a random trade to end up a loser, because of the mandatory risk–reward relation-
ship of at least 2:1 that you should have in place when entering the trade. That is,
because you should not enter into a trade if you don’t believe that the profit poten-
tial is at least two times the value of the loss, a shorter distance between the entry
point and the loss, than between the entry point and the estimated profit, still adds
to the likelihood for the trade to become a loser.
Another reason why a high percentage of profitable trades isn’t necessarily
better than a low percentage is that a system with a low percentage of profitable
trades is more likely to continue to produce that percentage, or better, in the future:
The dollar value of the winners and losers aside, each trade only has two possible
outcomes. It can end up either as a winner or as a loser. (Break-even trades don’t
count.) With each trade only having two outcomes, a sequence of two trades must
look like any of the following four sequences: (Win, Win), (Win, Loss), (Loss,
Win), or (Loss, Loss).
And a sequence of three trades must look like any of the following eight
sequences: (Win, Win, Win), (Win, Win, Loss), (Win, Loss, Win), (Win, Loss,
Loss), (Loss, Win, Win), (Loss, Win, Loss), (Loss, Loss, Win), or (Loss, Loss,
Loss).
Thus, for every trade added to the total number of trades, the number of
sequences doubles, so that with 10 trades, the number of possible sequences is
1,024 (2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 2^10) and for 100 trades, the num-
ber of possible sequences is 1,267,650,600,228,229,401,496,703,205,376 (2^100,
or approximately 12.7 billion * 10^20), ranging from 100 winners in a row to 100
losers in a row, covering every possible sequence in between, including the one
produced by the system in question.
With that many possible outcomes, it’s easy to see that the one sequence pro-
duced by any system is nothing but a freak occurrence that is very unlikely to
repeat itself in the future, and that any system, in the future, is much more likely
to produce any other sequence of trades but the one just produced. In fact, no mat-
ter the number of trades examined, the sequence just produced—no matter how
many winners and losers it held—is no more likely to repeat itself the next time
around than the one sequence containing only winning trades.
However, even if the likelihood for the exact same sequence to occur again
is infinitesimal, a good chance still remains that the system in question will pro-
duce a sequence holding the same percentage of winners. How good depends on
how many winners we’re looking for. For example, in the three-trade sequence
above, there is only a 12.5 percent chance (1 / 8) for each sequence to happen, but
an 87.5 percent chance (7 / 8) that the sequence will hold at least one winner, and
a 50 percent chance (4 / 8) that the sequence will hold at least two winners, placed
somewhere within the sequence.
One interesting question to ask yourself when you’re examining a trading
system is how likely is it for the system to continue to produce the same percent-CHAPTER 3 Probability and Percent of Profitable Trades 37