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What? the equity trader at JPM doesn't pay taxes? He probably pays more in both absolute terms and in % term than you. What did that equity trader ever do to get us in this mess? my point is, it's a disingenuous at best and morally corrupt at worst to group all the "professional" traders...

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

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)

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...

No dice. Suppose the flip outcome is tail tail head tail head head? you lose 50, lose 25, win 50 (so now your stack is $75). You can't bet $100 on the last cause you don't have it

Again, see my counter example: first flip, heads. you betted nothing. fine. Second flip, heads, great, you bet $100. third flip: tail. You lose the $100. You have nothing. Fourth flip: head. You won the game. You have nothing. You didn't meet the payoff you desired.

Very sorry about that. I seemed to have fat fingered that (very crucial) point. Hopefully the example I gave of a loss (which was correct) and the incorrect explanation at least gave people a pause to look for clarifications

I think you are missing the point (or I'm explaining it badly). The point is to figure out how to bet so that if you win the game, you are guaranteed to double the game. So, you never want to be in a situation that you've won the game, but you haven't made $100 on top of your initial stake...

indeed it does

I just posted a quick correction since I misstated the loss condition: you lose on the 3rd tail. You can't guarantee to win the game (in the terms of getting three heads). But you can guarantee to get the payoff if you win. The problem isn't about how to get win the game (you can't). It's...

OOPS CORRECTION: You lose on the 3rd TAIL!!! Sorry about the typo.

But you can't control when you win. Okay, say you win the first 2 rounds, you got $142.87 now. You lose the next round, you got $114.29 left. You lose again, you got $85.71 left. You win the next round and thus the game, but your purse of $85.71 means that even if you bet it all, you still can...

Nope. Remember my hint: you will need figure out the entire bet sizing strategy to arrive at the right answer;

What to tell me (and everyone here) how you got the answer? Much like in a real life interview (or a college exam), no credit will be given for an answer without showing work

Also, your probabilities are wrong. Just because the next flip after getting two heads is a tail doesn't mean you lose the game. This is a win: 1101.

The question ask for an exact answer. There is an exact strategy of sizing your bets so that you will always win $100 when you win the game (getting three heads before 3 tails show up). Under this strategy, you will get this result 100% of the time (not that you will win the game 100% of time...

Sign... not this old cliche of a question again (the other coin is a half $). What to start your own thread?

In case this wasn't sarcastic, it should be trivially easy to figure out once you figure out the correct answer to the above :)

Not even close. Say you got head on the first flip. You bet nothing. Head on the second flip. You bet it all. Tail on the third flip, you are out of all of your money. Head on the Fourth flip - you won the game, but you lost all your money instead of doubling it.

Btw, if you already work for a financial institution, please don't post your solution (but I'll be happy to tell you via PM whether it's right). I'd rather let the just-of-school want-a-shot-at-being-hated-by-the-populist guys have a shot