You now have $3000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach $6000. It turns out that you can maximize your chance of reaching $6000 by betting either the money you have on hand or $6000 minus the money you have on hand, whichever is smaller.
Use simulation to estimate the probability that you will reach your goal with this betting strategy.