quasar_1 has seen the chart of the 10,000 tosses. Ask him if it looks exactly like a stock chart.
I point out that in your sample space there are long runs where one side or the other persists. This is what happens to traders and gamblers. They get on a streak. In math we call this area of investigation "the theory of runs". The groupings of runs are randomly distributed also, so you don't know when a streak is likely to occur. The expectation of the game of coin tossing applies both locally and globally. Traders and gamblers both look at a streak as due to their skill.
If you assign a "1" to heads and a "-1" to tails and then sum the series over the sample space, you'll find the classic stock chart with all the patterns that are named in Edwards & McGee. You get head and shoulders tops, pennants, triangles, breakouts, consolidations with their six counts, Elliot Wave, the whole set of illusions. If you graph the summed series you find that it wanders for extended numbers of trials above and below zero. The sum over extremely large numbers of trials is zero, that is, the area under this wandering nets to zero, but at any instant it may be significantly positive or negative. Thus the expectation of the coin toss is zero or the odds are 50/50 that you will toss a head or tail next time.
The reason why both stock charts and coin tossing create similar patterns is that they both are stochastic processes. Each follows slightly more subtle laws which at lower order are equivalent. Sometimes stocks are modelled with martingale processes with Pareto distributions. The difference between that model and some other is not relevant for assessing whether you can expect to succeed at trading or gambling.
Although coin tossing is fair, it is never on-balance profitable. At least the expectation is flat. Trading and gambling slope downward so that gradually over time you may get ahead and then get behind only to pull ahead again, but the result is that you always are losing a little on-balance. This is the negative expectation. The rate of the loss is proportional to the cumulative area under the game's probabilistic structure.
Many studies have been done which try to assess the rates of loss of various games. Obviously this is critical in Lost Beggas, since the expectation determines the gross proceeds to the house. All games in Beggas are better than stock market trading except maybe slot machines. You have to be right something like 85% of the time. This is partially due to the asymmetry of price translation. Selling happens faster, but you can't get on the short side faster. |
