Playing games has helped me grasp the variety of settings where applying probability can be valuable. More specifically, it has aided me in getting a handle on how to use probability to assess acceptable risks and then accept losses given these risks.
I majored in math, so I love to see where I can find aspects of math in life. As it turns out life is pretty obliging when it comes to probability. I quite often see this area of study playing into my everyday life.
The probability of certain events occurring dictates the cost of insurance. There is a probability that we win the lottery or get in a car crash, or contract some disease based on our actions and environment. Large portions of finance are run off of the likelihood of default and the severity of such events.
It’s always good to consider probability when it is practical to do so. Playing games has helped me grasp the variety of settings where applying probability can be valuable. More specifically, it has aided me in getting a handle on how to use probability to assess acceptable risks and then accept losses given these risks.
Dice, Dice and More Dice!
One classic game that comes to mind when considering chance is Mario Party as well as pretty much any dice rolling game. I know people that will write these off as mostly luck and will not play them for this reason. It was always a little easier for me to get into Mario Party because it has clear elements of skill amongst the luck of the roll.
At the end of each turn, the minigame competitions for coins were for the most part skill-based which bolstered this feeling of efficacy. This was the aspect of the game that captured my attention the most. If I could win all these tests of manual dexterity then I could at least say I did the best I could, mostly ignoring board game antics.
At the end of each turn, the minigame competitions for coins were for the most part skill-based which bolstered this feeling of efficacy.
However, as I played more I started to analyze the board game aspects more heavily. What was the positioning that gave me the best opportunities? I stopped simply blaming bad rolls for messing with my game. It is always easy to blame bad luck. The moment I roll a one I want to forget the last three high rolls that got me into a good position in the first place. But once I gave more attention to the full board and open opportunities it no longer became a game of pure chance with mixed in elements of skill, and I started to appreciate the value of calculated risks.
From this sensation I moved to games such as Parcheesi and Backgammon. Both these games feel like heavily luck-based games at first glance. Again it can be easy to blame luck when the opponent hits some double to kill a pawn and instantly zoom around the map or when I cannot pull the number I need to get through an opponent’s blockade in my home territory in Backgammon. However, I know it is easy to mentally escalate continuous unfavorable actions in a compounding rate of frustration, disregarding the positive “anomalies” that I am blessed with each game.
However, I know it is easy to mentally escalate continuous unfavorable actions in a compounding rate of frustration, perhaps disregarding the positive “anomalies” that I am blessed with each game.
I’m not going to say there is no luck; there is dice rolling which means chance is involved and thus the omnipresent essence of luck. However, to consider the game an experience based heavily on chance bypasses the value of calculated risk. When I put a piece out there unprotected there should always be consideration behind that.
However, to consider the game an experience based heavily on chance bypasses the value of calculated risk.
What are the chances I get hit? If I get hit, what are the chances I can retaliate? How much of a setback is that lost pawn for me, and what about that retaliation for my opponent? Do I have a better move? Does this move set up something that is very valuable given I do not get hit?
It’s all about balancing those risks and rewards. Sometimes, when I double check my math, I realize I am just being ballsy for the sake of being ballsy and the reward is minimal. But sometimes I go out on a limb, praying my opponent doesn’t get a certain number because I know the rewards of the positioning I am setting up.
Calling something a game of luck implies there is no real better player… an idea that my mother has disproved to me many a time in these board games (arg, math major foiled by years of board game calculations and motherly intuition). Looking at these systems that involve chance with a lens towards probability allows us to better identify when we make the right choices and it was in fact luck that made us lose, and when we should have adjusted our strategy (or even when we won, but not because we made the right call).
Care About Small Percentages
Perhaps one of the lords of calculated risk in my gaming history, is the Fire Emblem series. This is a strategy series where if one of the characters dies on the battlefield, they are gone for good (permadeath). If I don’t consider every one of the little 1-5% critical hit chances (which cause 3x damage, and often imply death), someone is going to get picked off.
This is an easy trap; with small percentages it is simple to think that these unlikely occurrences won’t happen. We want to write off a 1% as a 0%, and that is a fallacy. Especially with high frequency actions, that 1% is likely to mean something and it is important to play accordingly. The 1% might mean 1 in 100, but when we test that 1% over and over again we need to open our eyes to the probability within the system, not a single event. Alone, it may only be 1%, but if in every level we can expect 50+ battles, the cumulative probability starts to become quite likely.
This is an easy trap; with small percentages it is simple to think that these unlikely occurrences won’t happen. We want to write off a 1% as a 0%, and that is a fallacy.
I cannot stop every random hit or critical but I can do my best to minimize opponent opportunities as well as minimize casualties. I can play heavy armor guys against sword masters so a critical is not going to be fatal for example.
The game is all about these calculated risks. How can I progress most effectively without giving away easy opportunities for my opponent? When all is said and done it is important to remember that they are, in fact, still risks and people may still get picked off even with the best preparations.
A similar phenomenon in Pokemon arises when trying to run the battle tower. No matter how much the party is built to take whichever dangers, when victory rests on the shoulders of many repeated battles it becomes likely that an unlikely event happens. For example, two pokemon get one-hit KOed (and let’s be honest, the computer cheats in pokemon).
…when victory rests on the shoulders of many repeated battles it becomes likely that an unlikely event happens.
One-Sided Benefits and the Folly of the Big Win
The risk in Fire Emblem helped elucidate another component as well. Just as the opponents have a chance to critical, so do I. So why is it that I don’t feel ecstatic when I get critical hits as a reciprocal of the dread I feel when one of my allies is tossed aside by one of the 2% chances.
Well, I don’t build my life around a big win. On my turn, I am planning out the plethora of options considering what will leave me in the best position to stand strong on my opponents turn. Under rare circumstances does the thought, “Hm, well if I just land a critical on this guy, I should be able to sweep up these other guys to achieve success.” That would be like buying lottery tickets to the point of financial ruin or investing my livelihood into a single company in the stock market. It’s just not a smart thing to be doing.
Though, I must admit, some of the greatest moments in gaming come from those times that you have run the numbers, know the shot-in-the-dark all-in strategy is your only chance, and the fates are on your side with some perfect rolls or heart of the cards. But this shouldn’t be the norm.
Generally, if those critical hits come about, then hooray! But I’m not building a strategy around them. On the other hand, the opponent’s critical hits are game enders. I restart my play (often losing 10-30 minutes of gameplay) and head back to the drawing board to consider my folly. This adds to the phenomenon where I feel like the opponent’s low percent chances are unluckily arising far more, since my low percent chances are merely minor victories that aid in a plan which doesn’t hinge on the big win.
This adds to the phenomenon where I feel like the opponent’s low percent chances are unluckily arising far more, since my low percent chances are merely minor victories that aid in a plan which doesn’t hinge on the big win.
The End… For Now
So these are some of the insights I’ve stumbled on with gaming. Let me know how you feel about chance and risks in gaming. Do you think there is a lot of room to really be good at games that rely heavily on chance? Do you enjoy playing Mario Party and similar games in a competitive setting, or do the chance aspects of the game leave it simply in a realm of casual party games for you? And have you ever considered altering the rules where feasible to cajole elements of chance into cooperating more? For example I know my brother enjoys playing Settlers of Catan with a deck of cards stacked with even probabilities according to the numbers.
Come back next time for Part II, where I will further discuss how these elements of risk versus reward and general probability have cropped up in my life. Until then, game on and learn on!