Just wanted to share because this type of information helps me process things when farming for rares/starters:

The odds of catching a starter are .5% or 1/200 (not including the guaranteed 2000 number)

For 50 trials the odds of catching one are:

22.17%

100 trials:

39.42%

200 trials:

63.32%

300 trials:

77.77%

400 trials:

86.53%

500 trials:

91.84%

The graph for these is logarithmic.

The odds of catching a rare is 1.25% or 1/80:

For 50 trials the odds of catching a rare are:

46.68%

100 trials:

71.57%

200 trials:

91.92%

300 trials:

97.7%

400 trials:

99.35%

500 trials:

99.81%

So what you’re saying is, the odds increase every number of trials?

Well mathematically they do, in a way hard to put into words, because hatchlings are .5 percent but if you try twice that means you have 2x the chance to see it since you tried twice, not that the percent goes up, but you have a better chance since instead of trying one times you try it twice, Like lets say you have a box full of beads, and you are looking for a red bead but there is only one and there are 200 beads, so you draw blindfolded, and if it isn’t the red one, put it back. You draw once, dont get it now put the bead back, now you try again, which means you have double the chance even though its still the same .5 percent chance, eventually, you will get it but it may take hundred, even thousands of attempts (even though we have a counter) but it is impossible for someone to never see it if they keep trying because the odds are they are guaranteed one after thousands upon thousands of attempts