### Coin Tossing - Lucky Dealer

Source: Credit Suisse Placement Test at IITB

Problem:
You bet 1\$ on a coin toss. A win gives u 1\$ gain, a loss gives you a 1\$ loss. The guy tossing the coin gets what he wants 80% of the time. You start with X\$. Find strategy so that you always win.

Update (Dec 04, 2010)

Assumption:
Note that the dealer is just an employee of the casino. You can take him in your group and make an offer he cannot refuse.

Solution: Posted by Gaurav Sinha (chera) (CSE IITK 1996 Graduate, Now working at Indian Revenue Service) in comments!

1. I donot get the problem, whether it is a game in which we switch sides to toss the coin and we call our sides and in that too when we toss we get 80% of time what we called for. OR there is a dealer and u have to go to him, make a call. but the dealer is able to get 80% time what he wants..

and does strategy means how shud we divide our x\$ and bet on different ocassions to always win.?

2. possible if coin tossing guy is only an employee of the betting game shop, and has no share in profit/loss of the shop. Then u can have a pact with him that in case u win u will give him a\$ and in case u lose, he will pay u b\$.

Expected gain to the guy is
0.8*a-0.2*b > 0 if a > b/4

choose any a,b so that a<1, 1<b<4a
e.g. a=0.5 and b=1.5.Then u get 0.5\$ if u win and u get 0.5\$, if u lose. expected gain to guy is 0.1\$.

3. @sumit. I too think this is a ridiculous problem. Could not understand it. Thought smarter people would help me out.

@chera. Interesting. Nice thought :) Thanks