Yeah, always betting $37.50 to start and going from there is what I arrived at as well. I came to the solution through this reasoning--What's the minimum amount I need to guarantee $200 if there's a winning sequence from these scenarios: two heads and one flip left $100 two heads and two flips left $150 two heads and three flips left $175 One head and two flips left $50 One head and three flips left $100 One head and four flips left $137.50 Took me two hours
gaak this is the worst worded teaser question I have ever seen. 14 pages and I'm still clueless. What happens if four or five heads come up? The OP says "a fair coin will be flipped five times in a row" not "up to 5 times".. Are those wins or losses? Or does the game automatically end after 3 heads? Are there any positive or negative ramifications of only partially fulfilling your goal vs. failing completely? There are 4 outcomes: a) lost game & did not double money b) lost game & doubled money c) won game & did not double money d) won game & doubled money Is d the only outcome that matters? Are all of the other outcomes equally bad?
My answer would be to learn from the largest banks and bet it all every time to get a big bonus. (and have the tax payer as a backstop.) However if I had to play by the rules regular traders do --- why bet prior to the second head. You preserve you captial until you have the best chance earning the highest return. Hence no bet until I see the second head.
Almost had it.............missed the 100 (tails,heads,heads) scenario Bet 50 on flip 1. If heads. Bet 50 on flip 2. If tails. Bet 25 on flip 2. if 00- you now have 200...make NO more bets, you've already doubled if you win the game. if 10-you now have 75 if 11-you now have 25 if 01- you have 100 for 10-bet 25: 101 will leave 50....100 will leave 100 for 11-bet 25: 111 will make it game over....110 will leave 50 for 01-bet 50: 011 will leave 50....010 will leave 150 if 101- bet 50. if tails, the game is over. if 1010, you're back to 100 if 100- bet if 110-bet 50. if 1101, the game is over. if 1100, you're back to 100 if 011-bet 50. if 0111 the game is over. if 0110 you're back to even. if 010-bet 50. 0100 will give you 200 and the win. 0101 will leave you with 100 in all scenarios, go all in. heads will give you 200 and tails will lose the game.
What about 100 37.5 W 137.5 -37.5 L 100 37.5 W 137.5 37.5 W 175 and game over you've only made it to 175 and not the goal of 200
Format is Result of first 2 flips and then bet for each flip <pre> Bet 1 2 3 4 5 WW 37.5 37.5 25 50 100 11001 137.5 175 150 100 200 1101 137.5 175 150 200 111 137.5 175 200 WL 37.5 37.5 50 50 100 10101 137.5 100 150 100 200 1011 137.5 100 150 200 10011 137.5 100 50 100 200 LW 37.5 37.5 50 50 100 0111 62.5 100 150 200 01101 62.5 100 150 100 200 01011 62.5 100 50 100 200 LL 37.5 37.5 25 50 100 00111 62.5 25 50 100 200 </pre>
In any other scenarios (other than the six options I've mentioned earlier), inluding 11110, don't do a thing. You don't care if it was a winner or loser. Your aim is to double the pot when you win.
I think KarateChop and MustPlayOptions have it. The first two bets are $37.50. Then the strategy for bets three, four and five depend on the result of the first two coin tosses.
bet 1/3 of your initial bankroll each of the first 4 flips. If you complete four flips w/out winning or losing, then you should be at $100, having won twice and lost twice. Bet $100 on the fifth flip.