Calling on all math wizzes *A fun post*

Preston Bigley

I am curious to know what the formulaic way of calculating the total number of worlds for any given game. Obviously, I will not use this during the test, this is based off pure curiosity to do on my free time! For example, for PT 30, S1, G4, I worked out 18 possible worlds that are definitive. Given the conditional nature of rules in a game, I think it would be fun to be able to go Good Will Hunting mode and see if I could plug in some numbers to a formula of some sort to see if I get the same output as 18. I was doing some online research and there is something called the combination formula!

Cant Get Right

An algorithm could do it fairly simply, but I’m not sure if that counts for what you’re looking for or not:

1. Represent first rule with split game boards.
2. Working only from your prior split game boards, represent next rule with split game boards.
3. Eliminate redundant and impossible boards. (You might also just avoid the creation of these in the first place. Avoiding impossible boards is easy, but redundant boards would be difficult to predict.)
4. Repeat steps 2 and 3 until all rules are represented.
5. Count ‘em up.

This would account for the impact of any and all inferences which are merely consequences of the rules. It would be 100% reliable for all common game types which utilize game boards, though I can think of a few miscellaneous games off the top of my head which might threaten to frustrate it because the rules, to the extent there are any, deviate pretty dramatically from the norm. Even for those, however, this would still work in theory. It would just take a bit of creativity as to what representing the rules even means.

Preston Bigley

@"Cant Get Right" said:
An algorithm could do it fairly simply, but I’m not sure if that counts for what you’re looking for or not:

1. Represent first rule with split game boards.
2. Working only from your prior split game boards, represent next rule with split game boards.
3. Eliminate redundant and impossible boards. (You might also just avoid the creation of these in the first place. Avoiding impossible boards is easy, but redundant boards would be difficult to predict.)
4. Repeat steps 2 and 3 until all rules are represented.
5. Count ‘em up.

This would account for the impact of any and all inferences which are merely consequences of the rules. It would be 100% reliable for all common game types which utilize game boards, though I can think of a few miscellaneous games off the top of my head which might threaten to frustrate it because the rules, to the extent there are any, deviate pretty dramatically from the norm. Even for those, however, this would still work in theory. It would just take a bit of creativity as to what representing the rules even means.

Awesome! I just finished a simple sequencing game, I am going to play with this! Thanks a lot for taking the time to post.

Cant Get Right

@"Preston Bigley" said:
Awesome! I just finished a simple sequencing game, I am going to play with this! Thanks a lot for taking the time to post.

You're welcome, let us know how it goes! This is not a good way to take Games, but it'll be a great exercise in splitting boards. Think about what makes some splits actually effective, other splits less so, and other splits disastrous. You're going to get into some real tedious work on this, but should be fun if you're into that kinda thing.

Hmm. Looking at this now, I'm realizing I missed a step, at least. You'll also have to account for all the possible distributions for your floaters. Anything else?