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> betting system wasn't valid because each bet was an event
> independent of previous events and that my next bet would therefore
> always have a 50/50 chance of going my way. Yet when I asked him
> what the odds of one color coming up, say, 5 times in a row, he
> said that the chance of that happening was about 3% (.5 * .5 * .5 *
> .5 * .5).
The chances of getting 5 blacks (or 5 heads/tails, if flipping a
coin) in a row are indeed 0.5^5.
However, the chance of getting ONE black "in a row" is 50%,
regardless of whether the previous 4 were black or not.
In other words, if at any point you asked "what are the chances of
the NEXT 5 spins being black?" the answer would be 0.5^5. But if you
get 4 blacks in a row, and ask "what are the chances of the next 1
spin being black?" the answer is 50%.
That's why this betting strategy isn't valid. You're trying to
incorporate the probability of the previous 4 spins into the
probability of the next spin. The previous spins have NO BEARING on
the next spin. Each is a 50/50 chance, regardless of the spins
before it.
(BTW to be exact, it isn't quite a 50% chance. The routlette wheel
has some green slots. The chance of red or black is something like
48%. That's one of the ways the "house" keeps the odds in its favor.)
The problem with applying this logic to trading systems is that you
assume each trade is totally independent from the previous ones.
Many people say that's a valid assumption -- e.g. Monte Carlo testing
is based on that assumption -- but in my opinion that's not always
true. The market can get into a particular state and stay there for
a while, and your system's response to the market will act
accordingly. E.g. look at the market for the last few weeks. It's
been stuck in a narrow range for quite a long time. A system that
tries to grab breakouts from a range might work quite well in normal
conditions, yet hand you loss after loss when the market stays in a
range like this. For another example, simple "buy the dip" systems
work great as long as the market is in an uptrend, but fail if the
market heads down. You can accurately predict that the system will
have a much higher percentage of wins or losses as long as the market
stays in the same mode. So I would claim the system's win/loss
behavior is NOT independent from trade to trade.
Gary
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