a little math problem
on Fri Mar 20 22:27:49 2009, Shaft snarfled angrily
Ok, a hypothetical situation that I would love some help on. Here is the premise.
I would like to know the chance that one could get 8 correct guesses in a row based on a coin flip, 50% scenario. To take this farther, lets say each day a person is able to make three guesses each one having a 50% probability of being right. How often can we assume that an 8 correctly picked streak will happen, once a month? once every two months?
Now lets take it farther.
A person bets one dollar per 50% coinflip. If a loss happens, the result goes back to $1, the person can never go below $1, if the person wins, they win 90 cents. Thereby giving them $1.90 This $1.90 is then bet again at 50% and if won, gets a 90% return, if lost, goes back to $1. A four game win streak would look like this, 1, 1.9, 3.61, 6.86, 13.03. If the person ever wins eight guesses in a row, they stop and start at $1 again, however, that dollar is not replenished if they lose again, so if they lose, now their dollar is taken away from any total winnings. They continue this pattern on and on hoping to have a profitable situation.
My question is if it is possible to have a profitable situation with this scenario, or, how many wins to stop a streak is profitable? 4, 5, 10, anything?
Let me know if this is confusing. Not that I do plan on implementing any of said strategy because one would need a 50% situation which is nearly impossible to find, but I am just curious and would appreciate the math help.