Coin Tossing - Lucky Dealer

Source: Credit Suisse Placement Test at IITB

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)

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


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