Chance, or say Randomness, is important in a game. Why is is important? Because randomness means uncertainty. Uncertainty means surprise. Human love surprise. For surprise there is two scenarios. One is when you stayed at home, you wife came back and told you: “Our lottery got the first prize!” Second is when you looking at the lottery show, your lottery matched every number on the screen. Which is is more exciting to you? Personally, I prefer the second one. The different between these two is that the second one is involved with anticipation before surprise. For human beings anticipations strengthen emotions.
For the followings, I will talk about the chance in anticipation → surprise models in games. The most common example is critical hit. “40% chance to critical attack.” This sentence tell you the possibility of surprise. Think about this moment: your character deployed a critical attack; Blood splashed from the enemy body; Even the enemy was taken down with a bullet time. It is so exciting that I make a critical attack! I am so powerful! And then think about another moment. The boss had only 20 HP left and your attack was 15 but only had 1 HP. You pressed the attack button and begged a critical attack. Nothing special happens. The boss killed you for the next attack. Oh, @#$%. I had such a bad luck. It has been such a long time that I can’t deploy a critical attack! It ruins me. My former mistakes of wrong strategy choices were not important. It is just my bad luck. Chance involves an significant part of the above situations. For the first one chance gives you a reason to anticipate and receiving the more exciting surprise. For the second one, chance gives you a excuse to blame and to hide your own mistake. So you are always doing good, the game is always fun.
It works very well in single player experience. However, in multiplayer arena experience, such as DOTA, your good luck means the opponents bad luck. So if I lose a game simply by bad luck so obviously, then it means all my efforts and strategy seem to be not important in the game. Audience and players tend to make a conclusion that the game is judged by chance instead of ourselves’ skills, which is not fun. So there is a clever modification to the chance system, it called “Faked chance”. It means the current chance of expected effect depends on how long you do not have that effect. It makes sure that the game is in balance most of the times with a cost of surprise. Another extreme is “deploying a critical attack for every 3 hits.” It is totally anticipatable.
In summary, in single player games. Chance is a great way to generate the fun of surprise and a great way to capture the players for more times and spending on the game. In multiplayer arena games, chance is a trade-off between balance and fun of surprise.
Reference: DOTA uses “Faked Chance” for critical attack. World of Warcraft uses a lot of “anticipatable critical attack”. And I guess that XCOM uses “Faked Chance” for hitting. It means when one of your soldiers hit the enemy by chance, other soldiers’ hitting chance will be diminished.