Lets play a game. I know: tic-tac-toe. Regardless of who goes first, who do you think will win? If you have played the game before, you know that the game will end in a draw unless one of us makes a mistake. There simply aren’t that many moves either one of can make. The first player can make 1 of 9 possible moves, while the second player can make 1 of 8. Each turn sees the options decrease by one until the end of the game in 9 moves.

Lets play another game. Poker, in particular Texas Hold’em. Its a lot more complicated isn’t it? You have randomization in the card shuffle which can lead to well over 1,000 starting hands and the pre-flop which can generate something like 1.4 x 10¹² which is an awfully big number. Throw in betting and you have a game that is infinitely more complex that tic-tact-toe. You can categorize the difference between games by their branching factors.

Now take poker. The starting hand alone gives you over 1 thousand branches to start from. The game tree has somewhere in the neighborhood of 10¹⁶⁵. The point is clear. The more complex something is, the greater the number of decisions we have to make. The larger the number the easier it is to get overwhelmed because the tree of potential outcomes have more paths to explore.

Branching factors simply represents the number of possible moves of a game given a position or state. Put another way, its simply all possible paths forward. Imagine a tree diagram which use branches to identify all possible outcomes or combinations in a game or process. Each node on the tree represents a decision path to make and follow. In tic-tac-toe, given an empty grid, there are exactly 9 branches in the tree, one per square. The next level down has 8 branches, one per each remaining square. If you average out the number of branches per turn (level), you come up with a branching factor of approximately 4. That means at given point in time during a game, you have an average of 4 moves, more in the beginning an less in the end.

We can extend this to real life. Given the amount of capital and technology in the world today, it is easier than ever before to create options by adding new branches to the tree. Take for instance Steve Jobs. His interest in calligraphy resulted in a new branch that resulted in the Macintosh computer, which showcased beautiful fonts and proportional spacing. He added more branches by creating the iPod and the iPhone, both of which had been discounted by other players in the computer industry.

This point connects nicely with a dot in the intelligence equation created by Alex Wissner-Gross we discussed earlier. Remember the key takeaway was that intelligence doesn’t like to get trapped so it keeps its options open. I would venture that intelligence likes a high branching factor when it does not have an obvious advantage.

We can define exactly what it is about complexity that causes high branching factors. Complex systems consist of many heterogeneous agents that possess agency. They can make decisions. in response to what is occurring in the environment surrounding them. As these intelligent agents adapt to change, they are capable of creating new actions, which in turn leads to something called emergence, which are novel behaviors arising from the interaction of simple parts and rules of the system. Each new behavior is a new path forward, another branch on the tree. Fueled by capital and technology, the branching factors we face are increasing exponentially.

We see this every day in one of the most complex systems on Earth, the U.S economy. At its core, the U.S economy is a collection of buyers and sellers organized into markets. These markets generate billions of transactions every year, with buyers and sellers exchanging goods and services. Buyers and sellers are intelligent agents (I am purposely excluding AI for the time being) that adapt to the state of the economy through several behaviors, such as adjusting demand and supply which in turn affect price, creating new companies and winding down existing ones, creating new products and retiring older ones, and creating new market segments. Throw in variables such as how to finance companies and you have an endless combination of choices that all play out to drive the economy forward within the rules the system sets, which in this case is capitalism. What we do know is that all of the decisions interact with others over time, further complexifying matters. The branching factor is so high, it is effectively incalculable.

This raises the question of how to deal with such complexity. The short answer is by using past history to create a set of models and rules that are used to guide us in the process of pruning branches off the tree. If the economy is in a recession and your revenue drops in half, you are constrained by what choices you can make while some choices become more likely (layoffs, cutting expenses, lowering prices, etc. ). Perhaps some new branches are added such as merging with another company or declaring bankruptcy (technically they were always on the tree, perhaps they were simply grayed out and not selectable).

Complexity and emergence obscure cause and effect primarily due to delays in decision making. NATO expansion eastward began in 1999 which antagonized Russia. Their final response to this expansion came in 2022 when they invaded Ukraine, not willing to see it become another NATO member. Humans are conditioned to see cause and effect occur instantaneously.

As the branching factor of real life increases, the effects on intelligence are profound. It becomes less about strategic planning and more about adaptability and keeping your options open. Its about the ability to pivot. It also requires a different way of looking at the world. Instead of one lens, looking at the world from multiple angles is needed. Monitoring the environment is not static, it is dynamic. And finally, our worldview, how we believe the world works, needs constant updating and tinkering, as what worked in the past is no longer feasible.