I’ll be honest, I don’t think that I’ve ever played the dark side in craps. To me, the fun is winning with the whole table, enjoying the celebration as a shooter hits one point, then another, and one more for good measure. And even in losing, there is some camaraderie and bonding—at least we’re all miserable together. It builds character.

However, a user of my craps simulator, Eric Brewer, found some head-scratching results as he compared the win percentages for some dark and light side strategies. As we will see, the chance of walking away from the table is higher than 50% under some dark side strategies. This phenomenon has a few downsides, of course, but this is surprisingly different from most pass-line strategies. In this post, we’ll dive deep into this surprising feature of the don’t pass strategy and discover more unexpected results along the way.

First, some Craps background

Craps experts—feel free to skip this section, I’m going to describe the key strategies used in this post to make sure everyone is on the same page. Both the pass line (which I’ve done a detailed analysis on here) and don’t pass bets are two-stage bets that are foundational to the game of Craps. They are almost exact opposites:

The wins and losses are all for even money. However, odds bets can be added in Phase 2 (up to a table maximum), which pay the true odds for a respective bet:

Because the odds bets pay even money, they don’t carry any house edge. The pass line and don’t pass bets have a reasonably small house edge of 1.41% and 1.36% per bet made. Pass line bets have a 2 to 1 advantage of winning in Phase 1 but are at a disadvantage in Phase 2. Because of this, you can’t take a pass line bet down in Phase 2. Don’t pass bets have an advantage in Phase 2, and so casinos will let you take the bet down at any point.

Let’s test some strategies

First, I wanted to get a sense of the difference between the dark side and light side strategies. Eric had done a similar experiment to this as a baseline, which forms the basis of these results. I changed the odds multipliers since I was curious in lower odds tables and adjusted the number of sessions, testing the following strategies:

Each strategy ran for 200,000 sessions, with 10 shooters used per session (this is a common way that people budget their betting, and it is easier to count shooters than to count rolls). I assume a $10 table1 and use a $100K bankroll to ensure that busting won’t be an issue. If there’s a chance that players can bust, the results will be slightly different.

We can understand the range of possible outcomes by looking at the following density plot, which summarizes the 200,000 sessions:

Even without odds, the two bets still can range within a much as a hundred dollars after 10 shooters. Maxing out odds on a 345x table increases the range to nearly $500 on either side. This emphasizes the need for a large bankroll at tables with increasing minimum bet sizes!

But perhaps more interestingly, the dark side and light side bets seem to almost mirror each other in each panel. The pass line has a slightly higher chance of big wins (since the brown line is higher on the far right side), but the don’t pass has a higher chance of more moderate wins. This pattern flips when considering losses: don’t pass has a higher chance for big losses, while the pass line has a higher chance for small losses.

We can take a deeper look through a more traditional boxplot-style visualization:

We let the main box represent the middle 50% of simulations and let the dark bar show the 50% line. This nicely splits an expected session into four regions, each happening 25% of the time: to the left of the main box, in the box but left of the bar, in the box but right of the bar, and right of the main box. We’re all hoping for the sessions to the right of the main box. To explain what happens in the extremes, I use curly braces {,} to denote the region containing 95% of the simulation data. Only 5% of the time would you expect to see a session outside this range.

The boxplots show an interesting trend more succinctly: The don’t pass strategies have winnings over 50% of the time after you add in odds. The dark brown box, representing don’t pass with 345x odds, has a bar above $0, which means that over 50% of the time, you end up with more money than you started! That was shocking to me when Eric contacted me showing this. He wanted to check that there wasn’t a bug in the simulator, and after some further testing, I’m confident the results are a feature of dark side betting.

Why does this happen? I think that after a point is established, the don’t pass bet is likely to win because it will either have 6:5, 3:2, or 2:1 odds in favor of rolling a 7. Placing odds must give you enough to overcome any pre-point losses, where the don’t pass bet is more likely to lose (it’s 2:1 odds that you roll a 7 or 11 loser than a 2, 3, 12 winner). Thus, over 10 sessions, you will likely win on most of the shooters, resulting in an overall win.

Do these results contradict the mantra where “the house always wins”? Not exactly. The house still has an advantage on the don’t pass bets, as we know (it’s 1.36% per bet made). That advantage is marked with the dashed line in the above plot, which we can see is slightly below $0. Even though a don’t pass with odds bettor wins more than 50% of the time on average, when they lose, it has the potential to be very large. So three $40 wins can get erased by a $150 loss, for example. There’s enough of an edge that the casino will win out in the long run with many players.

Metrics for Strategies on $10 table after 10 shooters
Betting System Average Winnings ($) Low 25% of Winnings ($) Mid 50% of Winnings ($) High 75% of Winnings ($) Chance of winning
Pass line -3.73 -40.00 -10.00 30.00 43.1%
Pass line (2x odds) -3.76 -108.00 -20.00 82.00 44.3%
Pass line (345x odds) -3.68 -180.00 -30.00 140.00 44.8%
Pass line (10x odds) -5.37 -400.00 -70.00 320.00 45.0%
Don’t Pass -3.36 -30.00 0.00 30.00 51.4%
Don’t Pass (2x odds) -3.17 -90.00 12.00 102.00 53.6%
Don’t Pass (345x odds) -4.15 -150.00 20.00 180.00 53.8%
Don’t Pass (10x odds) -4.02 -330.00 60.00 390.00 54.4%

The table above gives some hard metrics with these strategies, like the precise win chance and expected edge. For both the dark side and light side the chance of winning increases as the amount of odds increases. While the average winnings vary numerically, the values, in reality, should be constant for the light and dark sides. (I would need to run more simulations to see this, especially for 10x odds strategies, which are very volatile; there is extra volatility here since the number of rolls differs in each session.)

