Interesting teaser. I believe tha answer is as follows: Bet 1: $25 Win = $125 Loss = $75 Bet 2: $25 Win = $150 Loss = $50 Bet 3: $50 Win = $200 Loss = $0 (Note that there are only 2 additional flips and if you have lost all three there woul d be zero chance of success. This is just one possibility another using same betting patterns as follows: Bet 1: $25 you lose Balance = $75 Bet 2: $25 you win Balance = $100 Bet 3: $50 you win Balance = $150 Bet 4: $50 you lose Balance = $100 Bet 5: $100 you win Balance = $200 A final scenario Bet 1: $25 you win Balance = $125 Bet 2: $50 you lose Balance = $75 Bet 3: $25 you lose Balance = $100 Bet 4: $50 you win Balance = $150 Bet 5: $50 you win Balance = $200 The key is to ensure you have enough capital remaining at each round that you have the opportunity to meet your goal if heads occurs 3/5 example: first two rolls are tails. you would need at least $25 to have a chance at $200 ($100 return) first two rolls are heads. Here you would only need to bet enough to get you to $200 each flip, without jeopardizing your opportunity if the following two rolls are tails. Example Bet 1: $25 you win Balance = $125 Bet 2: $50 you win Balance = $175 Bet 3: $25 you lose Balance = $150 Bet 4: $50 you lose Balance = $100 Bet 5: $100 you win Balance = $200
the key is to bet in increments of $25 (25,50,100) and always ensure that for any future occurence of h/t you have the capital to double your capital if heads hits 3/5
At each flip, the individual must be aware of the required payout ($100 profit) and the capital required to achieve that payout for any future pattern. Here the pattern is limited to 5 flips, of which 3 must be heads (60% heads win rate).
Ah! Although you almost confused me again when you said it has to do with the odds. The point is you are getting payed on a won bet. Nothing to do with odds. The odds could have been a trillion to 1. You bet $10, you get $20 if you win. The payout is 1:1.
By coincidence I was watching a lecture on introductory game theory last night where the topic was sequential games. One method of finding the optimum strategy was called Rollback. This is where you start with the payoffs and work your way backwards through the branches. For this method to work, the game had to be: - Sequential - Non-cooperative - Finite - Have perfect information (You know everything that has happened in the past)
The odds of a coin flip is 50/50 for a fair coin. So the payout will reflect the odds. You bet $1, and if you win, you will get $1 in addition to your $1 bet. If you lose, you will lose the $1 that you bet. In the end, the payout is indeed 1:1. PS: I am just trying to confuse you one more time.
You are thinking this is a pari-mutual betting avenue, where the payout is set by the odds. They are distinct. For example, say there was a track take or a rake (like in horses or poker) and the odds were 1:1. The payout isn't $10 on $10, even thought the odds are 1:1. Or take roulette, where the odds are slightly against you but the payout is 1:1. You can set the payout to whatever you want, and the odds to whatever you want. They are different independent parameters.
I was thinking the same thing after my first crack at this. My problem scenario that always seemed to crush my system was: W W L L W Using your system, the first two bets would be $25 winners, leaving you at $150. Now you must bet at least $50 to get to $200 on the third roll. If you lose, you are now at $100. For the fourth roll you must bet $100 in order to achieve $200 with your third head. If you lose this flip, you are busted. You now have nothing left to bet for the fifth flip, which may be the "winning" flip that achieves 3/5 heads.
Well, the payout is indeed set by the odds of a coin toss for a fair coin, but the odds are set prior to the betting. So this is a fixed odd betting. For a parimutuel betting, the payout is not set prior to the bet and is depending on the betting pool. So, no, I was not thinking it is a parimutuel betting venue, and I do apologize if I made it seem like it was a parimutuel betting venue earlier.
In an earlier post, I posted the WWLW scenario using 25,50, or100. I have reattached below. Bet 1: $25 you win Balance = $125 Bet 2: $50 you win Balance = $175 Bet 3: $25 you lose Balance = $150 Bet 4: $50 you lose Balance = $100 Bet 5: $100 you win Balance = $200