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!
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.
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.
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.