Board game design seems like mathematical modeling

This is a big post with a lot of elements. It's a nice discussion.

#1 - video games are easier to design than board games because you don't have to create the mechanism

I think this is not true. With the most cutting edge technology available today, digital games still do not recreate reality 100%. You still have to use abstraction and approximation, and how deep to simulate each element of your game is the same kind of game design as finding the appropriate abstraction in a board game. You have some more flexibility in how much to simulate - but more simulation doesn't necessarily produce better gameplay.

I think that the main difference in designing for the two mediums is that video games still have a "novel" aspect. Pressing a button and seeing a reaction on a screen is a unique kind of experience that our brain interacts with in a different way than on a board game where we have to make all of the reactions happen ourselves. In both cases, I think that unexpected or surprising events are where the excitement comes from. It is certainly easier to produce surprise in the black box of a video game where the player of the game does not see the mechanisms.

The player of a non-digital game can see the mechanisms laid bare, so there is less space for the designer to hide.

At the same time, I don't see how creating, for instance, a platformer and borrowing jumping from mario, is any different than designing a deckbuilder and borrowing from dominion. (Which in turn borrowed some of it's inspiration from Magic)

There is really no need in either space to create a mechanism from whole cloth - borrowing, tweaking, and mixing mechanisms from elsewhere is a fine way to design.

#2 Games are math.

I don't feel very qualified to comment on anything related to math as I am terrible at it. Game theory shows a lot of the math involved in games, but at the same time, it is hard to see the math in games with heavy social calculus like Werewolf. Some games may need stronger modelling than others, and I know that there are designers with strong math backgrounds who start somewhere kind of like your problem solving techniques.

I think where that may break down with game design is that the product you are looking for is not a known quantity - it's a many solution problem. There may be 1000 very different final versions of your game that you would be happy with, and 1000 other final versions that you would not. How do you know you are on the path to one of the successes? I don't know that math is a great guide on that journey.

You talked about modelling reality, and while that is sometimes the desire, often the desire is somewhat different. In a war game, part of the desire may be to model war - but you most likely also want to model the excitement of two opposing war generals sitting across from each other and foiling each others plans - which obviously is not something that happens in real war. You want the feel of watching a movie where it keeps cutting from one general making an important decision and then cutting to the other general making an immediate response. Most of the time, you don't want the players to have to wait a week to see if their decision had any effect. (Barring a few exceptions like play by email games)

So however you are using your math, make sure you are using it to model the game experience that you want to provide, rather than coldly attempting to model the reality of whatever theme you may be inspired by.

#3 fear of board game design

If you are new to design, don't be afraid of just copying someone else's mechanism and making a game with that. You will learn a ton, and chances are that your game will still turn out different because of the choices you are making and your own goals. Along the way, some innovation may come to you, but trying too hard to be new and different when you haven't learned the structures that already exist can get you into trouble. Take it from me and my box of 100% unique and original game designs that I couldn't make work haha.

Hopefully I didn't derail things too much and give you some more things to think about. That stewart site is great and I'll be reading more of it for sure. Inductive reasoning for example is something that I think could apply - not in a directly mathematical way, but I do think that sometimes trying the mechanism you think WONT work can be as helpful as trying the mechanism you think WILL.