transcription: button that says "50% chance to get a cat girl, 50% chance to become a cat girl". pictured below: a catgirl with a catgirl on each arm

win-win

You can still yuri if you're a cat girl, so absolute win-win.

Then, you push the button a few times more and you feel a fundamental change. Additional voices, as before, but they’re closer now. Uniquely alluring. Resonant. Begging for more company. The button becomes lighter with every press. Harder to find. A maelstrom of fresh sensation and yearning overtakes your every pore with each delicious press of the button.

There are no longer any voices. Which is not to say that it has gone quiet. It’s grown louder than anything you’ve ever heard before, a cacophony of pleading, prostration, and bliss. A cat500girl500 has excellent hearing

I would have interpreted this as "50% chance of becoming the catgirl belonging to whoever got the other option." Shades of this Oglaf comic (NSFW).

What the fuck. (Very well-written, but what the fuck)

Are they independent chances? How many times would you need to hit the button to guarantee both effects if the chance is rolled independently each time?

I press it that many times.

My favorite type of compliment!

(◍＞◡＜◍)⋈。✧♡

It's okay. There's nothing in the rules that says I can't shred them like barbecue and then go and do whatever the hell I want to do.

anywhere from two to infinity times but I think you are down around a 1% chance of getting the same outcome six times in a row

That's a chance I'm willing to take :3

Your chance of getting a successive string of a single particular result is 0.5^n, where n is the number of presses.

The chance of getting a successive string of either result is 2*0.5^n.

Chance of reaching N presses without being a catgirl with a catgirl on each arm:

The number of presses required to reach a given probability is 1 + log base .5 (p)). If you only have natural log available to you that's equivalent to 1+ln(p)/ln(0.5).

So the presses required to hit a 1% chance is 1+ln(.01)/ln(0.5) or 7.64 presses.

EDIT: Sorry, didn't read the original text closely, thought that the button either turned one into a catgirl or provided one with the two catgirls, whereas it probably means that one gets only a single catgirl.

this is the correct yet slightly less fun way to say this yes

like the owner of a catgirl wouldn't let ger play with other catgirls

Which half is which half

Woof c: