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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9 Responses to Gambler’s Fallacy and Options Trading

  1. John Forman 09/01/2010 at 10:49 AM #

    “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?”
    The falacy part comes from the belief that if the odds of getting heads 10 times in a row is 0.098% then after 9 heads there must be a 99% chance of getting tails on the 10th toss – rather than the 50% that’s the actual odds.

  2. Mark Wolfinger 09/01/2010 at 10:52 AM #

    That’s what I thought was stated in the Wikipedia reference.
    The belief that the results are ‘forced’ to return to the statistical average – meaning tails ‘must’ be coming up next.
    Appreciate the clarification.

  3. Marty 09/01/2010 at 12:12 PM #

    Thanks for picking up my comment for a full post. I should mention that I am NOT a statistics expert, I only took the intro level in college. So I’m truly asking about this for my own enlightenment, not trying to prove a point.
    John’s response is the way I understand the Gambler’s Fallacy also…maybe I just phrased it in a confusing way. I think some people WOULD believe the chances of a 10th consecutive heads flip are 0.098% AFTER 9 prior heads flips (in my mind that’s similar to saying there’s a 99% chance of flipping tails.) Those people are using faulty logic that seems to make sense at first glance, which is why it’s a popular logical fallacy. If I understand correctly, the hot-hand fallacy is the logical inverse of gambler’s fallacy, but equally false.
    “.92^6 = .60 represents the chances of winning the NEXT six times the game is played.”
    Ok, now I see where 60% comes from. It’s not really the gambler’s fallacy at all since you’re talking about all 6 events taking place in the future.
    Thanks for the followup!

  4. Mark Wolfinger 09/01/2010 at 1:04 PM #

    You’ve had more statistics courses than I.
    The truth is that some people cannot think logically. Some are wired to make all decisions with their emotions. However, you can never explain that to them – they believe they are being logical.

  5. Marty 09/01/2010 at 4:05 PM #

    Thanks, Mark. Agreed.
    Can I ask an unrelated question? I know picking a directional bias for the UL (underlying asset) is not part of your playbook, but it’s something I’m looking into and I’d prefer to use options to do it. With options I can afford to enter spreads on more ULs simultaneously, giving me better diversification (hopefully). Over-leveraging is not part of my plan.
    My priorities for choosing the “perfect” spread for this application are as follows:
    1) High delta (+ or – depending on desired directional bias)
    2) Defined risk
    3) Positive theta
    4) Minimal vega, + or –
    5) large fries…chocolate shake
    I’m leaning toward front-month bull/bear credit spreads as they would satisfy the first three requirements. The problem is with #4. My plan is to have many spreads going all at once and the vega risk will just get larger with each credit spread I open. I need something to neutralize it as much as possible.
    So the question is, what could I mix in with the credit spreads such that it would hedge my vega without completely messing up the nice theme I have going in items 1-3? Call it “pre-insurance” for vega risk if you like…

  6. Mark Wolfinger 09/01/2010 at 5:48 PM #

    There is a lot more going on here than you realize, and the reply is lengthy.
    Let me just say this:
    1) Too many calories from fat and sugar. Suggest the diet soda and tomato slices.
    2) You write of ‘high delta’ credit spreads. I’m sure you know that selling a high delta (obviously ITM) call spread is equivalent to buying the low delta OTM put spread. Is that really what you want to do?
    It’s negative theta.
    It’s positive vega.
    So let’s get this part straightened out before going any further.
    I must be certain you are not writing about debit spreads.

  7. Marty 09/01/2010 at 7:36 PM #

    I’m asking about credit spreads. Here’s an example with SPY if I were expecting UL price to decline:
    SPY @ 108.64
    Sell 1 Sept 110 Call
    Buy 1 Sept 111 Call
    My calculator (thinkorswim) shows:
    delta -8.89
    gamma -0.64
    theta 0.60
    vega -0.86
    It’s not high delta, I guess what I was trying to say is that I want to find the “highest delta” I can while also optimizing the other factors. So I’d adjust the strikes of my credit spread to give me the “best” mix.
    PS – I’m working on the diet, it’s hard 🙁

  8. Mark Wolfinger 09/01/2010 at 8:16 PM #

    I love your questions, but please be careful with the language. High delta means ITM options and I could not understand why you would want to that. Hence my query.
    Ok we are now discussing the sale of OTM spreads. Because of market bias, you are choosing spreads that are less far OTM than you would choose for a ‘normal’ iron condor play. And you are playing only one side of the market for each underlying asset.
    Going back to the original problem:
    a) Many spreads at once is difficult to manage. Be certain you can handle that many. This is only a problem if you feel the need to make a bunch of adjustments at the same time.
    b) Vega. You will be short vega. You can do several things to minimize vega risk.
    1) Own a diagonal instead of a vertical spread. Or do some each type. Because of diag spread cost, this may not appeal.
    b) Buy OTM calendar spreads. If bearish, choose OTM put spreads. If stock declines towards strike, you profit.
    If bullish buy OTM all spreads.
    HOWEVER calls are less effective (and less costly) than put spreads because the rising market is likely to be accompanied by an IV decline. However, if the goal is to reduce vega exposure, this is a viable strategy. It’s also another method for playing the market bias.
    c) Own some naked options. Lots of vega, but not so cheap to buy. Or own some index put or call spreads (pay a debit). Limited gains, but + vega.
    These are the obvious + vega plays. Use these ideas as starting points.

  9. Marty 09/01/2010 at 8:31 PM #

    Thanks for the ideas, I’ll see if I can’t find something to buy on Amazon! And sorry about the lazy terminology. Now I see what you mean by high delta. What I really, REALLY meant to say is “a position that is not market neutral, but reacts strongly to movement in the underlying”. 🙂