Craps friends, it’s been a while. My craps simulator has been collecting dust (figuratively at least) since July 2019, when I looked into some of the best craps strategies on a budget. The global pandemic hasn’t helped with that either, since I’m unlikely to venture into a casino unless I can be elbow-to-elbow with other players. Craps is more fun that way in my book.

I have often thought about testing some of my craps theories. The folks at Best Craps Strategy provided the impetus to look deeper. On their site, they have a page on craps systems: detailed strategies usually involving multiple bets at different times. Since it is tricky to know how the combination of bets will affect wins and losses, you can’t just look up the odds for these systems. My simulator offers an opportunity for a detailed and rigorous analysis.

For this post, I put the 5 systems from bestcrapsstrategy.net through my simulator and spent some time crunching the numbers. What we’ll see is that each strategy has unique features—though some have significant drawbacks and make it hard to walk away as a winner. There are also a few surprises about strategy evaluation depending on how you budget for the table. Let’s dive in.

The 5 Craps Systems

For completeness, I’ll summarize the 5 systems here briefly. I encourage curious readers to check out the systems page (linked above) for full details and some helpful pictures. The systems are based on a $5 table (which I realize are hard to find these days) but can be scaled up appropriately for higher table minimums. I make a few standard assumptions about the table that you can read here.

Iron Cross

With Iron Cross, you will win some money on each dice roll, except for a seven, once a point is established.

  • $5 pass line bet with 2x odds
  • $5 field bet (while the point is ON)
  • $10 place bet on 5
  • $12 place bet on 6 and 8
  • If the point is a 5, 6, or 8, skip the place bet on that number

Hammerlock

I think the idea here is to capitalize on medium-length rolls from a shooter. You hope to sneak in a few place bet wins before ultimately hoping for a 7-out.

  • $5 pass line bet
  • $5 don’t pass bet, with a lay of $30 in odds
  • A phased place bet approach (no matter what the point is):
    • Start with $12 place bet each on 6 and 8
    • If one of these bets wins, shift to $22 inside (place the 5, 6, 8, and 9)
    • If one of the inside bets wins, take all place bets down

Risk 12 (a.k.a. a Strategy for Low Rollers)

Like the name suggests, this system only risks $12 on each shooter but offers some potential to make money on a hot roll.

  • Before a point is established:
    • $5 pass line
    • $5 field bet
  • After a point is established:
    • $6 place bet on 6 and 8, if you have winnings from the pre-point phase:
      • Generally, if the point is 4/9/10, you can take your field winnings plus $2 for the place bets
      • If the point is 5/6/8, you lost in the field, but if you had won on some combinations of earlier rolls (2, 12, 11) you might have enough to add one or both of the place bets.

I omitted the suggestion of risking the extra $2 on some prop bets (i.e. hard 6, hard 8) when you don’t have enough to place them.

Knockout

This one is pretty simple, as described it’s basically a “doey-don’t” before the point and max odds behind the pass line

  • $5 pass line
  • $5 don’t pass
  • 3-4-5x odds behind the pass line bet

Dice Doctor (a.k.a. “The Best” Craps System)

Want to try your luck on the field? That’s essentially the idea for Dice Doctor’s system:

  • $10 field bet, with a bet progression if you win.

The progression is $10 ⇨ $20 ⇨ $15 ⇨ $30 ⇨ $25 ⇨ $50 ⇨ $35 ⇨ $70 ⇨ $50 ⇨ $100 ⇨ $75 ⇨ $150 …

You are doubling on every other win, and moving slowly higher otherwise. After a field loss (which happens 55% of the time), you return to $10.

Let’s simulate

With the systems rigorously described, I was able to pass them through my python simulator to mimic the results of 200,000 sessions at the craps table. It’s not easy to come up with a perfect comparison, so I decided on letting each session finish after 20 shooters had gone at the table. This corresponds to between 133 and 211 rolls 80% of the time but ranged from 68 to 369 rolls across the 200,000 sessions. The average shooter had about 8.5 rolls.

