I'm skeptical that you can learn anything from coin flipping. It's been proven that stock price movements are not random walks and coin flipping is absolutely a random walk. But there is undoubtedly a stochastic component to price movement as well as a potentially infinite number of trading strategies, so to totally dismiss coin flipping as a research tool may prove premature. While I can't see how to apply this tool, others may have some success with this experiment. Good luck.
Coin flipping is a special case of the more general Monte Carlo Methods. Monte Carlo methods have been used extensively in understanding the financial markets and trading. I use a Monte Carlo based application to estimate the probability of an underlying financial instrument touching an option strike price. The results agree well with other methods of computing this estimate. I wrote a paper for my students to give them some insight into Monte Carlo Methods. Insights Into Monte Carlo Methods - Estimating the Value of Pi
You wrote in that paper: "The last step in setting up the problem to be solved by Monte Carlo methods is to realize that the number of points randomly generated within an area is proportional to the area." This does not help you. The proportionality constant may be different for the two areas. What you want to say, maybe, is that the ratio of the number of points generated from the Union of two surfaces as follows: No of points from intersection/No of points from relative difference is equal to the ratio of the surface areas of the surfaces. You have to prove it though or provide a reference of the proof.
I appreciate any help in making things understandable. I'm not quite clear about your concerns. Please elaborate. Thanks.
Sure. From pi = 4Ac/As you go to pi = 4 Pc/Ps after assuming that A = k x P where k is a proportionality constant. In general, Ac = k1 x Pc As = k2 x PS and the general result is pi = k1 x Pc/k2 x Ps You have to prove that K1/K2 = 1 This can be done by the way I proposed or some other way. But surely K is not a universal constant so that it has the same value for all situations. It is a constant that applies to the particular problem. You have to prove essentially the Ac/As = Pc/Ps. It may appear common sense but it is not in the context of sampling distributions. In a geometrical context it is common sense to consider the areas as collections of points and argue the result. But in the context of sampling distributions it should be a tough problem in Topology. Maybe not. I just said it has to be proved.
2 Consecutive RED/GREEN Daily candles Hypothesis Just an idea: apply limited martingale(max 1,2) for lot sizes traded on Daily candlestick chart, e.g, dow index futures: PreCondition: Say you have G,R,G,R,G (must be alternating colors) Daily candles chart(1 week). So you bet 1lot on the 6th candle to be G (or R if it were R,G,R,G,R)... If it's a win(exit on close G), wait for the next PreCondition to appear to restart If not(exit loss on close R), wait for the next appearance of G to place 2lots bet on G. for e.g, G,R,G,R,G...R!(lose),R,R,G, betG Restart and wait for next PreCondition regardless 2nd bet is a loss or win. Within 10 candles(2 weeks), there could be about 1-0.14 =0.86 probability of 2 consecutive same color daily candles? http://www.bjmath.com/bjmath/probable/flips.htm http://www.playroulette.co.uk/articles/odds-of-10reds-in-a-row-in-roulette.html
Another idea for fund managers: ask your secretary to associate a head or tail with a green or red(random choice) daily candle on Dow next day close but she cannot reveal to you what she wrote down. You then flip the coin and she buys or sell Dow futures according to what she wrote down for the result without you knowing what she did. On the day after the bet, she just need to show you heads or tails based on what the market did with what she associated, regardless it's a win or loss. http://www.remote-viewing.com/examplelarger.html http://www.youtube.com/watch?v=ObeI82f5OmI http://www.trvnews.com/tmn/072004/fxmarket.html
He may be trapped, as many people are, into thinking that the market has one variable which either goes up or down. You may be able to break away from this myth if you find that there are three possibilities. Then you may find that one of these possibilities does not matter and that informs you, further, about the nature of markets. Do a "what if" that assigns a coin flip to one or the other market variable. It is really hard to reason through changing market variables arbitrarily is like doing a coin flip. Rarely would anyone accept changing market variables arbitraily. It does happen though that some people, sophomorically, only use one market variable all the time and sKip the other one. Obviously, the better solution is to use the correct variable at the correct time. Mark Douglas suggests that 95% of people fail. But he never suggests that people use the correct variable at the correct time. It would be very very tough for any person to reason through how to use the correct variable at the correct time. Like flipping coins, which is senseless, is time involved in trading? LOL... It is like saying WHEN to flip a coin to get information for something to do with trading. When did behavioral finance first determing there were two kinds of events? What was the sense in their determination that the two kinds of events were orthogonal? The reason chosen was that it was TRUE that there are just two kinds of events and it is TRUE that they are orthogonal. So a lot of people fool around with a lot of ideas about this and that. This is a thread about making a silly connection between coin flipping and markets. Is it just as silly to apply Monte Carlo methods to markets that have no noise or anomalies? No it isn't, you do not know there is no noise and no anomalies. If a person doesn't know what he is doing nor WHY, then the answers he gets do not make any difference. Take a look at the Financial Industry, so far, the answers they are getting do not make any difference. See a movie about the financial industry; it is a comedy it turns out.