The Cost of a Waifu in Star Ocean: Anamnesis

I was curious about gacha costs in this game, so I did some math to calculate how much I should save to get a particular character and figured it might be useful to others. This math makes the large assumption that you only care about getting one specific character from an event banner; obviously the more characters you’d be happy with from a banner, the more likely any pull wll be “successful.”

The probability of getting a particular featured ace from a regular pull is 1%, and from a tenth pull is 3%. So the expected value of a 10-pull is 0.114 waifus, or put another way, the expected (average) number of pulls to get 1 waifu is 8.8 pulls or 44,000 gems.

But talking about averages can be a little misleading. Here’s a table that shows the chance you get your waifu after N pulls:

So even if you save up, e.g., 50,000 gems for 10 pulls, there’s still a 30% chance you won’t get your waifu. If you want to avoid a lot of negative feelings, be careful and try to minimize up your expectations for pulls.

EDIT: There’s been a little bit of confusion, so I thought I’d clarify how to use the table. The chart is used for advance planning. You pick a chance and cost that you are comfortable with, understanding exactly what the chance of failure is, and ideally appreciating that no matter what you do that the chance of failure always exists.

If you’ve already pulled, say, 10 times, the chart does not say that your 11th pull has a 73.6% chance of succeeding.

This is called the Gambler’s Fallacy and is a totally different concept. Every 10-pull has 11.4% chance of succeeding that never changes; the chart just tells you that you’re in a group of the 30% unlucky folks who failed to succeed after 10 pulls.