# Sid Meier and Rob Pardo on Probability and Player Psychology

by Brian Leahy, Mar 15, 2010 4:30pm PDT
Related Topics – GDC 2010

In their respective talks at GDC 2010, both Civilization creator Sid Meier and Blizzard executive vice president of game design Rob Pardo discussed the player's perceived understanding of probability in games. In essence, both discussed the fact that players don't understand probability, chance, and mathematics as they relate to gaming.

When designing the combat system in Civilization: Revolution, Sid Meier found himself up against some interesting design problems. His players didn't understand math. In Civ Rev, the strength of units were displayed up front to players before battle to show the odds of victory. For example, an attacking unit might be rated at 1.5 with the defending unit at 0.5. This is a 3-to-1 situation.

Unfortunately, the testers expected to win this battle every time despite there being a 25% chance of losing each time. Sid tweaked the math to make the player win more in this situation. Next, the reverse case was tested. The player had 1-to-3 odds. If they won, the math was functioning properly. They had a slim chance to win and they did.

Sid identified a few cases of interest. When the player was presented with 3-to-1 or 4-to-1 odds, they expect to win. With 2-to-1 odds, the player will accept losing some of the time, but expect to win at 20-to-10, which is just a larger expression of 2-to-1. When the numbers get larger, the perceived advantage grows.

To adjust for this, Sid actually changed the math again so that the outcomes of previous battles are taken into account. He found that if a player lost too many 2-to-1 battles in a row, they would get frustrated. Instead of risking a player shutting the game down, Sid changed the math.

Switching over to Blizzard, Rob Pardo discussed the rest experience system in World of Warcraft and the perception of bonuses versus punishments. One of the original design goals for WoW was to discourage marathon play sessions and avoid grinding. In the beta, to this end, the experience system worked as such:

When a player first logged in, they would earn 100% experience. After a set amount of time in-game, they would only earn 50% experience. This way, they would take a break. This felt like a punishment to players and it was universally hated among the testers. To fix this, Rob decided to do the exact same thing, but play off of player psychology.

Now, when a player first logs in, they receive 200% experience. After a set amount of time they drop down to 100% experience. To complete to ruse, Rob doubled the amount of experience required to level up across the board. The math ended up being exactly the same, but players loved this new system, which would become Rest XP. It was perceived as a bonus, not a punishment.

Furthermore, Rob talked briefly about drop rates for quest items. Apparently, players would get into cold streaks where they went a long time without getting a quest item drop. Instead of correctly attributing this to randomness, they would blame the math or random number generator. To get around this, Rob and his team actually changed the code to increase the drop rate after each kill until it hits 100% and then reset it for the next one.

It's interesting that players don't want to accept math when it doesn't work out for them, but are more than happy to accept it when it rewards them. Purists might dislike Sid Meier changing the match to appease players, but the game became more fun. Blizzard opts to package systems as a reward over penalties and takes a little randomness out of the equation.

• At least in the context of World of Warcraft, things like drop rates that are expressed as percentages are supposed to, at least nominally, represent rarity. However, absurdly low drop rates betray that representation in the player's narrative. It's one thing for The Magical Foo to be an extremely rare item, possessed by only a few of the Miremurk Shamans. It's another thing entirely if I have to kill every Miremurk Shaman five times over before (probably!?) finding one. Sure, the mechanics of the game are internally consistent, but the genocide I've just committed on the Miremurk Shaman population breaks immersion somewhat. The drop-rate on that item is so low that it ceases to be a reasonable representation of rarity, tearing away internal narrative and leaving just the dice-game hiding behind the curtain.

• The biggest problem that I've found with people is that they don't seem to realize that probability has no memory. You could flip a coin 100 times and have it come up heads 100 times in a row. The probability of that occurring is very low (0.5^100), but it can happen. And when it does happen, the chance for heads to come up on the next flip is still 50/50. It doesn't have a higher chance to happen because it happened 100 times before and it doesn't have a lower chance of happening because tails is "due" to come up.

That said, no one likes being on a losing streak, so it makes sense to stack the deck in the player's favor in an attempt to minimize the losing streaks (unless you're making casino games).

• Anyone interested in this subject needs to pick up and read the book "The Black Swan" by Nassim Nicholas Taleb.

http://www.fooledbyrandomness.com/

If you want to make games that involve chance, having a good understanding of how people perceive the predictions they make and how they create narratives to explain away their wrongness when their predictions fail. "I was almost right", "If it wasn't for XYZ, I would've been right", etc...

That book blew my mind. I'll never be the same after reading it.

• I understand perfectly well how I can lose even if I have a 90% chance of succes. I still expect to win because I would never lose if I actually had any control over the situation. Likewise, it isn't abnormal to win even if the chance of winning is 10%, because when I am in control in games I often pull that off.
It's got nothing to do with math. Maybe Sid Meier should consider that coin tosses are not a good gameplay mechanic.

• if they realized the problem and had to explain it with percentages, why not just put it as a percentage chance to win in the game?

• So basically they figured out that raw percentages aren't fun, so they tweaked the gameplay to fit players expectations and make the game more enjoyable.

It's nice to see that they actually consider this, and just don't rigidly stick to a design.

• If you told test subjects they had a 87% chance of surviving a jump from the 6th floor, most would jump without hesitating. This is a pure psychological issue. Humans have always had hope and always pushed their luck.

Especially in a very bad situation, any human will catch at a straw, even if his chances that it will actually work out are extremely low.

Ergo, the more desperate a situation is the more hope is out there even for a very low chance. The higher the chance that something has (about everything above 60%), the more confident we are that we will be lucky, even if math dictates an extremely low probability that this will recur every time.

• I think Sid's points were extremely narrow and not applicable to other games. Also, this time he seemed a bit out of touch? It was weird.

For example, he talked about using a text box to describe dancing bears, and how you don't have to show dancing bears for it to work, so it saves you money and time. But Civ Rev actually includes animated dancing bears. Really. http://www.youtube.com/watch?v=vjGjv-t6_0I

Also he seriously talked down against a narrative structure that involves a player that gets somewhere only to find out that the original questgiver was the bad guy and the whole journey up to that point was a distraction. He says that this is a terrible idea because the player feels like the time has been wasted. Hey, guess what the main plot twist of Bioshock was? (Oops, spoiler alert.)

I have tremendous respect for Sid Meier but his was very underwhelming this year.

• I had to take probability for my math minor for college. It was a fun class and I really liked it. I would've taken statistics also (the next class), but I'm set for graduation and I'm tired of school.

After taking a few psychology clases, I'm suprised it took this long for them to figure this out.