(cross-posting from BGG; sorry if you've already seen this)

Elder Sign always had a sweet spot in my heart, since the release of the core set. During the years we witnessed a constant evolution of the game: at first with Unseen Forces, which expanded the Elder Sign experience, making the game (apparently) harder. Then Gates of Arkham came, revolutionizing everything and basically giving the game a second life. Some fans loved Gates of Arkham over the previous ES experience, some others kept loving the Museum more; and finally some more decided to blend the two experiences, using some cards from the core set, and some others from GoA.

But how difficult to pass are the adventures? How good the rewards? What's the best way to deal with the different AOs? What are the secrets behind the adventure decks?

Well, a couple of months ago we started working on this project, thanks to the precious help given by a good friend and great fan of the Arkham universe, Jason Horner. Jason (I'm sure he'll comment and explain in better detail his brilliant work) created an algorythm able to resolve numerically all the adventures existing in the whole ES galaxy, so that thanks to his help it was possible to calculate the actual odds for passing each of the existing adventures. His work was then paired up with the work done by me and my husband on the stochastics of the game, and in the end we can now offer a complete mathematical analysis of the game.

There are two ways this could be made available to you, and I need your opinion on how to release the material. Please read what follows, and then go to BGG ( here ) and cast your vote:

a) complete analysis : all results will be made available, and an article will be written explaining the reader in detail how to read graphs and charts provided. This is the option that is "easier" to understand even for those who are not familiar with non-parametric statistics; this is also the option that is more time-demanding for us, so that results will be upped at quite a slower pace

b) plots and tables only : all results will be made available in the form of plots and tables. No article will be written, but guidelines on how to read the results will be hereby written (I'll edit the header once the poll is closed). This is probably not 100% users-friendly, but it's the easiest way to go and in case further material is released, updating the charts should be rather quick

So, your turn now. As soon as the poll is closed (on Friday), we'll start preparing the material. As soon as the files are approved on BGG, I'll post download links both here and on BGG, in the thread above linked.

If you took the time to read Julia's awesome post, I expect you'd be interested in reading another long post talking about my role in this endeavour. I want to thank Julia and her husband for involving me in this project, and I'm very excited that they will be posting our findings to the community. If this were a book, I feel like I should be writing the forward here.

Julia and her husband spent quite some time working out some the math behind the game in order to analyze the balance in terms of adventure probability, rewards gained, average number of elder signs offered as rewards, and other such things. Julia's husband put together some impressive Excel spreadsheets with some detailed formulas to calculate the probability of passing the adventures. But as it turns out, calculating the odds of passing a relatively easy adventure involves a long and tedious formula, even if you greatly simplify the assumptions and cut corners.

This is where I came in. I'm a computer scientist. Independently of Julia and her husband, I was thinking about how to write a program that calculated Elder Sign adventure probabilities by simulating them. At the early stages of the program's creation, I talked with Julia about it and that's when our team effort began.

I created a framework that can represent adventures, tasks, and dice, and developed an algorithm that can roll dice and use them to complete adventures much in the way a human would. If I repeat the process many, many times, I can find how many times I succeeded out of the total number of runs, and with a large enough number of trials, I can get a relatively good approximation of the true odds of passing the adventure by playing similar to the way a real human would (thanks to the law of large numbers).

Because it's a simulation, I didn't have to write any crazy formulas or do any real math other than some simple adding and subtracting. I was able to add support for things like:

* Retrying the adventure with one less die after a failed roll
* Handle adventures with many tasks and/or requirements
* Adding the red and/or yellow dice
* Adding the cursed (black) die
* Factoring in locked dice
* Terror effects that fail the adventure or devour you
* Trying to complete the most difficult adventure first when more than one can be completed with the rolled dice

Though my algorithm that attempts the adventure is far from perfect, it's good enough to get pretty good results, and Julia and her husband have been able to take these probabilities and use them to great effect in their analysis and really explore the deeper math behind the game. The program took a week or two to get preliminary results, and enhancements made gradually over the last few weeks have resulted in the improvements mentioned above. I maintain that my role in this was but a small part of Julia and her husband's overall analysis, but even so, this exercise has been an incredibly successful collaboration. Each of us has helped make the others' work better and the fruits of our labor will soon be made to all of you. I hope all of you enjoy reading about it as much as we did working on it.

The first chapter is available for download on BGG. Here

Wow, that's impressive! That'll be a big help in determining which adventure card to select or whether the improved odds are enough to justify using a common or unique item. Thanks for all the work you all put into it!

Glad it is of help! I hope chpater 2 will be ready at the beginning of August!