Thursday, August 16, 2012

Cribbage Pro Multiplayer Analysis - Tips & Strategy

Welcome to the first installment of "Cribbage Analysis - Tips & Strategy"!

Cribbage Pro is the most popular cribbage application for mobile devices and the only one offering cross-platform multiplayer today. We have hosted millions of online multiplayer games since releasing Cribbage Pro Online in 2009. The cribbage community has been very good to us, and we would like to continue to give back whenever we can. So, we will be publishing several articles about cribbage over the next few months, based on actual data from Cribbage Pro multiplayer games to help you develop your cribbage skill and strategy both when playing in Cribbage Pro or in the "real world".  You should subscribe (link on the right) to this blog now to get the very latest tips and analysis as soon as it is available and if you don't have Cribbage Pro yet, go download Cribbage Pro now so you can "play along".

In online multiplayer games we track every game played, including every hand dealt, every card played and every point scored. Armed with our database of millions of hands we can analyze the game in ways that nobody has ever attempted, based on real players playing real games against other real players. Want to know how to play 6-7-8-9? We have seen it played tens of thousands of times, and we know what has worked out best. Should you pair your opponent's lead? We have the data on that too, and we'll be sharing that and much more with you on this blog in the coming weeks.

One of the first questions you will probably have is about privacy in all of this data we are collecting. As our EULA states, all our analysis is done anonymously and in aggregate. We know that thousands of players like to lead a 4 from 4-5-6-6, but we don't track the corresponding names, addresses, or anything else about them and we secure the data using some of the best security technology available. You can rest assured that you can play online without worrying about your privacy. And please don't lead the 4 from 4-5-6-6!

With that out of the way, I would like to acknowledge the hard work of Aaron Harsh in pulling all of this together (more about Aaron in the guest post tag line at the bottom). Aaron has spent a lot of time and effort on pulling all of this together, and we are very grateful for his willingness to do all that work and be a guest author for us on the blog. Everything you read below comes directly from Aaron and his analysis of the data provided unless otherwise noted.

First topic: What makes the good players so darn good?

Some players are better than others. What are they doing differently, and what do we need to do to play as well as them? For our analysis we've ranked the players by the percentage of games they win[1]. We'll name these ranks "A", "B", "C", and "D". Around 3% of the players got an A, 16% got a B, 56% a C, and the bottom 25% got a D. The A players win around 54.3% of the time, on average, B players win 51.5% of the time, Cs win 50% of the time, and the D players on average win 48.1% of their games.

(Editor's Note: View your total win percentage by selecting the statistics button in Cribbage Pro. Refer to the footnote for how this is different than the calculation used here. When considering just "raw" data that includes forfeits and manual counting games, roughly 30% have a 53% or better win rate and 10% are at 60% or better)

Here's what this looks like visually:
The As are in blue, Bs in orange, Cs in yellow, and the Ds are in green. Those As are on a completely different level from the masses in group "C", but they're still not winning anywhere near 100% of the time. It looks like a 56% winning average across a large number of games would be a good goal. So how do we accomplish that? What are the great players doing differently than the casual player? Well, for starters..

Better players score more points

No surprise here: great players score more points than casual players. The surprise is that they're not scoring that many more points:

Average points/hand, by player's rank

Skill levelAverage points as dealerAverage points as non-dealer

The A players, on average, are scoring almost exactly the same number of points as the B players when they deal (taking into account hand, crib, and pegging), and only 0.16 more than the C players. Even compared to the D players they're only scoring 0.34 more points per hand when they deal. Cribbage is a subtle game!
The situation isn't much different for hands played as non-dealer. The A players score essentially the same number of points as the B players, 0.17 more than the C players, and 0.30 points more than the D players.

Let's break those numbers down a little:

Points as dealer, by player's rank

Skill levelHeelsPeggingHandCrib

There's not much skill involved in cutting a Jack, and all players end up with the same "Heels" average. Surprisingly, pegging doesn't show much of a difference, either. All players peg a similar amount each hand. The hand and crib counts are where things really pick up. Once again there's very little difference between the A and B players, but the C and D players have a small but noticable disadvantage. One fun fact is that the A players are apparently thinking more about their cribs than the B players, and lose some pegging points in the process.

The non-dealer numbers are about what you'd expect:

Points as non-dealer, by player's rank

Skill levelPeggingHand

Pegging's still close here, although the D players lose some ground when pegging as non-dealer. And the differences in the hand count show up again for the C and D players.
So now we've got our first step to being a better player: choose your hand and your crib more wisely. We'll talk more about that in future blog entries. So now we know what the good players are doing better: they're scoring more points. What else could there possibly be to cribbage besides scoring more points?

Better players keep their opponents from scoring points

Here's the complement to the first table we saw: average points per hand, based on the opponent's skill level.

Points/hand, by opponent's rank

Skill levelAverage points as dealerAverage points as non-dealer

There's some interesting stuff here. Dealers playing against an A player average only 15.86 points per hand, vs. 16.23 when playing against a D player. That's an advantage of 0.37 points per hand. Non-dealers playing against an A player average 9.88 points per hand, vs. 10.12 against a D player.

