To be clear: I am all for some sort of gating on pet rescue repeats. That said,
How many people do you need to have in a room before there’s a 50% chance that two of them have a shared birthday? There are 365 days in a year (discounting leap day birthdays), so you’d expect the number to be pretty big, right? Nope. It’s 23. It doesn’t matter which birthday the two people share, so the odds change dramatically.
Likewise, assume there are 40 pets that appear with equal probability: 2.5% chance each, whenever there is a pet rescue triggers. Let’s also assume that your guild triggers 24 pet rescues a day. What are the odds you will see four or more repeats of a specific pet in a 24-hour period? Just 0.28%. However, there are 40 different pets in our hypothetical scenario, so multiply by 40 for the odds of seeing any pet four or more times. That gets you 11%, or one out of every nine days. The odds that you will see a pet 3 or more times are a whopping 84%. Five out of six days will have a single pet show up three or more times during that 24-hour period. Probability is weird.