As I sat at the table staring at my Daimyo army, two options ran through my mind. I could continue to play defensively and try to eke out an advantage by burning Ben’s territories and hope to lure him into making a mistake, or I could go on the offensive and risk everything on a single attack on his Daimyo castle. On one hand, if I waited, I could try to make a comeback and potentially regain the advantage eventually, but on the other hand I could just take a roughly 20% chance at victory right now. After considering both options, I picked up the piece and made my decision.
The situation: I was playing a game of Shoudo with Ben, and I was losing. Early in the game I had lost one of my three armies and the game had gone downhill from there, with my Daimyo’s position slowly becoming weaker as Ben tightened the vise around me. I was faced with a tough decision, as often happens in Shoudo and any other well-designed game. If I wanted to win, I had to solve an intricate puzzle of possibilities and probabilities.
This kind of difficult problem is not restricted to just games. Often in life we are faced with similarly challenging puzzles – perhaps you’ve had to decide whether to sacrifice time with your family in favor of work, or to choose between finishing two tasks before you hit a deadline, or simply to decide whether to take a new route while driving or brave traffic. Without proper problem-solving skills, it can seem impossible to determine the best choice in many of these scenarios. Whatever shall we do?
Obviously, we should play some board games. No, seriously. While this sounds like a joke, games are, in my humble opinion, one of the best ways to cultivate many skills that are useful elsewhere in life, and problem analysis is one of them. Since games present us with so many of these challenging problems in so little time, and allow us the ability to repeat these puzzles over and over again with different methods, they are the perfect training ground to develop an intuition for analyzing hard problems. Humans learn by pattern recognition, and by developing that recognition we can become much faster than even computers (well, the ones that aren’t using neural nets) at solving complex problems.
So far, we’ve established that intuition is good for problem solving and games are good at building intuition for problem solving. However, this wouldn’t be a very useful article if all I did was tell you to go play a bunch of games and hope your intuition improves. After all, you’re not going to learn anything unless you know what to practice. So, what do you need to do to figure out the best solution to a problem? Ultimately, it comes down to mathematical analysis.
Alright, now it’s time to get out your math hats, because we’re going to be working out some probabilities and talking through the story I told at the beginning of the article to figure out which decision I should have made.
First, we need to establish what our goal is – what is the desired outcome of this decision? In the case of our story, we want to win the game. Thus, the option we choose should give us the highest possible chance to win. Note that I said highest possible, not highest. Obviously, if there was a choice that could give us a 100% chance to win we would take it, but such an option isn’t available. Looking at the choices we do have: we can attack Ben’s Daimyo castle with a roughly 20% chance of victory, or we can prolong the game and try to claw back into the lead. The first option doesn’t seem great – one in five isn’t great odds, so let’s look at the second case. In Shoudo, the player with more armies can generally burn more of their opponent’s territory each turn, resulting in a greater advantage each turn. Thus, our odds of victory actually decrease as each turn passes, since the disparity between our strength and our opponent’s widens each turn they have more armies than us. Thus, while we can’t give the second option a concrete percentage, we can assume that it is less than 20%, since our odds decrease each turn after this one. Based on this analysis, it’s clear what we need to do: attack!
Wait, you’re still here? Did you want to hear what happened in my story, whether my desperate attack succeeded or failed?
It doesn’t matter.
The outcome of your decision absolutely matters in the context of the game or situation you make it in, but you must be careful not to put too much weight on whether your choice worked. Far more important is the reasoning that led you to that decision. If you can prove that what you did was the most likely plan to succeed, then it doesn’t matter whether it succeeds or fails!
Thanks for taking the time to let me lecture you about problem solving; next time, we’ll talk about how you can learn to manipulate – I mean, influence – people through playing games. Until then, happy gaming, and may all your decisions be examined ones!