Competitive Cribbage - Summer 2022

It is time for the Cribbage Pro Summer 2022 Season of Competitive Matchmaking! If you are here primarily for what is new/changed, then scroll down to the final "News for The New Season" section below. The Spring 2022 season has fully wrapped up, and as usual it was entertaining to watch the rise and fall of different players throughout the season again. I still find myself cheering for different players on and off throughout the season. I admit I also often wish I could personally participate, but  we have a rule that employees/contractors are prohibited from this and Contest play (and from the leaderboards entirely, in case you were wondering).

The Top 50 had quite a few new faces yet again this season. It is great to see all the new challengers working so hard to make their way to the top! Everyone loves an underdog, I suppose. Things just seem to be getting more and more competitive, so thank you to all for participating and bringing your friends! Thank you also to everyone who participated in this great game of cribbage, even if you didn't quite make the Top 50. I hope you enjoyed the journey.

In 1st place for Spring 2022, we have "Mrpadre" for the first time! It is nice to see Mrpadre back this season, as they were in the top 10 last season as well! 2nd place is "ernie313", and ernie313 has been in the Top 50 many times in the past as well, finishing last season at 33rd. In 3rd we have "Dhrun", who was in 2nd last season and also becoming a regular around these parts. Other interesting movements in the Top 50 included "WhyADuck" who has placed in the Top 50 before, but wasn't there last season and is 4th this season, and "Br1Guy" who we have definitely seen before, moving up just a bit from 13th to 9th! "scoot1234" came up from 28th last season to finish 19th this season, while "jjonell" came from 42nd to finish 36th.

Everyone who finished the season in the Top 50 ("Recent" list), has been awarded both a special in-game "board peg" as well as Cribbage Pro Gold that can be used in the Cribbage Pro Contests system and then redeemed for cash (awards must be used at least once in a Contest to be cashed out to USDC, see the full terms and conditions for details). If you are awarded Gold, and are not sure what it is good for (or how to access the Contests system), read through the links above or email us any time if you have questions. On iOS you will need the "Cribbage Pro Contests" version of the app, and on Android you need to install the game using the Amazon Appstore. As it looks like many are not using the Cribbage Pro Gold they win (which makes it kind of a useless prize for them), this part of the prize may change for the Summer 2022 winners (please email us your suggestions). The Cribbage Pro Gold awards are as follows (not cumulative):

• 4 Gold for Top 50
• 7 Gold for Top 25
• 10 Gold for Top 10
• 20 Gold for 3rd Place
• 30 Gold for 2nd Place
• 50 Gold for 1st Place

The top finisher is awarded the "crown" board peg, and all others in the Top 50 are awarded a "star" board peg. These pegs are shown to everyone when playing in online multiplayer games, and they are permanent, so if you see your opponent has one of them you can know that they have earned it by finishing in the Top 50 in competitive play.

Remember: Complete 10 matches per week! See the FAQ for details.

Here was the final Top 50 for Spring 2022:

1	Mrpadre	26	koala29
2	ernie313	27	nvsru911
3	Dhrun	28	Domerzag
4	WhyADuck	29	gotupeggd
5	Gssj21	30	wfdove
6	nob4one	31	aela
7	iPeg	32	cyrusg
8	scout3	33	sagdog16
9	Br1Guy	34	Dempegs
10	shudbgolf	35	Legonaut
11	wightness	36	jjonell
12	PALONSO	37	bbaer1
13	236Postie	38	farleysma
14	VGKnights	39	pscohen
15	Cutch13	40	Paludeja
16	hillchem	41	vhray
17	nhguy	42	IAMFAST
18	hunterIT	43	Buikemad
19	scoot1234	44	SH00TER
20	cribfan44	45	james500
21	lbolt58	46	dph
22	UberPooch	47	jehcjehc
23	BigD4Life	48	brewski42
24	jwr13	49	dkatz1877
25	TC2	50	yank29

The levels in Competitive Matchmaking are available in the FAQ.

News for The New Season

Some of you have been asking, and patiently waiting, for some bigger changes. However, there will not be big changes for this season.

During the Spring 2022 season, while you were all playing (and we were watching all the ups and downs and crunching the numbers), we spent a lot of time working on several different ways to bring ideas around a single game match to the competitive system. The idea was to lighten the games required, and the time needed to participate, as not everyone is able to do so with a 3 game match. Ultimately, it just didn't work out as hoped, and so we couldn't release it.

We worked through several different ways to try to provide for a single game match, but in testing and analysis, it just could never provide good results. What I mean by that is our system simply could not accurately isolate the skill from the luck with just a single game, even if the total number of games played went up significantly (which it is also unclear if that would be the case). Playing more games against other players just doesn't compensate. This means, among other criteria, that it couldn't accurately predict the winner (meaning the skill calculated isn't good enough), or then subsequently calculate the skill rank adjustments to be made reliably as a result, when tested against real world game data. Either the skill ranking system we use (even with various tweaks/changes to it), or the game of cribbage itself, just doesn't allow for it to happen. I personally try to hold a high standard for everything we do, and if anything can't be shown to meet or exceed that standard, no matter if we have spent a lot of effort on it, we will not release it.

