Actual interview brainteaser at a top flight shop

I didnt have time to read thru all the posts but if someone answered it right, i apologize. There are a few assumptions we must make but based on your guidelines. I be lieve the answer is to bet $20 as initial. This is assuming that the 2nd flip is a loss and third is a win, to win the game we must obviously win three consecutive times. therefore bet 1 is $20(a loss), bet 2 - $20(a loss), bet 3 -$20(win), bet 4 -$40(win), bet 5 -80 (win). losses = $40, wins = $140, profit is 100 (double my money) and i doubled my winning bet sizes.

cheers
 
Hi sjfan, thanks for the brainteaser. It's fun and it help keep our brain sharp for the ultimate brainteaser--how to double your capital in the market within a year.

Merry Christmas!
 
Quote from Pension_Admin:

Hi sjfan, thanks for the brainteaser. It's fun and it help keep our brain sharp for the ultimate brainteaser--how to double your capital in the market within a year.

Merry Christmas!


You forgot to add--- MORE THAN ONE TIME to your post.

otherwise, bravo!


AC
 
This is a quick guess but this just looks like Kelly betting. If we want to optimize our portfolio growth we should be 2p-1 where p is the probability of winning. Like I said a quick guess, calculate p yourselves.
 
Quote from mtiano:

This is a quick guess but this just looks like Kelly betting. If we want to optimize our portfolio growth we should be 2p-1 where p is the probability of winning. Like I said a quick guess, calculate p yourselves.

Except that p changes with time. Your probability of winning the game before the first flip is different than after the first flip -- the information you learn changes your win/loss probability.
 
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Hey sjfan,

First you give us the incorrect rules for the game and then tells us that the correct answer is incorrect. Hopefully you were not the interviewer for this very question because you would have some very confused applicants. Do you double check your prices before submitting orders? Were you involved in any of these incidents below? Just curious.

Typically, a fat finger can be spotted by a `spike.' An abnormally large number of transactions hit the market and get executed at the start of the spike. Fat finger trades have a long history charted by The Times (February 2005): A broker tried to sell 15,000 shares in music publisher EMI at 280¼p but instead placed an order for 15 million in a transaction worth £41.5 million.

April 2003: A trader accidentally bought 500,000 shares in GlaxoSmithKline, the pharmaceuticals group, at £13 each when the market price was 70p less.

November 2002: A market maker confused the price of Ryanair shares in euros and sterling, sending the London quote up more than 61 per cent, from 404.5p to 653.7p.

October 2002: A keyboard error at Eurex, the world's largest derivatives market, halted trade for three hours and caused its index to fall 500 points after an unidentified London trader entered the wrong price during a futures transaction.

September 2002: A Eurex trader intended to sell one futures contract when the DAX, Germany's index of leading shares, reached 5,180. Instead, he sold 5,180 contracts, sending the market into a free fall. Five hours later, the exchange announced the cancellation of a raft of other trades.

December 2001: A trader at UBS Warburg, the Swiss investment bank, lost £71 million in seconds while trying to sell 16 shares in Japanese advertising giant Dentsu at 600,000 yen each. He sold 610,000 shares at six yen each.

May 2001: A trader at Lehman Brothers mistyped a trade and wiped £30 billion off the stock market. He wanted to sell £3 million of stock but typed too many zeros and sold £300 million. The bank attracted a £20,000-fine.

November 1999: A dealer put his elbow on the keyboard and inadvertently placed 600 trades in 16,000 of the Premier Oil's shares at 19p, worth more than £1.8 million.

However, the record in fat finger trading is still held by a trader of Mizuho Securities, the broking arm of the Mizuho Financial Group of Japan. The trader had managed to sell shares worth £1.6 billion in a local recruitment agency, J-Com, which had just been floated and had a market value of little more than £50 million. The December 8, 2005, "sell" order, was mistakenly placed for 600,000 shares, despite the fact that J-Com had only 14,000 shares in issue. The order had created chaos in the market and had resulted in a 301-point fall on Japan's main stock market index, the Nikkei 225.
 
There is a fundamental logic error with this problem. If I understand it correctly we must find the initial bet x such that, if you start with a $100 bankroll and double x each time the coin comes up heads (a win) you must achieve a final bankroll of $200 *IF* you win, where winning is defined as achieving 3 heads before the 3rd tail in a set of 5 tosses.

Let's look at the simplest case, 111, i.e. you just get the 3 heads initially. The equation can only be

100 + x + 2x + 4x = 200, i.e. x = 14 2/7.

But this value doesn't work for all (any?) of the other cases 0111, 1011, 10101 etc.

I really can't think of a way round this.
 
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