## Jan 19, 2010

### Heads I win, Tails I lose.

Akshit took out a coin of his pocket and said to me, 'Heads I win, Tails I lose. I bet half the money in my pocket.'
He tossed and lost. And the game continued for number of times, each time betting half the money in his pocket. We don't remember how many times the coin was tossed or how long the game went, but he lost exactly the same no. of times as he won the bet.
What do you think, did he, on the whole, gain or lose?

1. The first toss was all important.
Akshit must've ended up wid a loss.

Shivang

2. yeah true must be a loss

The base event was the first toss, once lost will take infinite times of winning of bet to get the money back.

4. obvio he lost

5. the 2nd term is less than first in even an infinite series with common ratio<1 so surely loss...

6. He lost it

7. Lost it! the first bet was imp!

8. Sure.. he lost it. It only depends on 1st toss.

9. If he had \$100 in his pocket he would lose \$50 on the first bet but might win \$25 next time and \$37.50 next. The problem has nothing to do with ∞ series.

At each bet he lose 1/2 his principal or wins 1/2 his principal so if P is his principal he has 1/2 P or 3/2 P. After 2n bets he has 3^n/2^2n=(3/4)^n P left. He loses big time. Nothng to do with the rsult of the first bet.