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!
~Dylan
Turn Based Living 
I have a tendency to prioritize moves with 100% accuracy (or as close to 100% as I can get) whenever possible, even if I can tell that on average it’s not the best option – mitigating frustration is worth a lot to me. I’m also a bit of a save addict, so randomly dying is unlikely to set me back by too much, but it does mean that in games where you can only save at the beginning/end of an area, I become extra paranoid about dying due to ‘bad luck’.
However, playing DnD has taught me to accept that, sometimes, it’s just better (and even more fun) if you widen your selection to include things with a lower chance to hit. Sure, I still go for the more accurate options, but I’ve stopped wishing everything was magic missile or has miss damage, since those small numbers often don’t mean much.
Hey Flo, thanks for commenting. Soooooo does that mean a lot of Swift? 😉 There can definitely be something comforting about certain progression provided by 100%, and many times it isn’t necessarily the wrong, but it is always good to put some extra thought into. Try to understand where that threshold is for the value of mitigated frustration vs the probability of success. Sounds like DnD is helping out on the front 🙂
~Dylan
Awesome entry. In contrast to the previous reply, I’m an all calculations kind of guy. If something is half as likely, but more than twice as effective, I’ll do that, and trust that over time, I’ll be rewarded more than the surer option – UNLESS – the “twice as effective” part isn’t relevant. For example, in D&D of course I’ll go for a more accurate attack against a monster with few enough HP that my Str modifier kills it.
Actually, one of my weaknesses as a player is maximizing impact, without looking at the broader picture. For example, when I play Magic, I often make the mistake of going for yet another 2-for-1, when there’s a play that would lose me a creature or two, but win me the game.
Always good to hear of people keeping the numbers in mind. I’m probably a little between both of you two, depending on my mood. Sometimes the law of large numbers is too irresistible, but sometimes there is comfort in that higher accuracy strategy.
Understanding the context that the probabilities play into the whole situation is quite important as well. If you are playing a game, for example, that has been designed in a way that the 100% accuracy route leads to victory, than it doesn’t matter how good the trade off is for a lower accuracy attack, because the variability presented by the loss of accuracy is not needed… like what you were saying with the – twice as effective being not that relevant.
Also, the law of large numbers can be deceptive when you consider something like the battle tower in pokemon. Even if some lower accuracy attacks may have a higher expected value, it just takes one loss to lose everything, so those battles mean a lot more than the macro concept of “doing well in the battle tower”. High variability will screw you in the long run, but low variability probably won’t be enough (otherwise that wouldn’t be super fun)… so it comes down to finding that balance of having a solid strategy that can win most games with high likelihood, and then having those cross your fingers skills for the times the rest just falls through.
~Dylan
I’m not a fan of that odd-based system. One problem is that even high percentages hurt when the object of it is done infrequently. A 50% drop rate for something that takes three to four hours a run to complete can be horrid in practice, especially if you have multiple people who need the drop. Once they start getting into the single percentage rates, it becomes sadistic. This is one of the reasons I no longer play MMOs.
I agree with large numbers, too. When I played FFXI, the single most vital stat in average combat was accuracy. Only when you could get it up to the point where the math had you hit an acceptable percentage would it be worthwhile, and then you could worry about adding attack or damage powers. Without it, no matter if you reached your cap and you could make single hits hurt, you weren’t of any use because damage over time was compromised. This made it impossible for many classes to use anything but the weapon they were the most highly rated for, because they took a huge accuracy hit otherwise.
To be honest, I think I’ve grown out of any desire for math-based risk in games. If you lose fights due to a random number generator rather than strategy, it isn’t compelling gameplay to me.
Thanks for commenting! I don’t know how I missed your comment, sorry I didn’t reply sooner (maybe Dust approved the comment and I just didn’t see it). I’ve never really been that much of an MMO player so I can’t speak directly to that, but I get that killer drop rates can suck. I remember playing Phantasy Star Online 2 (offline) and just running the same place over and over again just to go for the 1/16th chance I had for the boss drop… that game was even more frustrating because drops were based on your type, which was set in stone based on your name, so I couldn’t even get most of the good stuff I wanted. MMOs kinda beget that system though. As long as there are people and guilds willing to dedicate a large chunk of time to the games, the designers need some way to keep people playing, and that is an easy way to extend the gaming life. I do prefer a crafting style system though where you get things more assuredly but need more of them to make an end product.
Interesting note on FFXI. It’s always a little weird when they allow customizability but with crippling deterrents… it often leads to a choice between style and value optimization; while I think this is weighting will pop up in most games, I think some do a much better job at balancing options.
So, do you just try to steer clear of games with math based risk? I get what you mean, but think your comment slightly undermines the entwined nature of strategy and the random number generator. And I do think that having probabilistic risk it games often adds to the feasible layers of complexity. In Pokemon, for example, it would be hard to create the layers of complexity without accuracies and status ailment accuracies. Though I too would prefer the certainty of a game like Advance Wars (though it still has a luck component) versus a Fire Emblem from time to time.
~Dylan
Yeah, I steer clear of them. Mostly for the reasons you’ve already said, but if there’s a high level of RNG, you don’t wind up strategizing as opposed to fixing problems. Like say you get a high damage weapon with thirty percent accuracy. No one will ever accept it as it is, so you have to try and fix it. Maybe you give it to a guy and the guy can swing it four times instead of one. Or you give it to the low damage/high base accuracy character, and the weapon equalizes to a good level. If you can’t fix it, you junk it. But you have to fix for the RNG first, and then what happens after.
I don’t like that kind of play. Especially if it’s something that can cause a restart of a thirty minute long battle.
That’s an interesting point. I’ve never thought of it strictly in the “fixing problems” mindset, but I can definitely see that argument. I generally don’t like don’t like RNG much at all. If there is high variability it often ends up being obnoxious more often than not. I think it can sorta be used in interesting ways from time to time… For example, in Realm of the Mad God getting to level 20 is quite fast and many of the max stat increases aren’t terribly hard to find so it could be used for players to choose if they would rather play around with their max stat characters or do the quick restart. And a somewhat interesting culture of Pokemon breeding evolved out of the IV system. I think that the system is sort of interesting because you can breed relatively fast but there is a ton of variability, so there is a whole strategy to conceptualizing match ups and deciding what stats to cut your losses on. IVs and EVs are neat in that they aren’t overly obtrusive… many people have played Pokemon and not given them a second thought… they just add a layer of depth if you are interested in delving deeper.
Fire Emblem is its own beast. There is a lot of RNG, but it comes together in a very manageable way in my opinion. If you level characters appropriately and are very careful with your strategies, you should be able to nearly assuredly trump random flukes, on normal and for the most part hard. The super hard difficulties are masochistic and are not necessarily good game design (though I like that the choice is there; there is little reason to not have them as an option besides perhaps if it takes some feeling of accomplishment away from those that triumph over the lower difficulties). I couldn’t tell you what made me bother with the frustration involved with beating ludicrous and ludicrous+ in the most recent game… at the beginning, especially, it is RNG at it’s most destructive. I guess I wanted the game to push me to care about my characters and class choices more than hard had.
~Dylan