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Given a fixed time period,say 3 days, the stock/market can go up,down or stay sideways. A hedge fund can long, short or use rangebound(options strategy) to bet for that 3 days closing level.

Hedge fund manager A opened long position the stock/market on monday. On tuesday, there is some major news/economic data/earnings call that can be interpreted either way so the stock/market will breakout of the trading range to move in one unknown direction(3rd door is out).

Hedge fund manager B comes along immediately after the news. Should he (1) randomly pick one direction? (2) instead of analysing market direction, find out fund manager A's position and bet the opposite?

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Your assuming that manager A is an agent of Monty Hall (all knowing), and has exposed a goat behind door number 1, which is a long position. The flat position is not a viable option as you stated there is a breakout due on Tuesday, so you can eliminate it (but do you reassign the probability weight, and if so to what?). So you assume that long positions are goats, and you take the short position. – montyhall Dec 10 '12 at 21:49
3 days vs. 3 choices of the market direction plus market moving news, I don't think this is the same problem as what the Monty Hall problem is about. Monty hall only had 2 rewards a goat and a car, and 3 doors to choose from. I think you need to re-model the concept of what is a door, and what the 2 rewards are behind the 3 doors. I think you need to eliminate the flat position, and you only need to work with one day (Tuesday), leaving you with 2 rewards (goat/car, long/short). – montyhall Dec 10 '12 at 21:54
Not sure what the practical purpose of this is (regime-switching models of asset returns don't usually show much difference in the mean between regimes). Just think it through a second, if information comes out that the return on the market will be higher, would you try to take advantage of that, to the extent that the market will give you a fair price? – John Dec 10 '12 at 22:46
arxiv.org/pdf/quant-ph/0202120.pdf The Quantum Monty Hall Problem, arxiv.org/pdf/quant-ph/0109035v3.pdf Quantum version of the Monty Hall problem – montyhall Dec 20 '12 at 8:43

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