Craps: Best Strategies on a Budget
CRAPS, DATAVIZ, SIMULATION
Sean Kent
July 31, 2019
For those that read my last post, you’ll know that if I’m in a casino (especially on a cruise ship), it’s pretty likely I’ll be playing craps. Well, back in March, I was fortunate enough to be going on another cruise and wanted to know the best strategy for myself at the craps table. If you read any craps book (or amateur blog post), they will tell you that the best bet in craps is the pass line bet with as many odds behind it as the casino will allow. I wanted to use my craps simulator to test this theory with a few other common strategies. To go beyond just looking at the house edge, I programmed the simulator with a realistic scenario: someone (i.e. me) walks up to the table with $200, on a table with minimums of $10, and plays for about an hour. After that hour, and their bets finish out, what is their net winnings?
This scenario brings to light a few really interesting concepts in craps, gambling, and statistics at large. We’ll see that house edge matters, but the risk of each strategy (how much your winnings can vary from session to session), and your chance of losing everything can also be important points to consider when choosing a betting strategy. And at the end, I’ll reveal how I did gambling on the cruise following the lessons learned from this analysis.
Too many strategies to choose from
I couldn’t try every strategy in the book for this analysis. Each strategy is a bit tedious to code and I only had a limited time before the cruise. I was able to test 4 strategies that I believe to be common or interesting. The strategies are as follows:
- Pass line bet followed by 2 come bets (i.e. Three Point Molly with no odds)
- Pass line bet with 2x odds and no other bets
- Pass line bet followed by Placing the 6 and 8 after a point is set
- No pass line bet, but Place 6 and 8 after a point is set, and follow with 2 come bets to try and get on 4 numbers
I chose these strategies because they all include some of the lowest house edge bets (pass line and come bets (0.42% per roll), odds bets (with no house edge), and placing the 6 and 8 (0.46% per roll)). They differ in the combinations of the bets chosen, and some of them have hedging involved (e.g. using a come bet to protect a pass line bet’s loss on the first roll). I didn’t include any “dark side” strategies because for me it’s more fun to win when everyone else is winning, but it would be interesting to consider those in a future analysis.
For the avid craps player, these strategies may seem pretty tame, in that they don’t involve many bets or numbers at any given time. We will see that even these simple betting strategies offer plenty of variation in possible outcomes, and with a limited budget can easily end up with the player losing all of their money.
Show me the data
After running 200,000 simulations for each strategy, on a table with $10 minimum bets and a buy-in of $200, throughout 144 rolls (which roughly equates to 1 hour of play at a table with 5 players) the relative chance of each outcome is given in the plot below:
All of the strategies follow a similar pattern: they have a large portion of outcomes near $0, a few outcomes where the player won a lot of money, and a spike near -$200 where the player essentially busts out and looses almost all of their initial outlay.
Where the strategies differ is in how big the bust-out spike is, and how much potential upside the strategy has. There’s a lot of valuable information in this plot, but I think it doesn’t quite tell the whole story. For that, we will need some hard numbers.
The Statistics Nerd Stuff
I described in detail many of the metrics in the below table in my last post. They are fairly self-explanatory but give a good picture of the realistic wins and losses one can expect in a given hour of playing at the table.
| Betting Strategy | Average Winnings ($/hour) | Low 25% of Winnings ($/hour) | High 75% of Winnings ($/hour) | SD of Winnings ($/hour) | Chance of Busting (%) |
|---|---|---|---|---|---|
| Pass line w/ 2 Come Bets | -14.57 | -80.00 | 50.00 | 101.15 | 6.40 |
| Pass line w/ 2x Odds | -5.10 | -192.00 | 118.00 | 174.55 | 29.40 |
| Pass line and Place 6,8 | -12.58 | -114.00 | 78.00 | 129.22 | 16.50 |
| Place 6,8 w/ 2 Come Bets | -22.66 | -192.00 | 82.00 | 150.82 | 25.60 |
Here we see the real trade-off between these strategies. The ones with worse average winnings (high house edge) also tend to have lower risk (both in terms of S.D. of winnings and chance of busting), and vice versa. Let’s also visualize some of these table values on the outcome plot:
The winning strategy in terms of average winnings is no surprise: it’s the Pass line with 2x odds. This is the canonical wisdom of almost every craps book you can find. So, what’s the problem? That strategy also has the largest chance of busting at a whopping 29%. For someone who would very much like to play more than an hour or two of craps over a 7-day cruise, that’s too risky. Off the top of my head, I estimate I’d have less than a 10% chance of walking away with any money after 7 days of playing for an hour each \(((1-.29)^7 = 0.0909)\).
One strategy I eliminated right away was the Place 6/8 with 2 come bets strategy. This strategy has a high chance of busting (around 25%) but also is the worst in terms of average winnings per hour (I’d expect to lose about $22 each hour). It seems like hedging the place 6/8 bets with two come bets adds to the house edge, and you need the shooter to get on a hot streak to make any money. This is the worst of both worlds compared to the other strategies.
This left the two strategies that I (mostly) employed on the cruise: Pass line w/ 2 come bets and Pass line with Place 6/8 bets. For me, the average winnings per hour weren’t too outrageous, and the chance of busting was much more palatable. Both of these strategies lend themselves well to playing a lot of craps on my trip, minimizing the chance of losing all my money, and still offering the opportunity to walk away with a decent chunk of change. To me, that’s a win.
From the computer to reality
On my trip, I ended up mixing between Pass line w/ 2 come bets and Pass line with Place 6/8 bets strategies. However, I didn’t stick to this 100% of the time. Sometimes I added some odds behind my pass line bet if I was feeling riskier, or sometimes I would take my Place 6/8 bets down after they won twice if I was feeling less risky.
Did my strategy work? The problem in the casino is that you don’t get to see the results of 200,000 casino visits—you only get one shot. I didn’t play craps every day, but most of the days I played, I saw some really cold tables. By the fourth day, I was almost out of money. However, by reducing my chance of busting, I kept my money long enough to play on the latter days, when there were a few hot rollers. By the end of the trip, I had won over $300, although some of that was from the blackjack table. And more importantly, I had a lot of fun!
At the very least, it was an interesting exercise to look at these betting strategies in a realistic simulation. The big points here are that Pass line bets with odds can’t be beaten in terms of the house edge, but may be too risky for someone on a limited budget. In general, strategies that involve hedging hurt your house edge, but for some, the lower risk might be worth it. Generally, variance is a good thing in the casino, because without it you’d never walk away from the table a winner. However, knowing the risk that you’re taking when you walk into the casino is always recommended.
I hope you enjoyed this analysis as much as I did. I may explore other strategies in the future, so if you have some in mind, please reach out on twitter @Sean__Kent or via email spkent@wisc.edu. I’d love to hear your thoughts and comments.