One day I was pondering the question of Battle Value in Classic Battletech (CBT), which is a complex sort of mathematical problem, and then I had one of those deep thoughts: If CBT were a game that people gamble on, then this complex problem would have been worked out long ago.
A basic principle that serves me well both personally and professionally, it that when I don't really understand something, it is usually because I have not property considered the basics of the problem. The solution is to tear the problem apart - simplify the problem down to something that is understood. Then, and only then, you can try to understand the more complex question. I started thinking about the basic properties of CBT as a game, so I could look for other games with known mathematical properties.
So how do I simplify CBT? By throwing out components of the game that don't matter to the most basic mechanics of the game. Start with a one-on-one game. Get rid of the Map - no movement, no terrain, no ranges (or all the same range). Make all weapons the same (or consider only one weapon). Get rid of initiative, ammo, heat, critical hits and pilot hits, seperate hit locations (consider just one), critical hits, the distinction between armor and internal structure. (Did I miss anything?)
Now, consider what is left: A mech has been reduced to one big pile of "points", representing how much damage it can absorb before it is destroyed. It can attack and has some probability of doing some amount of damage "points" to another Mech (another pile of points) controlled by another player. Simplified this way, CBT is in a class of point scoring games. In this case a game where you try to score points against the other player, like Hearts. Scoring for yourself or against the other player isn't actually relevant, it just a matter of reaching a particular point total before the other player does.
Point scoring games are EVERYWHERE. I already mentioned Hearts, but I thought there might be a better match, so I kept looking for other games with more in common. In CBT we use a Mech Sheet to keep track of these points ...
... and some card games also involve a board to keep track of points too, like this one from Cribbage. The similarities do not end there: CBT has rules for weapons and movement on a map which affects how weapons can come into play, and dice are used to randomize the results. Cribbage has rules for how cards can be played and the points scores for each play, and the shuffle to randomize the results.
So, what I am (finally) getting at is the game of Classic Battletech has much in common with other point scoring games such as Cribbage. The rules of play are very different. No one would ever mistake the rules of CBT for the rules of Cribbage, but these games share a common mechanic which makes them mathematical cousins. This was the sort of link I was looking for; a link between CBT and a well understood game where the math has already been worked out.
While this describes one aspect of what I was looking for, it still doesn't give me quite what I needed. It did, however, put me on the right track for something important: Metal Fatigue.