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By the way - in the actual interview where this was deployed (I wasn't on either side of that desk), the candidates who solved the question correctly would then be asked to write a script (excel and/or vba, matlab, or whatever the candidate is familiar with) that solves for a general case of...

Yeah, I got no excuse for this. I should have paid more attention to the post rather than skim through them quickly trying to catch up on all the ones that accumulated overnight. In another news, I would argue that this is nothing like the kelly criterion solely due to the fact that is a fair...

That was an unfortunate typo on my part. The correction is on the second page or so. (Someone pointed it out to me - but by then it was over 30 minutes since the initial post so I couldn't correct it)

We just need to meet the required payoff in its future value, not its present value. So , no need for the risk free rate

This is actually the correct answer I didn't read that last part (when the first two diverges) when I was flipping through the back log replies. Here's how I thought about the solution. Work backwards from all the terminal cases. Consider HHTTH. You would end up with $200. Consider...

Chop, you are definately on the right path. You are noticing a key requirement here. But you aren't exactly right yet. If you want to keep going, my hint (in addition to my post previous to this) is to actually chart out all the ways the game can progress (it's not that much) and see how you...

No one has the right solution so far though a few might be on the right track. Let me clarify a few things since there are points of confusion: (1) You win the game when you got 3 heads (not necessarily in a row). You lose when you got 3 tails (not necessarily in a row). Either case must...

I went away to do christmas shopping yesterday and look at the number of replies! Okay, I'll respond to everyone, but right off the bat, this is wrong. You aren't accounting for all the possibilities of winning. The trick isn't to figure out how to meet the payoff in one scenario, but in...

Hint: it might prove very very useful to draw a tree of all the way the game can progress it's actually not a very large at all

This is what I don't understand... so when do you end up in a situation where you only have $25 left? If there's still a possibility of winning on the next flip or two flips, then how would $25 ever get you to the $200 you need?

Really? So if you have $25 dollar, you've seen two heads so far, you got it all. Heads come up. you won the game. but you only have $50 instead of $200. Otherwise, I think you are beginning to think about the problem in the right way

The inability to understand why you wouldn't want to trade just your own money is .... hard to understand. (1) leverage. getting a 2/20 payout on OPM means you make money a lot faster (2) scale. a lot of strategies have high fixed costs (see fixed income arbitrage for example). (3)...

The numbers aren't entirely right and the cases aren't entirely right, but I think you might be on the most correct path of thinking so far.

Okay, I'm not doing any more guesses without an explanation of why it would work for all cases. Because the actual solution is slightly more complicated in that it needs to describe what to do in all cases (though, it's not tedious, because there's a very simple logic and pattern in all cases)

Sorry if I didn't make that clear. Essentially, the payoff of each bet is actuarially fair to the probability of those payoffs. So HINT #3 this should rule out both simple martingale and anti-martingale strategies (but not all complex strategies that are either martingale or...

First true break-thru insight!: you'd need to have something so that if you have lost the first two, you can still win. the second point is some what off the mark and the third point completely. But the first point you made is big conceptual step.

I'm not sure the betting math is right here. In round two, you have $50 on hand. You bet $25. You win. You back back $50. But since you paid $25 to make this bet, your total cash on hand is $75, not $100.

To clarify: you double you bet if you win. So, if you bet $50, and you win, you get back $100. If you lose, you get back nothing. Another way to look at it is, if you have $100 and you bet $50, your cash will be $150 you win and $50 if you lose. I keep switching between the two forms of...

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...

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.