You win the first time three heads show up. So, if head = 1 and tail is 0, and the following is the sequence of flips: 111 -> you win 1011 -> you win 0111 -> you win 01011 -> you win 000 -> you lose 1000 -> you lose 10100 -> you lose Does this make sense where the 3 heads you win and 3 tail you lose comes in? you get to bet before each flip. you want to double your initial stake whenever you win
Just to be clear: whether you win or not is not up to you (it's a fair coin after all). But when you win, you need to double. That's the requirement. (Don't care what happens when you lose, but in the correct solution, a very logical thing happens)
Apologize. I did type out a loss scenario. Try this, tail head head tail head -50, +25, +25, -50 = -50. This means your stake is now $50. you can't bet $100 on the final round
"Question: what is the size of the first bet that you should make?" I am thinking $50 on the first bet and 50% of the accumulated capital on the subsequent bet. I don't have any mathematical proof, but I have attached an Excel file to simulate the flips.
I came up with $50 as well. You bet half your stack at all times unless you have $100 and 1 roll left, at which time you bet it all. How long would you have to answer that type of question in an interview?
What happens if you have tail, head, tail, head, head? Round 1. Bet $50, tail, = $50 Round 2. Bet $25, head = $75 Round 3. Bet $37.5, tail = 37.5 Round 4. Bet 18.75, head = 56.25 Round 5. Bet 28.125, head = 84.375 You fall short of $200 even though you won the game.
Incorrect for the reasons already stated. The typical interview is an hour. I would expect to reserve a good 20 min for the preliminaries and questions. So figure 40 min? But keep in mind, you might be given some hints if you look completely lost or confused. I'll give a few hints as time goes on to simulate that. Speaking of which, HINT #2: If you already seen two heads and you are in your final bet, and the outcome is going to head (so you double your bet), what's the minimum amount of money you need to have on hand to meet the required payout? (don't need to reply with an answer. this is a hint question)
That's why I added the part above. On your t,h,t,h,h scenario you get Bet 1 - 50 / New Bank Roll - 50 Bet 2 - 25 / New Bank Roll - 100 Bet 3 - 50 / New Bank Roll -50 Bet 4 - 25 / New Bank Roll - 100 Now use the exception to the strategy above and Bet 5 100 / New Bank Roll - 200