when to splitting game boards

loganmaddoxmay

I have recently come across a challenging hurdle for me in setting up game boards. I have been splitting boards when i get an X/Y inference but when I watch the explanation video JY doesnt do it, but he will for other games. Is there a clear cut way to know when to split a game board? and if not is there something I can infer off the bat from the rules that would hint whether or not I needed to split it?

RaphaelP

No, it's not an exact science. Sometimes you can split and should. Other times you can split and shouldn't. Technically speaking, every single game "can" be split, since that just means carving it into two worlds. But here are the questions I ask myself when deciding if a split is desirable or not:

1) Does this split allow me to make inferences (i.e., find out other stuff about the other rules or boards)?

2) Is this a split that lets me place a piece and not have to worry about it again?

3) Does this split create very few boards, instead of an overwhelming amount?

KevinLuminateLSAT

The best way to learn when and how to split is to try games over again in different ways. Take a game that you solved without splitting and try it again while looking for an opportunity to split. And maybe try it again while splitting based on a different rule. Keep track of when the split allows you to complete the game more quickly and easily (and when it doesn't.) Then see if you can create some personal rules to follow regarding when to split based on your experience.

You'll need to refine those rules as you apply them because sometimes they may be over- or under-inclusive. For example, let's say you think "I'm going to split based on a block whenever I get one in an ordering game." That strategy will work for many games, but you'll no doubt run into some where it's a complete waste of time. Then based on your review of the games where the strategy didn't work, you might say, "Ok, I'm going to split based on the block if it goes in 4 different places. But not if it goes in more than 4 places." Then you may notice that because of this rule you didn't split in a game when it actually would have been very useful to do so. And you'll study why in that particular game splitting even though there were 5 places for a block still would have been a good idea. Over time, you'll have a system of rules that you understand and that you can apply both automatically but also flexibly - you're able to do so because you've put in the work to come up with them and you've seen the results of those rules through experience.

For example, here's a list of rules that I've come to follow based on my own style of doing games. If some of these don't make sense to you, that's OK - the point is not for you to follow exactly what I do, but as a jumping off point for how to think about coming up with your own system.

Ordering

Blocks (variables with a fixed relationship to each other) that fit only in 2 or 3 places -> Almost always split

Blocks that fit in 4 different places -> Split if there's another restrictive rule that's clearly affected by placement of block

"Or, but not both" relative order rule (A is before B or C, but not both) -> Create two ordering chains based on this rule if there are other rules that mention one of the variables in the rule

Variable fits only in two different slots -> Split using this rule if I'm not splitting on a block and if there is another rule that mentions this variable

Slot is limited to only two different variables -> Split using this rule if I'm not splitting on a block and if there is another rule that mentions one of the variables

Biconditional -> Almost always split

Two conditional rules that trigger based on opposite sufficient conditions -> Almost always split

Stand-alone Conditional that's not a biconditional -> Rarely split on this (can be useful if it's a rule that's difficult to visualize/apply and there's no other option for splitting)

Grouping

Two variables that must be in the same group, and they can only go in 2 or 3 groups -> Almost always split

Biconditional or two conditional rules that trigger based on opposite sufficient conditions -> Almost always split

"Or, but not both" -> Usually useful for splitting

Variable fits only in two different groups -> Useful for splitting if there's another rule that's affected

Slot is limited to only two different variables -> Often useful for splitting if there's another rule that's affected

Standalone conditional that's not a biconditional -> Useful to split on if there's no better option (splitting on a stand-alone condition is usually more useful in grouping than in ordering)

In/Out game with categories -> Splitting is usually not a good way to solve the game (except if there's a biconditional). Instead, thinking about the different # distributions is more useful.

I usually don't do "sub-splits" (splitting a game board on a second rule after an initial split on a different rule), but sometimes they can be useful if you can clearly see that an additional split will resolve every rule or would resolve a rule that's difficult to keep track of.

Another thing to keep in mind is that these same strategies apply to individual questions - if a question presents a new condition and it's not clear what happens after inputting that new condition, in many cases the best approach is to then look for a useful way to split the board even if only for that single question.

taniyuhh

i think it depends on the person and the game. for me personally, i started off by splitting the game board every time. through trial and error i developed an instinct, for lack of a better word, for when i should or shouldn't split the game board.