Each session’s craps table has 1 player following each of the systems and follows a few reasonable table assumptions. Since the systems are designed for different budgets, each player has a budget corresponding to what Best Craps Strategy suggested:

Betting System Budget
Iron Cross $540
Hammerlock $600
Risk 12 $120
Knockout $250
Dice Doctor $500

These budgets follow a common approach that guarantees enough bankroll for 10 shooters. Thus, the systems with higher bankrolls are the ones making more bets on the table for each shooter. Budgets play a key role in determining which system is right for you, and the 10 shooter measure provides a reasonable comparison.

The results are in

200,000 sessions fly by in about 1 hour of CPU time, and we can take a look at the range of outcomes that each system had. The plot below shows the winnings (final cash - initial bankroll) after the 20 shooters. The height gives a sense of the relative chance of each outcome happening for a given system.

A couple of things jump out right away. Most strategies show a spike on the low end of their winnings, which corresponds to “busting out” with no money left. Different strategies have different peak heights, which gives a sense of the chance of busting. With different budgets, these peaks would change, and with an unlimited budget, we wouldn’t see them at all.

The systems also show significant differences in the range of outcomes (stats people call this variance). The Risk 12 system displays the smallest outcome range, and it is well contained between -$120 and $200. Iron Cross and Dice Doctor have a wide range of outcomes, and they even had occasions where they won as much as $2000 (you have to move the plot over to see it).

By the way, the plot above is interactive. You can click on a strategy in the legend to omit it from the comparison. Hover over an outline to remind you which strategy is which. You can also click and drag to zoom in on a region of interest or reset the view with the “home” button at the top.

In more detail

We can take a more extensive look at each strategy with some hard metrics. I calculate these measures on a $/hour basis by using the rule-of-thumb that 144 rolls roughly correspond to an hour at the craps table, which I’ve used in previous posts.

Average winnings are similar to the house edge. The Low 25%, Mid 50%, and High 75% of winnings give you a sense of what is likely to happen in any given session. 25% of the time you will fall below the Low, 25% of the time you will fall between Low and Mid, another 25% for between Mid and High, and the luckiest 25% of sessions will be above the High.

Metrics for Betting Systems on $5 table
Betting System Average Winnings ($/hour) Low 25% of Winnings ($/hour) Mid 50% of Winnings ($/hour) High 75% of Winnings ($/hour)
Hammerlock -10.46 -81.29 -13.02 57.80
Risk 12 -20.04 -63.36 -17.89 23.92
Knockout -23.17 -104.52 -16.00 64.42
Dice Doctor -69.99 -213.18 -80.50 59.02
Iron Cross -70.13 -196.11 -50.44 77.23

This table gives some additional context to the plot. We see that Iron Cross and Dice Doctor have a tremendous house edge of $70 per hour. While they also have some of the highest potential winnings, that house edge is way more than I am ever willing to give away on a $5 table. Plus, this assumes the field has a number that pays triple, and it only gets worse if that is not true.

Hammerlock, Risk 12, and Knockout show a much lower house edge, and in-fact the High 75% for Hammerlock and Knockout at pretty close to the Iron Cross and Dice Doctor. This reveals that their upsides are comparable at that level, while you do much better in the average session.

Risk 12, unsurprisingly, has a much narrower range of potential winnings and losses. This is a conservative strategy, which has a time and place for the budget player. However, it’s important to point out that, on average, Risk 12 has higher losses than Hammerlock. So the narrow range comes at some price for the average session.

Looking at the data in a slightly different way, we can see what these metrics look like in $/20 shooters, i.e. $/session. The below table shows those measures, along with the chance of busting and the chance of walking away with any winnings.

