Inertia Posted:

I’ve thought of something.

To make simple bumume the win/lose chance is 50/50

Immediately after the first loss, I have a 50% chance of breaking even

after the second loss, 25% (2 wins in a row)

after the third, 12.5% (3 wins in a row)

and so on

So after the first loss, I have (50+25+12.5+6.25+...) % chance to break even if I keep playing to infinity. That adds up to almost 1.

Immediately after the second loss, (25+12.5+6.25+3.125+...) %. which adds up to almost 50%

3rd, ~25%

4th, ~12.5%

and so on

Reverse Zeno’s paradox?

my head hurts again.

srtop it. This makes my head hurt more and I don’t want to dig up my statistics notes But I do remember that you can’t add them like that, that’s not how it works. The other numbers are right though, two wins in a row [(.50)(.50)], three wins in a row [(.50)(.50)(.50)] are figured out in this way. But basically if you had a 50% chance of winning you would win ~50% of the games. The more games you play, the closer you get to a true value of 50%. (you might flip a coin 10 times, and get 6 heads, that 60%, not very close to 50%. If you fliped it 1000 times, you might get 525 heads, that’s ~52%, and a lot closer)