Let's break those numbers down and see where the difference is coming from:

Points as dealer, by opponent's rank

Skill levelHeelsPeggingHandCrib

Points as non-dealer, by opponent's rank

Skill levelPeggingHand

Even great players can't keep themselves from cutting a Jack. They don't seem to have much effect on their opponents' hands, either. But great players take away 0.1 or 0.2 points of pegging points from their opponents, and they do about the same to their opponents' cribs, too. This looks like the real difference between the A and B players -- Bs score just as many points as As, but the As are better at keeping their opponents from scoring.

One interesting point in this data -- players' hands contain slightly fewer points when they're playing better opponents. A player can't directly affect the number of points in her opponent's hand, so what's going on here? Is this because the players are keeping different cards in an attempt to peg more? Or is this because the opponents get so far behind they make rash decisions in an attempt to catch up? Maybe we'll investigate this in a future blog post.

Executive summary: in two hands (one as dealer, one as non-dealer), a great player will score 0.34 more points than a D player, and he'll lower his opponent's score by 0.37 points. Altogether, an A player has net advantage of 0.70 points per hand. The A players score more points, and their opponents score fewer points.

That might seem like the end of the story, but there's one more thing:

Better players play differently based on their board position

An understanding of board position is probably the biggest different between a great player and the rest. It's a little deep for our first blog entry, though, so let's save it for future blog posts.

That's it for today

We'll dig deeper into all these topics in future blog posts. Do you have something in particular you'd like us to look at? Leave us a comment and we'll see what we can do.

1. To be precise, we've ranked each player based on a Bayesian posterior mean of the player's win rate, to take into account the number of games played. The more games a player plays, the closer their ranking will be to their win percentage. We've also excluded manual-count games since we want to identify players with good strategy, rather than players with good counting abilities. The formula used is: (25 + # games won) / (50 + # games played) where "games won" and "games played" are the number observed in the sample.

Editor's Note: This is a guest post by Aaron Harsh. Aaron lives in Portland, Oregon with his wife Stacy and daughter Audrey. He spends his evenings analyzing cribbage strategy for Fuller Systems, and his days analyzing television viewership for Rentrak Corporation's Advanced Media & Information group. You can play him on Cribbage Pro Online as user "aaronhars", or in person at American Cribbage Congress grassroots club #28 (Oregon's Finest).


  1. I think this is great - I look forward to more articles in the series.

    I would love to get a look at my own data as well as the aggregated data.

    1. Hi "dph", thanks for the comments. The next post is nearly ready to go, so stay tuned.

      We don't have your "own data", as that is not how we track things. As noted above about privacy, it is only done anonymously and in aggregate, so we wouldn't be able to show you anything beyond what you already see in your own stats.

    2. Josh, thanks for the reply.

      As a 'wish list' item - I would like to be able to get at my own data. Perhaps this could be accomplished if more information about each game were stored on the local device (my phone) and I could download it from there.

      As I've said before - you're doing a great job with this app (but that won't stop me from asking for even more!).

    3. Thanks for the suggestion. It is something we have tried to do before, but stopped short due to the size/complexity of the data and similar concerns on the different kinds of devices and their ability to hold it all.

      One thing I'm thinking about is keeping game files for each player if they opt-in and find a way to save them on the server in a format that people can easily understand. Right now the logs we keep are so verbose and "ugly" that you would not find them very helpful unfortunately. So, I'm working on it...

    4. I can handle ugly -- I've made a software career out of parsing ugly!

      I love that you actually consider suggestions and don't merely dismiss them because they mean more work for you and your crew.

  2. Any chance we can see partner cribbage or three-person cut throat?

    1. Hi Joe, right now we are still very focused on the two player version of cribbage and getting everything out for it that we have on our list (the list is still quite long of things we want to do). 3 or 4 person cribbage is something we have considered, but we do not currently have any active plans or dates to provide at this time.

  3. Can you play with others on line for free?

    1. Yes, absolutely. The payment option you can find in the game is only to remove the advertising. All features of the game are otherwise available to everyone.

  4. I'm a relatively new player. I'm impressed on how you broke down each hand. Is there a score card or a system players can use keep score.

    1. In cribbage, you use the cribbage game board to track each player's score.

  5. Can the odds be determined of one player pegging six points twice in the same hand by playing the same card?

    Example: The first three cards played are K, K, K. After a go, the next series includes the first player scoring six or more again after 5, 5, 5. What are the odds of this happening twice in the same hand?

    I would love to know the answer. How is that answer determined?

    1. The short answer is, yes, the probabilities can be determined using standard math. You would have to integrate the probabilities of everything from having those cards in your hand, having your opponent having those cards, them being played in that order, etc. We could determine how often something like this happens in reality, but we don't currently have the data to run that calculation against today.

  6. I am missing info on the x-axis in the coloured histogram. The text says that "roughly 30% have a 53% or better win rate and 10% are at 60% or better". This can't be correct. The way I read the plot (x-axis) this is true for a very small minority.

    1. What you are missing is the line just prior to that quote you provided where it says "When considering just "raw" data...", which means looking at just the raw stats data overall and NOT the graph below.

    2. Ah, sorry. I misread that :)
      I love playing cribbage in the app. I think the only thing that I am missing is good individual statistics. Specifically I would really like to be able to follow my improvements over time (like a floating average in a time plot) instead of just seeing a compressed total average.

    3. No problem, thanks for the suggestion and for your support for Cribbage Pro! We do want to add more stats in the future, so thanks for your input.


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