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.

The probabilities don’t add like that. For example, the 25% chance of breaking even through a winning streak once you lose twice must be multiplied by the 25% chance of losing twice. Also, you’re not counting all the possible sequences of wins and losses that would result in breaking even.