A deeper look at win percentage

Knowing that the dark side strategies can end up with win percentages over 50%, I wanted to dig deeper and see how far I could push it. I suspected that eventually, if someone stayed at the table long enough, the win percentage would have to drop below 50%. To find out, I set up the following simulation experiment:

The results are summarized fairly well in the following plots:

Win percentage

I want to take a quick look at the below plot because it has several surprising and counterintuitive results in it. Each line provided displays the win percentage of the given strategy as we increase the length of the session.

[Side note: win percentage is somewhat tricky to define because of ties. When you walk away with your initial bankroll, some would consider that a win and some a loss—since I don’t care about ties and want the win percentage + loss percentage to equal 100%, I put half of the ties into each bucket. Counting all ties as wins results in the line given by the upper shaded area, and counting all ties as losses results in the lower shaded area line, in case you want to make those comparisions]

First, look at the green line in the right plot. While the dark side strategy with 345x odds has a decreasing win percentage, it is surprisingly still above 50% even after 75 shooters. A session of 75 shooters is typically between 500 and 700 rolls, or 3-5 hours of play, if not more.

What surprised me more was that for pass line bet with 345x odds, the win percentage first increases as one stays at the table longer. It does flatten out and eventually starts to dip after 100 or so shooters, but it seems extremely counterintuitive that you’re more likely to win if you stay for a few hours than just one.

I’m impressed by how long the strategies using aggressive odds hold on to decent win percentages. We see that not putting down odds results in a win percentage that starts to drop off as the number of shooters increases—by 100 shooters it’s only about 40% for the pass line and 43% for don’t pass.

House edge

With all this interesting information, it’s important not to forget that the win percentage is only one metric. If we look at the average winnings, i.e. house edge, we can see a familiar pattern:

The longer we stay at the table, the more we lose on average, under all strategies2. The lines on the right plot deviate from the expected straight line because the number of simulations is relatively small, but the trend is clear in both. On average, the don’t pass bets have less house edge, which matches the theoretical quantities.

Volatility

Of course, the longer we stay at the table, the wider range of outcomes we would expect to see. Each box below only shows the middle 50% of the data, so half of the time we end out outside this range. It’s clear how much more risk and reward the strategies with odds have, and so taking advantage of the high win percentages will require substantial bankroll. If not properly bankrolled, we’ve seen in past posts that these volatile strategies can end up with high chances of busting, which is never a fun way to leave the table.

Wrap up

I have to admit that the analysis here makes the dark side strategies in craps way more interesting to me. We have seen that a don’t pass bet with odds can often keep win percentages above 50% while having a lower house edge than a comparable pass line bet. This high win percentage is also surprisingly robust to large sessions. These nice theoretical features still face my two main drawbacks to the dark side betting:

The first point will vary from person to person. But the second point is important to elaborate on. Many gamblers play for those elusive, huge wins. Anyone that is pressing bets at the table is hoping for a long roll by a shooter which will make them enough money for a great story. That memory is worth something extra to them, and they don’t mind suffering a few losing sessions to get it.

But maybe taking the opposite approach can also increase your fun. Having more winning sessions can feel great, as you’re less likely to walk away from the table a loser. When you do lose, it could be dramatic with a don’t pass bet, and so you have to figure out if those few large losses are worth the increased number of wins.

I hope in the future to explore these two sides and some of the strategies that can skew things in either direction. Strategies like triple lux (where you power press bets hoping for 3 hits on a given number) seem like they will push even more for big wins, at the expense of very low win chances. On the opposite end, anything with a martingale-type approach (i.e. doubling your bets on a loss to try and recover) will skew the other direction: you can push your win percentage up higher but the losing sessions will be devastating. But having both options is what makes craps such an interesting game in my mind—in no other casino game can you have such an influence on the style of winning and losing that occurs.

If you enjoyed this post, or have some thoughts, feel free to reach out on Twitter @Sean__Kent or via email at spkent@wisc.edu. I have a few ideas for future posts and hope to share those with you all soon.

Disclosures

This blog post is for informational and entertainment purposes only. Any form of gambling carries an inherent risk. Never gamble with money you cannot afford to lose. Anyone who believes they, or someone they know, may have a gambling addiction, please seek help. National Problem Gambling Helpline 1-800-522-4700 Call Text or Chat NCPGambling.org

Endnotes

Other Craps Blog Posts


  1. $10 isn’t a realistic table minimum in all markets these days, but it’s simple to scale up or down. For example, to convert to a $25 table, you can multiply all dollar values by 2.5.↩︎

  2. Also, notice how the two figures have the same scale. Some people claim that adding odds to a pass line bet reduces your house edge. While this is true in terms of percentages, it’s not true in dollar terms. I always like to think of odds as “free variance”, since you get to increase your range of outcomes while not adding any house edge.↩︎

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