Metrics for Betting Systems on $5 table
Betting System Average Winnings ($/20 shooters) Low 25% of Winnings ($/20 shooters) High 75% of Winnings ($/20 shooters) Chance of Busting (%) Chance of Any Winnings (%)
Knockout -7.03 -110.00 85.00 4.62% 44.29%
Risk 12 -14.00 -67.00 31.00 12.18% 38.56%
Hammerlock -17.91 -98.00 65.00 0.00% 44.85%
Iron Cross -41.92 -204.00 101.00 0.84% 39.75%
Dice Doctor -70.23 -240.00 70.00 3.44% 34.29%

Take another look at the difference between the two tables. The ordering in terms of average winnings changed! In all honesty, I am still not 100% sure what causes this. One reason the metrics differ is that each session has a varying number of rolls, and typically longer rolls are per shooter are better for the systems (except Hammerlock). So looking on a per roll basis, and knowing that it corresponds to exactly 20 shooters, provides some information that may bias the first table. Think about the Knockout strategy; if there were many rolls, then I know the shooters probably were making some points, making the player money. I think this second table is more representative in this case because the number of shooters is what each simulation was restricted to.

Are you more likely to join the table for a fixed time or a fixed number of shooters? This may affect how you budget and choose from relevant strategies. For example, the results from this post apply if you are more likely to play with a fixed number of shooters. The data here would suggest that Knockout has the smallest losses during that session, but not necessarily the lowest losses per roll, among the given systems.

Another metric to consider is the chance of walking away with any winnings. This is simply the percentage of sessions where your ending bankroll is larger than your initial bankroll. For Knockout and Hammerlock, this number is relatively high at 44-45%. However, the other strategies range from 34% to 40%. I think this metric is important to factor in because it shows how often you can walk away feeling good with the session.

Hot table or Cold table?

Most craps players intuitively know that in a given session, someone playing the pass line is going to have almost the opposite luck as someone playing the don’t pass. For the most part, one of those players will walk away as a winner and the other a loser, because the payouts are almost inverted (don’t forget the push on 12 for the don’t pass). But if you play the pass line with odds and your friend plays a place 6/8 strategy, how often do you both end up as winners? or losers?

This notion is formalized statistically as correlation, which measures how similar two things are under identical conditions. Since the results of the simulations were all from the same 200,000 table sessions, I’m able to look at the correlation among the 5 systems.

A correlation close to 1 indicates nearly identical winnings—if you won $100, your friend won close to $100. A correlation close to 0 suggests the strategies aren’t similar, and we can’t tell what your friend won based on your winnings. On the other side, correlations can be close to -1 and suggest that if your friend won, you probably lost. For example, the pass line and don’t pass strategies probably have a correlation close to -1.

The plot above shows the correlation between the 5 systems. Take the top row as an example. Hammerlock has a correlation of 1 with itself (this always happens), but it negatively correlated with the other 4 systems. Hammerlock and Knockout have a correlation of -0.67, which likely comes from one relying on winning the pass odds and the other wanting to win the lay odds. Hammerlock does well on a cold table while Knockout does well with a few hot shooters.

Some of the systems show high correlation, such as Iron Cross vs Knockout (correlation = 0.78) and Risk 12 vs Iron Cross (correlation = 0.74). These three strategies all rely on a pass line bet and do poorly when the shooter 7-outs.

Unsurprisingly, the Dice Doctor strategy shows the lowest correlation with any other strategies. The correlation ranges from 0.09 to 0.22 because the field bet is so different from the pass line, don’t pass, and place bets. The strongest correlation is with Iron Cross, which also features frequent field betting.

Takeaways

There’s a lot of information in this post, but I still feel like we have only scratched the surface in analyzing craps systems. The 5 systems described highlight a variety of different bets and offer a little bit for everyone. Here are a few things that I took away from this analysis:

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

For transparency, the folks at Best Craps Strategy provided funding for my time to perform this analysis and write the results. I understand that they are genuinely interested in improving their growing site with good craps information, and will use this information to expand their systems page. I don’t make any money if you check out their site or click the links in this post.

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

Table Assumptions

I make the following assumption for the simulations in this post:

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