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Gambler’s Fallacy and Options Trading

Hi Mark,

I don't want this to sound nit-picky, but when you mention the
probabilities of playing a vertical (or any spread) repeatedly it brings
up something I've wondered about before. If the spread in question has
a P of 92% and you repeat the same spread (same P value) 5 additional
times, how would that result in a 60% probability of success long-term?

It's sort of a rhetorical question…I understand the formula you
used is 0.92^6 = 60%, but that's the Gambler's fallacy/Hot-Hand fallacy
is it not? In other words if I were to flip a coin (which has a single
event probability of 50% heads) 9 times and get all heads, the 10th flip
still has a single event probability of 50% heads. Whereas the
gambler's fallacy says I have only a 0.5^10 = 0.098% chance! And
if someone were watching the first 9 flips and offered me 1000:1 odds
(or even 10:1) that I couldn't flip heads again, I'd take that bet all
day long. The coin has no memory.

Perhaps options are different somehow since I see nearly everyone use
the same logic to argue against placing this kind of low-return,
high-probability trade as an income strategy? Do options have "memory"?



Thanks for this discussion.

To me it's similar to any statistical event.  Toss a coin and there is 1/2 chance of heads.  Toss twice and there is a 1/4 chance of both being heads.

.92^6 = .60 represents the chances of winning the NEXT six times the game is played.

This is NOT the probability of success long term.

This is NOT the probability of winning the sixth time, after five consecutive wins. 

It is the probability of winning the NEXT SIX TIMES the bet is placed.  Previous wins do not count (except to give further encouragement to the gambler).

The gambler's fallacy, by my interpretation is not as you described (see Wikipedia).  However, if it is based on the thought process you described, it's a lot worse than a fallacy.  It's nonsense. 

Once the coin HAS ALREADY BEEN FLIPPED NINE TIMES AND HEADS HAS BEEN THE RESULT NINE TIMES, no one would believe the chances of heads the next time is 0.098%.  Would they? Everyone knows it's 50% per flip – assuming it's a fair coin. If the gambler wants to wager on a 'hot hand' does he/she really and truly believe in that 'hot hand?'  Perhaps they do.  In my opinion, it's far more likely that the person's gambling persona is out of control.

The thought process of each individual is not smooth and scientific, and it's definitely not logical.  Our emotions get in the way and we see things that don't exist.  One such example is the ability to believe that it's a gimmie to rack up easy profits from betting against low probability events.

Options are 'different' in the sense that people 'know' what the market can and cannot do.  They don't think of it as a game based on statistics and probabilities.  They believe they 'have a feel' for market direction and surely they understand that they have no such feel for a spinning wheel.

They get emotionally caught up in their ability to 'know' that AAPL cannot fall below 200 this month.  They just know that Steve Jobs will remain healthy and that no catastrophic events will occur in the world.

When spinning the roulette wheel, they have no special knowledge of the future.  They don't believe they can predict.  Thus, traders who believe in that special ability to know what will happen, and who take chances based on that belief, are well placed to get destroyed by that false belief.



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