As we have tested lots of different skill ranking systems before selecting the one used today, I honestly don't think that is the problem, but likely this is just the nature of cribbage that there can often be a non-trivial amount of luck in a single game. Frankly, the "Best of 3" isn't perfect (and I think there are things we can still do to help more there), but given the limitations (like the amount of time people can play), it ends up being a good compromise. So, because of all that time working on these things that didn't result in changes this season, we decided to not make any other core changes. There just wasn't enough time. There are some minor things, but mostly just around making the system more reliable, and bug fixes. So, we have decided to put this task aside for now, and to move on to other improvements that many are also asking for.

As a reminder, if you have played a few seasons here and have some thoughts on what you would like to see around prizes, structure or anything else, please email us at support@FullerSystems.com with your suggestions.

Calculating the Odds of Winning a Cribbage Game – Part 1

A Guest post by Donald E. Heller

As an almost life-long and daily cribbage player, one of the things I enjoy about the game is the ebb and flow of a typical match. At any point in time, player 1 can have a strong lead, looking like a lock to win the game, and then player 2 can get two or three great hands and pass her opponent to go on and win the game.

As this occurs, I often think about what the odds were of player 1 winning the game given the score and position on the board. For example, if I am ahead of the other player 90 to 75, what are the odds that I will win the game? This calculation is similar to what sports websites often do for games in progress. One example from ESPN is shown in figure 1 below.

Figure 1: ESPN win probability chart for Major League Baseball (screenshot courtesy ESPN)

In this game, in the top of the 4th inning and none out, and Cleveland ahead 2-0, ESPN calculates that Cleveland has a 67.3% chance of winning the game. This is based on the score and point in the game, along with ESPN’s calculations of the skills and track records of each of the two teams and their respective players.

Is it possible to calculate similar odds of winning in cribbage? My curiosity led me to a web search, but I could not find anything along the lines of what I was looking for. Being a user of Cribbage Pro, I reached out to the team there to see if they knew of anyone who had ever done these calculations. They did not, but said that they were willing to share some data with me if I was interested in doing the calculations myself. Being an experienced quantitative researcher, I agreed to take on the challenge.

Fuller Systems (the developer of Cribbage Pro) generously provided me with the data necessary to do the calculations from their log files of Cribbage Pro users. After providing me with a small sample file of anonymous data (data that couldn’t be tied back to any Cribbage Pro user), I worked on extracting the data and analyzing it. I was able to do the odds calculations I had hoped for, so Fuller Systems then provided me with a set of larger files – 72 files, each representing a consecutive hour’s worth of log records from Cribbage Pro games over the course of three days, and containing the step-by-step records of games played on the app. These are massive files, each one of the 72 with over one million records in it. In order to make the data analyzable in Stata, the statistical software that I use, I had to extract samples from each game and then combine these samples from the 72 files into a single, smaller file that could be analyzed to do the odds calculations.

This smaller file represented over 600,000 games that were completed during the 72-hour period for which Fuller Systems provided me with the data. From the scores at each point in time, and knowing who won each game, I was able to calculate the odds of each player winning the game given the score.

There are certainly some limitations to these calculations. I did not know anything about the players, so I could not conduct a sophisticated point-in-time prediction for each game that takes into account the skill and track record of each player, similar to what ESPN does in its predictions. So these predictions are what I would describe as “player-neutral,” i.e., they only relate what we know about a score at a given point with who won the game in the end, but nothing about the skill of the players.

Another limitation is that I did not calculate the odds for every potential score. To keep the analysis simple, I analyzed scores that were reasonably close and would typically be found in games. In other words, I did not calculate the odds of winning when the score was 115 for player 1 to 60 for player 2 (though one could intuit that player 1 would have very high odds of winning the game and skunking player 2).

With these caveats, table 1 shows some examples of what I found. The full table can be found here (note: in the table the “Win %” is the percentage of games won by player 2; the win percentages were calculated only for those scores that had at least 100 occurrences in the data).

Table 1 – Odds of winning for a variety of scores

Player 1 score	Player 2 score	Odds of player 2 winning
30	40	61%
60	70	78%
60	80	84%
90	91	54%
90	95	61%
90	100	76%
100	110	78%

In general, the wider the margin between the two players, the greater are the odds that the player who is ahead will win. But this pattern, however, is not perfect. Figure 2 below provides one example. As noted, the closer player 2 is to winning when player 1 has a score of 100, the greater the odds are that player 2 will win the game. But you will note the interesting dip starting when player 2 has a score of 117.

Figure 2: Calculated odds that player 2 wins the game when player 1 has 100 points

The reason for this can be found in the laws of probability. For example, if you flip a true coin, you know the odds are 50 percent that it will come up tails, and 50 percent that it will come up heads. If you flip it ten times, you would expect five heads and five tails. But if you conducted this experiment of ten coin flips a number of times, you would probably find that it was not always split 50 percent between heads and tails. And if you conducted 100 coin flips, the same would be true – you would likely not have exactly 50 heads and 50 tales.

The same is true in the game of cribbage. While you would expect that a wider lead would lead to an increased chance of winning the game, this is not necessarily always true, even over the hundreds of games represented by each of the scores in the table. Another reason for this is that the scores used in my analysis are taken at random points in time, e.g., at the end of the hand, or during the counting of a hand, etc. So who wins the game could be impacted by who has the deal and who is counting when the score in the analysis was used.

Part 2 of this post will explore this phenomenon further. For now, I hope that you enjoy using the table to look up your odds of winning the game as you play cribbage. But remember – these predictions are not perfect, and as they say, your mileage may vary!

Donald E. Heller is a retired professor and college administrator, and lives in San Francisco. He was taught the game of cribbage as a child, and plays daily with his wife as well as on Cribbage Pro.