I recently acquired my first Mr Pinchy and burned through his three wishes without getting the pet. Earlier I caught my second Mr Pinchy, and I was curious about what my chances would be of getting the pet out of the six total tries available to me.
I used the following formula to come to my findings:
1-((F^T)/(O^T))
F = the failure rate (in other words, the chance of NOT catching Mr Pinchy, which is 4 of the 5 possible outcomes)
O = the possible outcomes, which is 5 (gift, pet, furious, benevolent, blessing)
T = the number of tries.
NOTE: this formula could very well not be accurate; even though I'm pretty strong with math, probability is not my forte. If I've done something wrong with my figures, please let me know.
Using the formula I came up with the following odds to catch him:
1 wish: 20%
2 wishes: 36%
3 wishes: 48.8%
6 wishes: 73.8%
9 wishes: 86.6%
12 wishes: 93.1%
15 wishes: 96.5%
18 wishes: 98.2%
21 wishes: 99.1%
Keep in mind that this only reflects the wishes you have left, not the ones you've already used. In other words, if you've already burned through 4 Mr Pinchies and you have just caught your 5th, you have 3 wishes coming to you for a 48.8% chance of catching him, rather than the 96.5% chance reflected for 15 wishes.
