrong direction -, why do it at all?

And ultimately yes, just in case that rally comes – have a bigger bankroll if you play the don’ts. Because let’s face it: it could come right now. Right out of the gate! But 95% of the time it isn’t coming. Not the one that empties your bankroll right now. Because before a downward spike comes – small or large – the don’t better will most likely have already won enough don’t wins to weather the inevitable storm. And get back to Steve Wynn’s favorite place.

The downward burn line.

Duff

## RoadGambler says:

I need to buy a simulator. I’ve chatted with a few guys who have such a simulator.

I enjoyed your comment and the read. I agree with much of what you wrote.

The only part I disagree with is your treatment of the extreme outliers. While they are extreme and thus rare, the extreme outliers are indicative of the rest of the data points and how the light side and dayside data points correlate to each other.

I’ll look into a simulator as soon as things slow down a bit around here. I’m very curious now.

## Duffer says:

Something else to consider or just a way to look at it overall.

If it weren’t for the fact that the house has a 2 to 1 edge on don’t pass / don’t come bets when it comes to sevens and elevens versus twos and threes (12 is a push), don’t odds would rack up the winnings for us.

Do odds would rack up even larger losses if it weren’t for getting paid on 7/11, which reduce our losses back down to the 1.41% burn line. The don’t losers on the come-out take our winnings on odds away and bring our overall loss rate back to the 1.36% burn line.

The reason is that the do/don’t odds are so, so close together that it is the come out that makes all the difference to the house. And of course place bets, which are sure winners either way, so we can pick them up any time we want.

Hence the reason why we can’t pick up the pass line bet (but we can pick up the odds), and we can feel free any time to pick up the don’t pass bet. House very happy about that (dumb) choice.

So if we compare don’t odds to do odds – minus the effect of the come-outs -, don’t odds win hands down.

Duff

## Duffer says:

I think I need to correct something.

The don’t odds don’t net winning results. They simply break even I believe. But the do odds definitely lose for us. The 7/11 reduces this loss.

The don’t side come-out gives the house its profit on that side. If don’t odds net winning results, we could always make money by maxing our odds enough to overwhelm the come-outs.

So sorry, think I’m wrong on that last post. Still – don’t odds play better than do odds.

Duff

## Duffer says:

Come to think of it, both odds break even.

House makes its money on come-outs either way.

What was I thinking. Never mind.

## RoadGambler says:

It’s all good, my friend.

Late evening. Still working late hours. Time for a nice cold brew. Cheers!